Knowledge Mapping of Transformable Architecture Using Bibliometrics: Programmable Mechanical Metamaterials

Abstract

Programmable mechanical metamaterials enable precise regulation of mechanical responses through geometric design, ushering in transformative paradigms for transformable structures. To systematically map the knowledge landscape and development trends in this field, this study employs knowledge mapping methods to analyze the current research status, core hotspots, and future directions of programmable mechanical metamaterials. During the research process, we expanded keywords using the litsearchr tool to optimize the retrieval strategy. Bibliometric tools, including CiteSpace 6.3.R3 and bibliometrix, were utilized to conduct multidimensional analyses on 2017 original papers related to mechanical metamaterials in transformable architecture from 2015 to 2025. These analyses encompass co-word analysis, co-citation clustering, and structural variation analysis. Key aspects include (1) identifying core journals and their attributes to clarify interdisciplinary dynamics, (2) mapping research themes and evolutionary trends through keyword analysis and clustering, and (3) pinpointing research hotspots and future directions based on citation networks and clustering results. The results reveal significant interdisciplinary characteristics, with core knowledge emerging from the intersection of materials science, mechanics, and civil engineering. Mathematical system theory provides a cross-scale modeling foundation for metamaterial microstructure design. The field is evolving from static structural design toward environment-adaptive intelligent systems. Future efforts should prioritize multi-physics collaborative regulation, engineering integration, and technical chain refinement. These findings offer a theoretical reference for the innovative development of transformable architecture.

1. Introduction

Mechanical metamaterials, characterized by extraordinary mechanical properties achieved through artificially designed microstructures, are fundamentally transforming the design paradigm of transformable architecture. Unlike conventional materials, the macroscopic mechanical behavior of these metamaterials is governed not by the base material’s constitutive relationship, but primarily by the geometric topology and spatial arrangement of their microstructures [1]. This unique characteristic enables them to surpass the performance limits of traditional materials, achieving mechanical responses rarely found in nature, such as negative Poisson’s ratio [2], programmable stiffness [3], and multistable switching [4]. In recent years, within the field of transformable architecture, mechanical metamaterials have garnered significant attention due to their programmable deformation, lightweight nature, high strength-to-weight ratio, and multifunctional integration capabilities. Their lightweight substantially reduces structural self-weight, while the high strength-to-weight ratio ensures efficient load-bearing capacity [5]. Moreover, their programmable deformation capability endows buildings with the ability to dynamically adapt to environmental changes. This capability manifests not only in the active adjustment of macroscopic form but also in functional integration at the material level [6].

Among various mechanical metamaterial configurations, negative Poisson’s ratio honeycomb structures and origami metamaterials have emerged as prominent research foci due to their distinct geometrically driven deformation mechanisms. Although morphologically different, both rely on geometric instability for deformation and share the core characteristics of a “geometry-dominated deformation mechanism” and “programmable mechanical properties”. Through collaborative design, they achieve intelligent deformation capabilities unmatched by traditional structures [7]. Specifically, negative Poisson’s ratio structures exhibit deformation behaviors opposite to conventional materials: they expand transversely when stretched and contract transversely when compressed. Their mechanical properties primarily depend on the topological configuration of periodic microstructure units (e.g., re-entrant, star-shaped, chiral structures) [8]. Origami metamaterials, conversely, construct and reconfigure three-dimensional morphologies by folding two-dimensional sheets [9]. Their deformation behavior is determined by the geometric topology of crease patterns, with classic configurations including Miura, Waterbomb, and Kresling. Crucially, origami deformation involves the rotational movement of rigid panels around creases, not strain within the material itself. This kinematic characteristic allows for large deformations far exceeding the material’s fracture limit and inherently provides potential for multistability [10]. Recent research on negative Poisson’s ratio honeycombs has incorporated multi-level microstructures (e.g., fractal and gradient designs) to enhance energy absorption and deformation capabilities [11,12,13]. For origami structures, utilizing folding kinematics enables lock-free, multistable morphing mechanisms, significantly reducing actuation and control complexity [14,15]. However, large-scale applications still face core challenges. While 3D printing struggles to meet the large-scale demands of buildings, researchers have developed alternative techniques such as bonding technologies [16], step-by-step assembly methods [17], and planar cutting/assembly approaches [18] to establish a technical chain from microstructure optimization to building system integration.

This study employs a visual bibliometric analysis to examine the research progress on mechanical metamaterials from 2015 to 2025. By systematically collecting and deeply analyzing existing research, it aims to explore the current state of the field, identify core research hotspots, and prospectively investigate future research directions. This approach provides methodological support for subsequent researchers to efficiently review existing achievements and foster the inheritance and innovative development of related research.

Navigating the complexity of existing research to develop a systematic and comprehensive understanding of this topic requires complementary methodological approaches. Traditional narrative reviews excel at providing deep critical synthesis, offering insightful interpretations of research findings, theoretical frameworks, and practical implications through the expertise of domain scholars. They play an irreplaceable role in clarifying complex academic debates, integrating fragmented ideas, and guiding the direction of theoretical exploration. In contrast, knowledge mapping, as a bibliometric method utilizing data mining techniques, offers distinct advantages in systematically organizing and visualizing large-scale literature data. It provides a structured perspective on the knowledge landscape, evolutionary trajectories, and interdisciplinary connections of a research field. Conventional bibliometric methods often remain confined to descriptive statistics of generated data, such as publication trends and co-authorship network analysis, lacking in-depth exploration of the underlying associative pathways between literature. For instance, studies on digital watermarking [19], industrial upgrading [20], carbon footprint in LCA perspective [21], forest education [22], symmetry research [23], and human–computer interaction in healthcare [24] have applied traditional bibliometric approaches to summarize research status and distribution characteristics, but failed to reveal the evolutionary logic and knowledge connections within the fields due to the absence of knowledge mapping techniques. Even in research closely related to this study’s core theme, “programmable mechanical metamaterials and deformable structures”, similar limitations persist: studies on mechanical metamaterials [25] and biomimetic lattice structures [26] only used traditional bibliometric methods to sort out basic research distributions (e.g., core authors, institutional collaborations, keyword frequencies). Without knowledge mapping tools, they failed to deeply explore the technical evolution context or the internal correlation between structural design and performance optimization.

Therefore, this study employs the knowledge mapping approach within bibliometrics, aiming to leverage its strengths in systematic data processing while complementing it with qualitative interpretation, rather than positioning it as a replacement for traditional narrative reviews. The two approaches are mutually complementary: traditional narrative reviews provide depth of critical analysis, while knowledge mapping offers breadth of systematic coverage, together advancing the comprehensive understanding of the field.

2. Data Collection and Research Methods

2.1. Data Sources and Search Strategy

This study utilized two authoritative databases, Web of Science and Scopus, as literature sources to ensure comprehensive and representative data retrieval.

To formulate the search strategy, the seed literature was first collected. The R language’s litsearchr open-source package [27] was then employed to perform text mining and network analysis on the titles and abstracts of these seed papers. This process aimed to extract and expand keywords, thereby constructing and refining the search query. The litsearchr package generated a list of candidate terms containing numerous potentially relevant keywords. This approach minimizes the risk of insufficient keyword coverage due to the researcher’s personal knowledge limitations and is particularly suitable for systematic literature reviews. The specific search strategy comprised three keyword categories:

• Mechanical Metamaterials

“auxet* materi*” OR “auxet* structur*” OR “negat* poisson* ratio*” OR “auxet* meta-structur*” OR “auxet* behavior*” OR “auxet* deform*” OR “auxet* effect*” OR “auxet* honeycomb*” OR “auxet* core*” OR “array* origami*” OR “center* creas*” OR “creas* origami*” OR “creas* rotat* stiff*” OR “creas* stiff*” OR “nonlinear* creas*” OR “origami* array*” OR “origami* structur*” OR “pure* rotat* creas*” OR “uniform* singl* creas*” OR “Origami* Structur*” OR “Deploy* Structur*” OR “Telescop* Structur*” OR “Fold* Structur*” OR “Tensegr* Structur*” OR “Flexibl* Structur*” OR “shape* memor* material*” OR “smart* material*”.

2.

Engineering Application and System Design

“shock* absorpt*” OR amort* OR “shock* attenu*” OR absorb* OR damp* OR “absorpt* of shock*” OR nonrattl* OR “seismic* reduct*” OR “vibrat* reduct*” OR “seismic* mitig*” OR “seismic* respons* reduct*” OR “earthquak* mitig*” OR vibration-reduc* OR isol* OR “seismic* attenu*” OR insulate-earthquak* OR “seismic* insul*” OR “vibrat* insul*” OR “architectur* system*” OR “build* system*” OR “build* structur*” OR “architectur* structur*” OR architectur* OR “build* construct*” OR “architectur* construct*”.

3.

Mechanical Performance and Structural Analysis

“Mechan* Properti*” OR “Deform* Mechan*” OR “Structur* Reliabl*” OR “Fatigu* Life*” OR “Stabil* Analysi*” OR “Safeti* Assessment*” OR “Nonlinear* Mechan*” OR “Dynam* Analysi*” OR “Stabil* Theori*”.

The search combined the “Mechanical Metamaterials” keywords with each of the other two keyword categories. The following filters were applied:

Document type: Article [28] (retaining only peer-reviewed research papers to represent original scientific progress).

Time span: 2015–2025.

This search strategy yielded 2017 relevant publications. The “record content” included full records and cited references. The detailed process of this study is illustrated in Figure 1.

2.2. Research Methods

To ensure comprehensive and in-depth bibliometric analysis, we first compared mainstream bibliometric tools and selected the most suitable one for this study, then designed a step-by-step analysis framework and standardized parameter settings.

VOSviewer 1.6.20 prioritizes visualizing bibliometric networks (e.g., co-authorship, keyword co-occurrence, bibliographic coupling), as exemplified by Wang et al. [29], who used it to analyze home IoT-related papers and delineate core research directions via keyword co-occurrence clustering, though it lacks depth in temporal evolution and structural variation analysis of papers. SciMAT v1.1.06 specializes in science mapping and thematic evolution, enabling systematic tracking of theme dynamics across periods and identification of core, emerging, and declining themes. Karakose et al. [30] leveraged it to trace the century-long trajectory of educational leadership research through analyzing relevant papers; however, it imposes higher learning costs and offers limited parameter adjustment flexibility when processing large volumes of papers. Gephi 0.10.1 rooted in social network analysis, is compatible with bibliometric data and boasts robust dynamic visualization for large-scale paper networks, supporting flexible adjustments of parameters like node size and edge weight. Kiani et al. [31] employed it in cross-docking research to conduct Research Focus Parallelship Network (RFPN) and keyword co-occurrence analyses on related papers, clearly partitioning core research clusters through modular clustering. In contrast, as a professional bibliometric tool integrating knowledge mapping capabilities [32,33,34], CiteSpace excels in visual analysis of scientific literature. It integrates functions such as knowledge mapping generation, research hotspot identification, development trend tracing, and core literature mining—effectively compensating for the shortcomings of other tools in temporal evolution and structural variation analysis. Its cluster dependency analysis and citation burst detection functions are particularly critical for exploring research frontiers and knowledge source relationships, which align with the core objectives of this study. Therefore, we selected CiteSpace as the primary analysis tool, supplemented by the “bibliometrix” R open-source package [35,36] for diachronic keyword evolution indicators to enhance analysis comprehensiveness.

To understand the developmental trajectory of this topic, we first performed keyword co-occurrence analysis. This involved identifying high-frequency keywords and their co-occurrence relationships to construct a keyword network mapping. This approach provides a quick, macroscopic overview of overall research hotspots, core topic distribution, and the relevance between research directions, laying the groundwork for subsequent in-depth analysis.

Building on this macro trend analysis, the core step involved conducting literature co-citation analysis. Using CiteSpace 6.3.R3, we generated a co-citation network mapping to visualize the research foundation and knowledge structure of the field. Core literature with foundational importance and strong influence was identified based on metrics like centrality and citation bursts. To explore research frontiers, CiteSpace’s cluster dependency analysis function was crucial. This helped delve into knowledge transfer and dependency relationships between different research topics, enabling the precise identification of current research frontiers and their knowledge sources. Additionally, the “bibliometrix” R open-source package was used to supplement the analysis with diachronic keyword evolution indicators, aiding comprehensive interpretation.

The core parameter settings during the research are as follows: the time slicing is set to 2015–2025 (1 year per slice), with the Look Back Years (LBY) = 5 (adjustable to −1 when all references need to be covered), and cluster labels are extracted from the Title, Keywords, and Abstract (T + K + A fields) of citing literature. For the selection criteria, TopN = 50 is adopted in combination with the g-index (scaling factor k = 25), supplemented by linear interpolation of three-stage thresholds (C, CC, CCV). Synonyms are merged via the citespace.alias file to effectively avoid interference from low-correlation nodes. For link adjustment, LRF = 2.5 and L/N = 10 are used (both set to −1 when there are insufficient links), combined with composite pruning to eliminate redundant edges. The keyword co-occurrence strength is normalized by cosine similarity, the co-citation frequency is corrected using the CCV coefficient, and the citation paths in the journal dual-map overlay are standardized by Z-score (z > 2.5). Subsequently, entropy calculation is employed to identify the outbreak periods of research hotspots, and modular clustering (resolution = 1.0, minimum cluster size = 30) is used for thematic classification, ensuring coherent analysis logic and reliable results.

3. Results and Discussion

3.1. Article Feature Analysis

3.1.1. Core Journal Distribution Based on Bradford’s Law

Bradford’s law was applied to partition journal sources and identify core knowledge bases in this field. As shown in Figure 2, the Bradford core zone comprises only 13 journals but accounts for 680 related publications. This distribution exhibits the characteristic pattern where a few core journals concentrate most field-specific achievements. The list of core journals highlights the high degree of interdisciplinary integration among materials science, solid mechanics, structural engineering, and intelligent technology. These journals represent authoritative platforms in materials, mechanics, and civil engineering, indicating a stable academic ecosystem and mature publication channels. Notably, the frequent appearance of Smart Materials and Structures underscores that “intelligent response” and “programmable mechanical behavior” are becoming cutting-edge growth points, driving metamaterials’ evolution from static structures to environment-adaptive systems.

3.1.2. Journal Dual-Map Overlay

The journal dual-map overlay analysis reveals interdisciplinary knowledge flow patterns in mechanical metamaterial research for transformable architecture. In Figure 3, the left side represents citing journals, while the right side represents cited journals. Two significant citation paths highlight core interdisciplinary mechanisms:

• Path 1 (z = 2.57, f = 1171): Extends from Mathematics/Systems Science (left) to Chemistry/Materials/Physics (right). Mathematical tools (e.g., topology optimization, discrete geometry, differential equations) provide cross-scale modeling foundations for metamaterial microstructure design, bridging molecular dynamics simulations with macroscopic mechanical responses.
• Path 2 (z = 4.59, f = 1968): Connects Mathematics/Systems Science (left) to Mathematics/Mechanics (right). Formal tools (e.g., tensor analysis, nonlinear dynamics) drive innovations in programmable metamaterial constitutive theory, shifting paradigms from empirical design to inverse design based on geometric constraints and variational principles.

These paths demonstrate a breakthrough beyond traditional civil engineering boundaries, forming a new research paradigm with intelligent algorithms as the engine, geometric topology as the framework, and multifunctional materials as the carrier.

3.2. Co-Word Analysis

The temporal distribution of keywords reveals clear phase shifts in research focus. As shown in Figure 4, foundational terms like “flexible structure,” “damping,” and “vibration control” emerged in 2015. These, combined with high-centrality terms such as “finite element method” and “structural dynamics,” characterize the methodological foundation period. After 2017, keywords like “metamaterials” and “3D printing” reflect innovations in manufacturing, driving the transition from theory to practice. By 2020, terms such as “seismic response” and “sandwich structure” signal expanded application scopes.

Notably, the evolution of “negative Poisson’s ratio”-related keywords follows a distinct trajectory:

• 2015: Foundational terms appear.
• 2017: “Mechanical metamaterials” emerges, highlighting interdisciplinary growth.
• 2019: “Auxetic honeycomb” enters, emphasizing specific applications.
• 2021 onward: Focus shifts to performance metrics like “energy absorption capacity”.

This progression confirms the developmental pathway: basic research–material design–performance optimization–engineering application.

As shown in Figure 5, keyword co-occurrence clusters reveal distinct thematic patterns. Clusters center on interrelated concepts: vibration control (#0), energy absorption (#1), dissipation (#4), and specific technologies like tuned mass dampers (#3). The emergence of smart materials (#7) and shape memory alloys (#6) underscores innovative material applications. Crucially, manufacturing and structural design clusters—3D printing (#2), deployable structures (#8), and sandwich panels (#10)—demonstrate convergence between fabrication technologies and adaptive structures. Application focuses are split between tall buildings (#9) and industrial challenges (#13).

Dynamic theme evolution (Figure 6) shows vibration control persisting as the core objective across all three periods. Metamaterial-related topics evolved as follows: “negative Poisson’s ratio,” “auxetic,” and “mechanical metamaterials” dominated 2015–2018; “auxetic behavior,” “auxetic structure,” and “metamaterial” gained prominence in 2019–2021; by 2022–2025, these terms integrated into broader designs (e.g., flexible/deployable structures) as foundational technologies. Control strategies progressed from “active damping control” (2015–2018) to “semi-active control” (2019–2021), then to dual emphasis on “active vibration control” and “semi-active control” (2022–2025), indicating sustained advancement in both domains, with renewed focus on active methods.

3.3. Co-Citation and Cluster Analysis

3.3.1. Cluster Dependency Analysis

Using CiteSpace’s literature co-citation analysis, the literature was divided into distinct clusters. As shown in Figure 7, each cluster represents a relatively independent knowledge base or research topic. To identify research frontiers and their knowledge sources, we further explored the dependencies between these clusters. The blue–red gradient arrows in Figure 7 indicate these dependencies, signifying that some clusters build upon others or provide a foundational knowledge base for others. This dependency reveals whether the development of one cluster relies on the research findings of another. Specifically, we identified the direction of knowledge transfer by analyzing citation paths between literature items. Dependency relationships are constructed based on interactions between citing and cited literature, reflected in how citing literature references items from multiple clusters, thereby connecting different clusters. The cluster at the arrow’s start represents the citing party, while the cluster at the arrow’s end represents the cited party.

CiteSpace’s cluster dependency analysis clearly depicts the hierarchical knowledge evolution network of mechanical metamaterials in architectural engineering. This structure strictly follows the citation paths between literature items.

• The foundational core layer: Cluster #7 (Negative Poisson’s ratio) and Cluster #8 (Computational investigation) form the starting points, laying the foundation for material design principles, mechanical behavior analysis, and computational frameworks.
• Application technology development layer: Knowledge then differentiates towards clusters focused on application technology, such as #2 (Auxetic honeycomb structures), #4 (Geometrically programmed metamaterials), and #5 (Mechanical response). Cluster #2 (Auxetic honeycomb structures) significantly improves building protection capabilities. Cluster #4 integrates #1 (Energy absorption mechanism—gradient design) and #8 (intelligent frameworks) to explore geometric programming for achieving thermal deformation and wave control.
• Engineering application and design innovation layer: Clusters #0 (Programmable strength), #1 (Energy absorption mechanism), and #3 (Origami dynamics) build upon the technical method layer and directly address application needs.
• Design method innovation and integration layer: Cluster #4 (Geometrically programmed metamaterials) plays a key role in knowledge convergence. Its development inherits the gradient design concept from #1 (Energy absorption mechanism) and absorbs results from #2 (Extreme protection research). Simultaneously, Cluster #3 (Origami dynamics) directly builds upon #7 (Structural basic mechanics), with its kinematic models supporting morphological innovation in deployable buildings. The energy absorption mechanism of #1 deepens the gradient and hierarchical design to achieve multi-platform stress characteristics and programmable energy absorption.
• Frontier exploration layer: As the most recent development, the intelligent response of Cluster #6 (High-performance auxetic metamaterials) guides materials towards exploring directions like disaster adaptability and dynamic energy consumption regulation.

This knowledge network rigorously presents the evolution path: “Basic theory foundation (#7, #8) to application technology differentiation (#2, #5, #0) to design method integration and deepening (#4, #1, #3) to frontier intelligent exploration (#6)”. Among these, #4 acts as an integration hub dependent on multiple previous levels, while #1 and #3 deepen specific mechanisms based on foundational and application technologies. Collectively, they provide a clear systemic perspective and knowledge evolution direction for understanding the key technical chain of mechanical metamaterials from fundamentals to architectural applications, improving building resilience, and promoting intelligent construction.

3.3.2. Citing Literature and Cited References

In analyzing literature co-citation networks, identifying key literature is crucial for understanding the knowledge base of specific research topics. CiteSpace software provides several quantitative indicators to evaluate the influence and role of literature within the network:

• Freq (Frequency): The number of times a literature item is co-cited by other literature in the network, reflecting its universality and core status as a knowledge base (e.g., larger nodes in the co-citation network, Figure 8).
• Burst: Measures the intensity of citations to a literature item within a specific period, indicating its leading role or breakthrough contribution as an emerging hotspot (e.g., red node literature, Figure 8).
• Degree: Represents the number of nodes directly connected to a literature item in the network; a high value indicates it occupies a hub position in knowledge diffusion, connecting multiple research fields (e.g., isolated node, Figure 9).
• Sigma (Σ): A comprehensive influence index combining burstiness and centrality. A value > 1 usually indicates the literature possesses both innovative and hub properties.
• Half-life: Characterizes the duration of a literature item’s influence. A long half-life signifies a lasting contribution, marking the literature as more classic.

This section focuses on core references (research foundation) with significant index values in each cluster, discussing how citing literature deepens, innovates, and expands applications based on these knowledge bases (research frontiers). This clearly shows the inheritance, evolution, and breakthroughs within each topical field.

• Cluster 0: Programmable Strength
  • Research Base

Cluster 0 focuses on research concerning the adjustable strength and growth structure design of negative Poisson’s ratio materials. Important reference nodes, shown in Table 1, systematically support the research context in the citing literature. Review studies have laid a solid theoretical foundation and constructed a comprehensive framework from design to application. The review by Luo et al. [37] provides systematic support for subsequent research on design methods, performance evaluation, and application scenarios. Ren et al. [38] systematically classified six auxetic cell models, linking the research chain of “structural design-performance-application realization”. Multiple citing literature items simultaneously cite their model classification and performance analysis, forming a theory-to-practice feedback loop.

In structural design innovation, the auxetic structures proposed by Ingrole et al. [39] pioneered a design paradigm for adjustable deformation paths; their ideas have been continued in subsequent structural iterations, hybrid configuration designs, multi-physics field expansions, and cross-scale applications. Yang et al. [40] established a pioneering three-dimensional auxetic honeycomb analytical model. Teng et al. [41] developed rotating concave three-dimensional auxetic metamaterials to achieve high compression ratios and long stress plateaus, leading to structural optimization, manufacturing innovation, and functional development. Studies by Frenzel [42], Boldrin [43], and others made breakthroughs in novel structural design and gradient honeycomb vibration characteristics, respectively. In characterizing and optimizing mechanical properties, research by Jin et al. [44] on the anti-blast performance of negative Poisson’s ratio honeycomb sandwich structures established a collaborative “gradient and cross arrangement” optimization paradigm, providing key parameter configuration schemes for anti-blast design. The above research collectively promoted the effective transformation of negative Poisson’s ratio structures from theoretical modeling to practical engineering applications.

Table 1. Main reference nodes of Cluster 0.

Label	Freq	Burst	Degree	Sigma	Half-Life
Ren X (2018) [38]	35	2.79	44	1	4.5
Ingrole A (2017) [39]	18	3.09	22	1.12	5.5
Teng XC (2022) [41]	10	0	16	1	1.5
Frenzel T (2017) [42]	9	0	35	1	5.5
Jin XC (2016) [44]	9	3.63	6	1.02	6.5
Yang L (2015) [40]	9	0	20	1	7.5
Luo C (2021) [37]	7	2.82	15	1.03	1.5
Boldrin L (2016) [43]	7	0	25	1	4.5

Table 1. Main reference nodes of Cluster 0.

Label	Freq	Burst	Degree	Sigma	Half-Life
Ren X (2018) [38]	35	2.79	44	1	4.5
Ingrole A (2017) [39]	18	3.09	22	1.12	5.5
Teng XC (2022) [41]	10	0	16	1	1.5
Frenzel T (2017) [42]	9	0	35	1	5.5
Jin XC (2016) [44]	9	3.63	6	1.02	6.5
Yang L (2015) [40]	9	0	20	1	7.5
Luo C (2021) [37]	7	2.82	15	1.03	1.5
Boldrin L (2016) [43]	7	0	25	1	4.5

• • Research Frontier

Citing literature covers core directions such as structural design innovation (Figure 10a,b) [17,45,46,47], mechanical properties [48,49,50,51,52], preparation methods [7,53,54], and engineering transformation [55,56,57,58,59,60]. In structural design and innovation, the focus is on improving material performance through geometric configuration optimization. Energy absorption performance is optimized through gradient and hierarchical negative Poisson’s ratio structures (Figure 10c) [17,54,61], multi-material filling (Figure 10d) [58,62], and theoretical modeling [63,64]. Focusing on different structures, substrates, and load conditions, the energy absorption, hardening response, and dynamic mechanical properties of auxetic materials are analyzed in depth to achieve universality in multi-mode deformation regulation. Preparation method exploration is crucial for the practical application of auxetic materials, with core strategies including low-cost assembly technology [3], additive manufacturing parameter control [7], and 3D printing, aiming to overcome technical bottlenecks in large-scale production and performance control. The research results of this cluster provide core theoretical support for the geometric programmable design of Cluster 4, and its gradient design concept has promoted the development of subsequent dynamic load protection structures.

2.

Cluster 1: Enhanced Energy Absorption Performance

• Research Base

Cluster 1 builds upon the gradient design and structural innovation foundation of Cluster 0. This cluster’s core focus is enhancing energy absorption capacity and stiffness, particularly achieving multi-platform stress characteristics and programmable mechanical behavior through design. The references in Cluster 1 (Table 2) systematically support the depth of the citing literature. Their contributions span theoretical construction, structural innovation, performance verification, and engineering applications. In theoretical foundation and framework construction, Zhang et al. [65] provided a systematic theoretical framework and manufacturing basis for research on the plastic deformation and energy absorption of additively manufactured auxetic materials. The limitations they identified, such as the lack of dynamic models, directly stimulated subsequent multi-mechanism coupling innovation and effectively promoted the translation of theoretical results to engineering applications. Wu et al. [66] systematically established the theoretical system for chiral mechanical metamaterials, laying a foundation for subsequent performance optimization in vibration attenuation, impact energy absorption, and practical applications like medical stents and intelligent buildings. Hu et al. [67] focused on constructing a theoretical model for auxetic honeycombs under dynamic loads, establishing the foundation for understanding dynamic response in this field; their theories are widely cited by subsequent studies.

In platform stress and hierarchical mechanisms, the RSH honeycomb structure proposed (Figure 11a) by Wang et al. [68] has had a systematic impact due to its dual-platform stress characteristics and high energy absorption capacity. Its design concept triggered extensive structural derivations, performance optimization strategies, and mechanism exploration, integrating functional gradients with multi-objective optimization algorithms. Liu et al. [69] established an analysis framework for the dynamic impact response of re-entrant auxetic honeycombs (Figure 11b), proposed gradient and disorder design criteria, and inspired the development of various novel structures. Their established finite element analysis paradigm and identified engineering limitations are widely used and drive subsequent innovations (e.g., origami structures, negative gradient design). Research by Qi’s team verified the core advantages of re-entrant hexagonal honeycomb sandwich panels under blast impact [70]. The subsequently proposed double-arc cell-wall re-entrant honeycomb (REC) [71] realized a hierarchical energy dissipation mechanism through geometric innovation. Its parameterized paradigm further inspired gradient structure expansion and intelligent material integration, continuously promoting lightweight design innovation in impact and seismic protection. Dong et al. [72] systematically revealed the compressive properties of metal re-entrant honeycombs, especially the influence of cell-wall thickness on deformation modes and size effects, providing experimental support for subsequent research in stiffness optimization, gradient design applications, and deepening understanding of material properties and NPR energy absorption mechanisms. An et al. [73] designed a bidirectional re-entrant honeycomb (BRH) to achieve hierarchical energy absorption through adjustable negative Poisson’s ratio and dual-platform stress zone design (Figure 11c); its analysis method is widely used in subsequent studies to verify dual-platform universality, extend to multi-material systems, and combine with origami structures to improve performance. These representative studies collectively verify the universality of multi-platform mechanisms and combination strategies in improving energy absorption performance, successfully overcoming limitations of early multi-level energy absorption designs.

Table 2. Main reference nodes of Cluster 1.

Label	Freq	Burst	Degree	Sigma	Half-Life
Zhang JJ (2020) [65]	23	0	42	1	3.5
Qi C (2017) [70]	20	0	31	1	4.5
Liu WY (2016) [69]	20	0	52	1	5.5
Qi C (2020) [71]	16	0	41	1	2.5
Wang H (2019) [68]	14	3.67	39	1.01	2.5
Wu WW (2019) [66]	10	0	19	1	4.5
Hu LL (2018) [67]	10	0	17	1	5.5
Dong ZC (2019) [72]	8	0	20	1	3.5
An MR (2022) [73]	6	0	31	1	1.5

Table 2. Main reference nodes of Cluster 1.

Label	Freq	Burst	Degree	Sigma	Half-Life
Zhang JJ (2020) [65]	23	0	42	1	3.5
Qi C (2017) [70]	20	0	31	1	4.5
Liu WY (2016) [69]	20	0	52	1	5.5
Qi C (2020) [71]	16	0	41	1	2.5
Wang H (2019) [68]	14	3.67	39	1.01	2.5
Wu WW (2019) [66]	10	0	19	1	4.5
Hu LL (2018) [67]	10	0	17	1	5.5
Dong ZC (2019) [72]	8	0	20	1	3.5
An MR (2022) [73]	6	0	31	1	1.5

• • Research Frontier

The core theme of the citing literature is the multi-platform stress characteristics and programmable mechanical behavior of novel honeycomb structures under dynamic loads. Key strategies in this field include multi-platform stress mechanism design and gradient design optimization. Multi-platform stress mechanism design focuses on raising the platform stress level through innovative structural design [74] and geometric ordering of layered re-entrant honeycombs [75]. Furthermore, multi-platform designs [76,77,78,79] and platform stress enhancement technologies [80,81,82] have been developed to achieve complex hierarchical energy absorption responses. Gradient design optimization precisely regulates the energy absorption path and inertial effect by adjusting the gradient distribution of materials or structures (e.g., thickness, density, curvature). This is reflected in in-depth research on gradient direction dependence [13,83], bidirectional gradient synergy [84], and dynamic response laws [80,85]. Additionally, the “matrix filler” gradient coupling effect in composite structures [62] provides a new optimization dimension. Multi-platform stress characteristics are regarded as the core strategy for achieving efficient dynamic energy management, while gradient structures are key tools for achieving precise programming of platform stress. The coupled design of both is considered an important direction for further expanding material performance boundaries [17]. Their coupling and synergy are crucial paths to unlocking the programmable energy absorption potential of honeycomb structures, serving as a technical breakthrough for the next generation of impact and vibration reduction systems.

3.

Cluster 2: Auxetic Honeycomb

• Research Base

In Cluster 2, the core research based on the literature focuses on significantly improving impact resistance through innovative auxetic structure design. Important nodes are shown in Table 3. Qiao et al. [86] proposed a functionally graded double-arrow honeycomb (DAH), achieving functional gradient through cell wall thickness regulation. Its dynamic platform stress model and deformation map provide a core verification benchmark for subsequent research and were later extended to building protection. In performance optimization mechanisms and model establishment, Fu et al. [87] enhanced the stiffness and buckling strength of re-entrant honeycombs by embedding diamond configurations (Figure 12a); the proposed trade-off law of “stiffness enhancement leads to negative Poisson’s ratio weakening” became a core goal for subsequent optimization. The related buckling constraint mechanism lays a foundation for multi-level energy absorption design. Qi et al. [70] studied the anti-blast performance of honeycomb sandwich panels using a combined experimental–numerical method, revealing material aggregation effects and the evolution law of negative Poisson’s ratio under high strain rates (weakening negative value), and proposed a composite protection system (steel–aluminum sandwich) providing a paradigm for engineering lightweight design. Furthermore, Imbalzano et al. [88,89] established a simplified calculation model and a model associating geometric parameters with anti-blast performance, revealed the anti-blast performance advantages of auxetic structures, and laid a foundation for subsequent research.

Table 3. Main reference nodes of Cluster 2.

Label	Freq	Burst	Degree	Sigma	Half-Life
Qi C (2017) [70]	19	0	23	1	4.5
Qiao JX (2015) [86]	15	3.51	36	1.2	3.5
Fu MH (2017) [87]	14	0	47	1	5.5
Imbalzano G (2018) [89]	12	0	11	1	3.5
Imbalzano G (2016) [88]	12	2.71	14	1.04	4.5

Table 3. Main reference nodes of Cluster 2.

Label	Freq	Burst	Degree	Sigma	Half-Life
Qi C (2017) [70]	19	0	23	1	4.5
Qiao JX (2015) [86]	15	3.51	36	1.2	3.5
Fu MH (2017) [87]	14	0	47	1	5.5
Imbalzano G (2018) [89]	12	0	11	1	3.5
Imbalzano G (2016) [88]	12	2.71	14	1.04	4.5

• • Research Frontier

Citing literature focuses on the protection mechanisms and energy management strategies of auxetic structures under extreme dynamic loads such as explosions, impacts, and vibrations. This field integrates the core issues of Clusters #0 and #1, aiming to overcome the strength and energy absorption efficiency limitations of traditional protective structures through structural innovation.

In structural innovation, scholars primarily explore new auxetic honeycomb and metamaterial configurations, emphasizing the coupled design of negative Poisson’s ratio characteristics and energy absorption performance. Specific strategies include geometric reconstruction [68,90,91], topology optimization [92], multi-unit hierarchical composite design (Figure 12b) [93], etc. In performance optimization and mechanism exploration, research deeply analyzes the influence of key load conditions [48,94,95] and structural variable parameters [96,97] on dynamic responses, aiming to establish theoretical models guiding performance prediction and optimization [98]. In expanding auxetic structure application scenarios, research focuses on verifying the actual effectiveness of protective structures under extreme dynamic loads, including sandwich panel structures with excellent anti-blast performance (Figure 12c) [96,99], sacrificial layer protection systems [100], and exploring the potential and mechanisms of auxetic structures in vibration control.

Figure 12. Impact resistance enhancement of auxetic honeycombs: (a) re-entrant honeycomb with embedded diamond configuration [87]; (b) schematic diagram of deformation of multi-unit hierarchical composite auxetic structure [93]. The red wireframe marks the local failure concentration area in the composite structure caused by uneven stress transfer at the hierarchical interface; and (c) sandwich panel structures [96].

Figure 12. Impact resistance enhancement of auxetic honeycombs: (a) re-entrant honeycomb with embedded diamond configuration [87]; (b) schematic diagram of deformation of multi-unit hierarchical composite auxetic structure [93]. The red wireframe marks the local failure concentration area in the composite structure caused by uneven stress transfer at the hierarchical interface; and (c) sandwich panel structures [96].

4.

Cluster 3: Origami Metamaterial

• Research Base

Cluster 3 focuses on origami, showing close bidirectional interaction between theoretical construction and application expansion. Key references in Table 4 are primarily foundational systematic reviews and key research papers. Meloni et al. [101] systematically integrated the core knowledge system of origami engineering, established mainstream origami modes, and summarized reverse/forward design methods and computational toolchains. Bertoldi et al. [1] and Yu et al. [102] systematically classified mechanical metamaterials and defined key functional goals like negative Poisson’s ratio, multistability, and topological protection. These reviews, acting as “knowledge hubs,” prospectively point out key challenges such as manufacturing bottlenecks and dynamic behavior regulation, guiding the direction of technical breakthroughs in subsequent research. In computational mechanics models and dynamic analysis frameworks, core research papers provide powerful tools for cutting-edge exploration. The rod hinge model joint theory proposed by Liu et al. [103] forms a key computational framework for addressing geometric nonlinearity and multistable behavior. Building on the mechanical theory and dynamic behavior analysis framework established by the review of Li et al. [104], subsequent studies made breakthroughs in energy capture, programmable impact response, and defect-insensitive systems. These studies are cornerstones for understanding nonlinear dynamics tuning and realizing customized dynamic responses, confirming the transition of origami mechanics from theoretical exploration to engineering practice.

• • Research Frontier

The theoretical foundation and geometric programming paradigm of Cluster 3 depend to some extent on Cluster #7, particularly origami mechanics modeling and dynamic analysis. This cluster explores origami-inspired mechanical metamaterials and deployable structures, focusing on realizing customized dynamic responses and shape control through geometric programming of folding topology. In dynamic response tuning, research explores the nonlinear dynamic behavior of origami structures and their driving mechanisms, such as pneumatic actuation (Figure 13a) [105,106], fluid dynamics models (Figure 13b) [107], and topological phase transition regulation [108], revealing their unique advantages in dynamic tuning. To realize the programmable mechanical response of multistable metamaterials, folding paths are encoded into mechanical response functions, and synergistic programming of multiple parameters (e.g., Poisson’s ratio, stiffness) is achieved through structures like bistable auxetic modules [4], graphene origami auxetic materials [109], water bomb crease cell structures (Figure 13c) [110], and inflatable bistable panels [106].

In engineering application and design theory, Zhang et al. [111] established a mechanical theoretical model and equivalent analysis method for single-crease origami arrays, systematically studying the coupling effect between crease stiffness and panel deformation. For aerospace engineering [112,113], building structures, and other scenarios, Meloni et al. [114] established a shape–motion inverse design framework for origami building systems to realize collaborative optimization of folding paths and environmental avoidance. Ma et al. [115] established a unified static framework for integrated origami-tensegrity systems, deriving explicit nonlinear equilibrium equations and linearized forms, proposing geometric kinematics descriptions and stiffness matrix calculation methods, and uniformly describing both structural paradigms through rod–hinge models, providing a theoretical basis for designing and analyzing large-scale deployable structures. Addressing the demand for low-frequency vibration isolation, origami structures with quasi-zero stiffness characteristics are designed based on the principle of geometric non-uniqueness [116,117]. The strong nonlinear effect induced by folding is utilized to effectively expand the low-frequency vibration suppression bandwidth. Such studies generally rely on high-dimensional coupling modeling frameworks [118,119].

5.

Cluster 4: Geometrically Programmed Metamaterials

• Research Base

Cluster 4 reflects the application of geometrically driven multifunctional architectural metamaterials in basic research. Theoretical development in origami engineering shows a clear progressive context. Referencing Cluster #4 literature in Table 4, Schenk et al. [120] quantitatively revealed the negative Poisson’s ratio mechanism of Miura origami units by establishing geometric and kinematic models, proposing the “interlayer compatible stacking” design paradigm. This work laid the theoretical foundation for the scale invariance of origami structure mechanical behavior and provided key support for subsequent Poisson’s ratio regulation and programmable deformation. Subsequently, Filipov et al. [121] pioneered zipper-coupled origami tube structures, achieving stiffness jump and single-degree-of-freedom rigid folding through geometric coupling. Their geometric parameterized model and eigenvalue band gap theory provided key support for adjustable metamaterials and parameterized design standards. Dudte et al. [122] further expanded the research dimension to complex surface programming. Their developed origami mosaic computational design method (e.g., constraint optimization algorithm) became a general bridge for cross-scale applications, from building deployable structures and mechanical metamaterials to reconfigurable systems, while deepening the understanding of mechanical behaviors like bistable control and promoting breakthroughs in engineering bottlenecks like thick-plate origami.

• • Research Frontier

In citing literature, the core methodology depends on research from Clusters #1 (gradient and hierarchical design), #2 (protection and wave application), and #0 (multi-material and preparation), and builds upon the computational design framework from Cluster #8. This cluster focuses on introducing architectured metamaterials with programmable mechanical, thermal, and wave dynamic properties through geometric manipulation design. The core is realizing material performance tunability via origami folding mechanisms [14,101,123,124] and multi-material hierarchical lattices [85,125]. Major achievements include independent or synergistic regulation of Poisson’s ratio and thermal expansion coefficient [126], adjustable wave propagation characteristics [123,127], efficient computational design frameworks [124,128,129,130], and enhanced mechanical properties [131]. These studies mark a paradigm shift towards geometrically driven multifunctionality, controlling the static and dynamic properties of structures through precise design of folding topology and material distribution.

6.

Cluster 5: Mechanical Response

• Research Base

Research related to Cluster 5 in the auxetic structures field shows significant knowledge inheritance and expansion. Referencing Cluster #5 literature in Table 4, the double-arrow auxetic structure proposed by Gao et al. [132] laid an important foundation, and their geometric parameter sensitivity analysis provided a key basis for subsequent optimization research. Simultaneously, the pioneering work of Imbalzano’s team on the anti-blast performance of negative Poisson’s ratio composite panels, through efficient numerical models and quantitative energy absorption advantages, established a methodological benchmark and performance reference for subsequent impact resistance research [88]; their 2018 research was further systematized, proposing a parameterized design framework, performance comparison methods, and revealing the “local densification” mechanism [89]. This was widely used to explain anti-blast mechanisms and guide new structure designs, promoted extension of the theoretical system to multi-material composites and reconfigurable structures, and drove innovative exploration of engineering applications like lightweight armor and concrete protection.

Table 4. Main reference nodes of Clusters 3, 4, and 5.

Label	Freq	Burst	Degree	Sigma	Half-Life	Cluster ID
Meloni M (2021) [101]	16	3.68	12	1.05	2.5	3
Yu XL (2018) [102]	13	0	14	1	5.5	3
Bertoldi K (2017) [1]	11	0	14	1	5.5	3
Li SY (2019) [104]	10	0	12	1	4.5	3
Liu K (2017) [103]	10	0	14	1	6.5	3
Schenk M (2013) [120]	10	3.77	21	1.2	7.5	4
Dudte LH (2016) [122]	7	0	12	1	6.5	4
Filipov ET (2015) [121]	6	0	16	1	7.5	4
Imbalzano G (2018) [89]	13	0	21	1	3.5	5
Imbalzano G (2016) [88]	8	3.21	13	1.02	4.5	5
Gao Q (2019) [132]	7	3.61	22	1.1	1.5	5

Table 4. Main reference nodes of Clusters 3, 4, and 5.

Label	Freq	Burst	Degree	Sigma	Half-Life	Cluster ID
Meloni M (2021) [101]	16	3.68	12	1.05	2.5	3
Yu XL (2018) [102]	13	0	14	1	5.5	3
Bertoldi K (2017) [1]	11	0	14	1	5.5	3
Li SY (2019) [104]	10	0	12	1	4.5	3
Liu K (2017) [103]	10	0	14	1	6.5	3
Schenk M (2013) [120]	10	3.77	21	1.2	7.5	4
Dudte LH (2016) [122]	7	0	12	1	6.5	4
Filipov ET (2015) [121]	6	0	16	1	7.5	4
Imbalzano G (2018) [89]	13	0	21	1	3.5	5
Imbalzano G (2016) [88]	8	3.21	13	1.02	4.5	5
Gao Q (2019) [132]	7	3.61	22	1.1	1.5	5

• • Research Frontier

Citing literature research relates to the performance goals of Cluster #1 and the structural foundation of Cluster #7. This cluster focuses on structural innovation and optimization of auxetic materials, integration of advanced manufacturing technologies, and verification in multi-scenario applications. At the structural design level, researchers have moved beyond traditional configurations to innovate (Figure 14a) and optimize structures [2,82,133,134,135,136]. Drawing on energy absorption performance quantification methods and understanding of anti-blast mechanisms, researchers designed 3D re-entrant structures (Figure 14b) [137], four-chiral structures [55], and sandwich structures with truss cores [138] that exhibit impact resistance superior to traditional honeycombs. In structural enhancement, embedding 3D auxetic truss lattice materials in concrete increases peak strength (Figure 14c) [139]. In vibration control, carbon fiber reinforced re-entrant core cylindrical shells (Figure 14d) [140] optimize vibration damping through modal strain energy. In health monitoring, the star-shaped hourglass structure ultrasonic guided wave monitoring framework [141] combines probabilistic neural networks to achieve damage quantification. Additionally, excellent energy management characteristics under dynamic loads [142] further confirm its engineering potential. In manufacturing technology, laser powder bed fusion accurately prepares steel and aluminum trusses; photocuring and fused deposition support 4D printing of shape memory polymers, endowing sinusoidal lattices [136] and re-entrant structures [143] with heat-driven self-healing capabilities. Applications have successfully expanded to multiple engineering scenarios, including building enhancement, vibration control, and health monitoring, systematically verifying the significant potential of auxetic metamaterials in dynamic load management.

7.

Cluster 6: High-Performance Auxetic Metamaterials

• Research Base

The knowledge base of Cluster 6 can be referenced in Cluster #6 literature in Table 5. Chen et al. [144] conducted systematic research on double-arrow metal honeycomb structures, exploring gradient design and filling optimization strategies; their proposed gradient design ideas and multi-mechanism synergy concepts provided important guidance for innovation in multifunctional auxetic structures and energy-absorbing materials. Simultaneously, the geometric optimization method and low-rotational-stiffness node concept proposed by Choudhry et al. [145] became a common paradigm for cross-field research by establishing energy-absorption performance benchmarks and parameterized design frameworks. Its node design concept was adapted to the development of multifunctional coupling mechanisms, and optimization technologies were extended to multi-physics field analysis, promoting the evolution of auxetic materials from single-function to integrated design.

• • Research Frontier

As relatively new research results, the citing literature in this cluster builds upon findings from Clusters #0–#5. This cluster explores breaking through the performance limits of auxetic materials through innovative structural design strategies, tapping their potential in high energy absorption [11,146,147], vibration suppression [148,149], and adjustable mechanical response (Figure 15a) [150,151] using advanced concepts like multi-mechanism integration [146], gradient design [11,147], hierarchical strategies [152], and intelligent control [153]. Crucially, this frontier realizes active programming of mechanical responses by integrating functional materials or utilizing external fields, promoting auxetic metamaterials towards key directions such as large strain stable response (Figure 15b) [146], high reusability [154], and active programmability [152].

8.

Cluster 7: Negative Poisson’s Ratio

• Research Base

The knowledge base of Cluster 7 is reflected in key theoretical breakthroughs and engineering methods. According to the foundational Cluster #7 literature in Table 5, at the theoretical level, the review on Poisson’s ratio by Greaves et al. [155] systematically explains the physical mechanism of negative Poisson’s ratio and the material design framework, providing core theoretical support for understanding the relationship between microstructure deformation principles and macroscopic properties (e.g., energy absorption, fracture toughness). At the cross-scale analysis level, Prawoto et al. [156] reviewed forward prediction for disordered microstructures and generalized homogenization calculation methods, laying a methodological foundation for designing and analyzing complex aperiodic structures. Chen et al. [157] established a standardized optimization paradigm through innovative topological configurations and parameterized design methods.

Table 5. Main reference nodes of Clusters 6, 7, and 8.

Label	Freq	Burst	Degree	Sigma	Half-Life	Cluster ID
Choudhry NK (2022) [145]	7	0	23	1	1.5	6
Chen GC (2021) [144]	2	0	20	1	3.5	6
Prawoto Y (2012) [156]	10	4.2	17	1.18	6.5	7
Greaves GN (2011) [155]	6	2.86	9	1.02	5.5	7
Chen Z (2018) [157]	4	0	13	1	2.5	7
Frenzel T (2017) [42]	6	2.75	2	1.01	4.5	8

Table 5. Main reference nodes of Clusters 6, 7, and 8.

Label	Freq	Burst	Degree	Sigma	Half-Life	Cluster ID
Choudhry NK (2022) [145]	7	0	23	1	1.5	6
Chen GC (2021) [144]	2	0	20	1	3.5	6
Prawoto Y (2012) [156]	10	4.2	17	1.18	6.5	7
Greaves GN (2011) [155]	6	2.86	9	1.02	5.5	7
Chen Z (2018) [157]	4	0	13	1	2.5	7
Frenzel T (2017) [42]	6	2.75	2	1.01	4.5	8

• • Research Frontier

Cluster 7 research serves as an important foundation for Clusters #0, #1, #2, #3, and #5. This cluster fundamentally studies the design principles, mechanical behavior optimization mechanisms, and composite synergistic strategies of auxetic honeycombs and their derived structures. Researchers aim to overcome the performance limitations of traditional auxetic structures. On one hand, through innovative topological configurations like star-triangle honeycombs (Figure 16a) [158], concave arc honeycombs (Figure 16b) [159], and 3D cross-chiral structures (Figure 16c) [160] to improve strength, stiffness, and the negative Poisson’s ratio effect. On the other hand, based on accurate theoretical modeling and analysis systems [161], they conduct in-depth analysis of complex structure behavior concerning dynamic response, platform stress, failure modes, and deformation mechanisms, providing key support for performance prediction. Composite and hybrid strategies have proven effective for synergistic performance enhancement, significantly improving energy absorption efficiency and multifunctionality. Representative schemes include hybrid honeycomb superstructures [58,74,161], multi-lattice designs [162], foam filling [163], composite material integration [164,165], etc. The research scope has expanded from static mechanical behavior to performance characterization and exploration of emerging applications under multi-physics field coupling, such as dynamic impact and blast loads.

9.

Cluster 8: Computational Investigation

• Research Base

In the field of auxetic material research, Cluster 8 begins with the theoretical foundation laid by Frenzel [42] and progressively builds a multi-scale intelligent control system, continuously advancing this field.

• • Research Frontier

A multi-scale intelligent control system is built within auxetic material research, providing foundational theory for subsequent studies. Research in this cluster focuses on three core directions: computation-driven design [166,167], advanced manufacturing [168,169], and active control [61], aiming to advance auxetic metamaterials from static structural systems to dynamic intelligent systems. Among these, intelligent reconfigurability [170] and multifunctional integration characteristics [171,172] are becoming key trends and important driving forces in the development of this field.

3.4. Citation Bursts

Table 6. References with the strongest citation bursts. The rightmost column, “2015–2025”, uses a bar chart to visualize the citation burst intensity of each reference across years. The height of the bars corresponds to the relative intensity of citations in that year. The bar color gradient (light cyan to dark cyan) indicates the increasing intensity of citation bursts: light cyan, medium cyan, and dark cyan, while red denotes the citation burst phase. The “Begin” and “End” columns mark the start and end years of the citation burst period, while “Strength” represents the absolute intensity of the burst.

References	Year	Strength	Begin	End	2015                      2025
Prawoto Y, 2012 [156]	2012	4.2	2016	2020	▂▃▃▃▃▃▂▂▂▂▂
Greaves GN, 2011 [155]	2011	2.86	2016	2019	▂▃▃▃▃▂▂▂▂▂▂
Schenk M, 2013 [120]	2013	3.77	2018	2021	▂▂▂▃▃▃▃▂▂▂▂
Qiao JX, 2015 [86]	2015	3.51	2018	2019	▂▂▂▃▃▂▂▂▂▂▂
Gao Q, 2019 [132]	2019	3.61	2020	2021	▂▂▂▂▂▃▃▂▂▂▂
Imbalzano G, 2016 [88]	2016	3.21	2020	2022	▂▂▂▂▂▃▃▃▂▂▂
Ingrole A, 2017 [39]	2017	3.09	2020	2023	▂▂▂▂▂▃▃▃▃▂▂
Wang H, 2019 [90]	2019	3.67	2021	2022	▂▂▂▂▂▂▃▃▂▂▂
Ren X, 2018 [38]	2018	2.79	2021	2023	▂▂▂▂▂▂▃▃▃▂▂
Frenzel T, 2017 [42]	2017	2.75	2021	2022	▂▂▂▂▂▂▃▃▂▂▂
Jin XC, 2016 [44]	2016	3.63	2022	2023	▂▂▂▂▂▂▂▃▃▂▂
Luo C, 2021 [37]	2021	2.82	2022	2023	▂▂▂▂▂▂▂▃▃▂▂
Meloni M, 2021 [101]	2021	3.68	2023	2025	▂▂▂▂▂▂▂▂▃▃▃

presents publications exhibiting significant citation bursts. These bursts confirm and deepen the preceding cluster dependency network analysis by revealing spatiotemporal patterns. The burst time windows (2015–2025) of these publications are highly synchronized with the cluster evolution stages:

• Early Bursts (Active: 2016–2019). Publications like Greaves (2011) [155] and Prawoto (2012) [156] are concentrated within Cluster #7 (Structural foundation). They provided sustained influence on negative Poisson’s ratio mechanisms and cross-scale analysis theories, forming the foundational layer of the dependency network.
• Mid-Term Burst Peak (Active: 2018–2022). This peak directly drove the development of the engineering application layer. Breakthrough work by Qiao (2015) [86] and Imbalzano (2016) [88] in protective mechanics promoted the formation of Cluster #2 (Extreme protection). Empirical research by Wang (2019) [68] and Gao (2019) [132] on energy absorption mechanisms strengthened the scientific foundation of Cluster #1 (Multi-platform stress). Concurrently, the citation burst of Schenk’s (2013) [120] origami geometric model supported the algorithmic framework construction for Clusters #3 (Origami dynamics) and #4 (Geometric programming).
• Recent Frontier-Oriented Publications (Active: 2021–2025). Meloni (2021) [101], exhibiting the current highest burst intensity (3.68), leads origami engineering review research. This work continuously enables cross-exploration between the #4 design method integration layer and the #6 intelligent response frontier cluster, confirming the transformation trend of programmable materials towards disaster adaptability.

3.5. Network Structure Variation Analysis

CiteSpace’s Structural Variation Analysis (SVA) effectively captures the dynamic reorganization mechanisms within the research knowledge structure. The modularity of the knowledge network serves as a global measure of its overall organization. Changes in local structures may trigger global modifications, though this is not always the case. The theoretical basis stems from Chen et al. [173] structural variation theory, which posits that innovation often arises from connecting previously disparate research fields.

CiteSpace’s SVA quantifies the impact of new publications on the knowledge network using three key indicators (see

Table 7. Articles causing network changes after publication.

Citing Articles	Freq	∆Modularity	∆Cluster Linkage	∆Centrality	Year
Wang H, 2019 [68]	242	86.81	100	0.36	2019
Dinh Duc Nguyen, 2017 [164]	164	100	0	0	2017
Yang H, 2019 [168]	140	100	−100	0	2019
Wang T, 2021 [174]	112	100	−100	0	2021
Zhong R, 2022 [58]	104	100	−94.85	0.02	2022
Bohara Rp, 2023 [92]	103	24.89	−100	0	2023
Zhu Y, 2022 [45]	91	89.44	−69.08	0.01	2022
Xu F, 2021 [51]	83	97.12	−4.71	0.29	2021
Bohara RP, 2021 [82]	76	88.25	−78.82	0.05	2021
Linforth S, 2021 [95]	71	94.36	−57.65	0.09	2021
Wei L, 2021 [79]	65	94.13	−73.53	0.31	2021
Nedoushan RJ, 2021 [175]	65	100	−100	0	2021
Chen J, 2021 [126]	58	29.51	−100	0	2021
Jiang F, 2023 [17]	56	93.32	−69.72	0.06	2023
Bohara RP, 2022 [56]	38	67	−100	0	2022
Kalubadanage D, 2021 [100]	37	100	−94.71	0.12	2021

):

• Module Change Rate (∆Modularity): Quantifies the percentage change in the network’s community structure induced by new publications.
• Cluster Linkage (∆Cluster Linkage): Directly measures the increment in connections established by new publications between different knowledge clusters.
• Centrality Dispersion (∆Centrality): Evaluates changes in the distribution of node betweenness centrality using Kullback–Leibler (KL) divergence, reflecting how new publications disrupt the status of key hub nodes.

The visualization of structural variation is presented in Figure 17. Within this network, red curves represent newly added connections; pink solid lines represent existing connections. Publications marked with red five-pointed stars indicate new literature meeting the citation criteria for causing structural variation.

Analysis of the network structural variation data reveals three distinct types of creative reorganization in this field (specific publication nodes are listed in Table 7):

• Cross-Field Integration Engine: Wang H (2019) [68], through its research on dual-platform stress honeycombs (central to Cluster #1 energy absorption), acted as an integration engine. It triggered a high module change rate (∆Modularity = 86.81) and 100% cluster connection growth (∆Cluster Linkage = 100) by simultaneously bridging three clusters: #0 (programmable strength), #1 (energy absorption), and #2 (auxetic honeycomb structure).
• New Path Pioneers: Yang H (2019) [168] and Wang T (2021) [174] functioned as pioneers, opening new knowledge branches (indicated by cluster linkage change values ∆Cluster Linkage ≈ −100). Their work facilitated the penetration of auxetic materials from fundamental configurations into engineering protection systems.
• Structural Optimization Paradigm Leader: Xu F (2021) [52] led a structural optimization paradigm. Research on sinusoidal curve negative Poisson’s ratio honeycombs achieved improvements in specific energy absorption (SEA) and reductions in peak crushing force (PCF) via multi-objective optimization. This strengthened the technical relevance of Cluster #1 (energy absorption), evidenced by ∆Centrality = 0.29, and offered a novel approach for lightweight protection design.

This structural variation exhibits a distinct temporal trajectory:

• Technical Breakthrough Period (2019–2021): Studies like Zhong R (2022) [58], which prepared negative pressure layered honeycomb concrete composites, demonstrated significant negative connection variation (∆Cluster Linkage = −94.85%). This realized the application transition from material design (Cluster #7) to seismic scenarios (Cluster #0).
• Intelligent Transition Period (2021–2023): Bohara RP (2023) [92] triggered 100% negative connection variation by systematically reviewing auxetic structure topology design, manufacturing technology, and performance evaluation frameworks. This review integrated fragmented knowledge modules, guiding the structured consolidation and paradigm shift within the domain knowledge.

Collectively, these variations constitute the creative driving force of the knowledge network. An average modular growth exceeding 90 breaks down disciplinary barriers, while polar link variations (|∆Cluster Linkage| > 94) reshape the evolution path from “basic theory to technical application to intelligent frontier.” This ultimately provides a continuously evolving adaptive knowledge framework for transformable architecture.

3.6. Term Information Entropy Growth

An increase in information entropy typically signifies rising complexity within a research field. The keyword time-zone map (Figure 4) illustrates this expansion: research topics broadened from foundational terms like “finite element method” in 2015 to application-oriented terms such as “seismic response” after 2020. Concurrently, keywords related to “negative Poisson’s ratio” followed a deepening trajectory from “basic research to engineering application”.

This thematic diffusion aligns with entropy growth, indicating that as research dimensions diversify, keyword distribution becomes more dispersed. Findings from the Structural Variation Analysis (SVA) provide strong corroboration. After 2020, studies like Xu et al. (2021) [52] significantly enhanced network connectivity through cross-cluster integration. This aligns perfectly with the accelerated entropy growth observed during the same period, as depicted in the entropy growth curve (Figure 18).

Furthermore, the “structural variation” triggered by Bohara RP (2023) [72] and others, which promoted the formation of Cluster #6, drove the entropy value to its peak (12.56) in 2024. This demonstrates that innovative recombination periodically escalates field complexity.

4. Research Summary

This study demonstrates the significant utility of bibliometric network analysis for conducting systematic and objective literature reviews in the rapidly evolving field of mechanical metamaterials for transformable architecture. The employed methodology offers distinct advantages over traditional review approaches:

• Enhanced Retrieval Rigor and Reduced Bias

The multi-stage retrieval strategy, particularly the use of the litsearchr tool for text mining of seed literature to generate and expand the candidate vocabulary database, directly addresses a core limitation of conventional reviews. This approach minimizes researcher-induced keyword coverage bias, ensuring a more comprehensive and representative dataset that captures the interdisciplinary nature of the field. This systematic optimization of the search string significantly strengthens the foundation for subsequent analysis.

2.

Objectivity in Mapping Knowledge Structure

By utilizing bibliometric tools, this study transcends the subjectivity inherent in expert-led qualitative reviews. The multi-dimensional analyses—including co-word analysis for topic evolution, co-citation clustering to identify foundational knowledge bases, and cluster dependency networks to reveal hierarchical research frontiers—provide quantifiable and visual evidence of the field’s intellectual structure. This offers an unbiased, data-driven perspective on research status, core themes, and emerging directions.

3.

Quantifying Knowledge Evolution and Innovation

The introduction of Structural Variation Analysis (SVA) represents a key methodological advancement. By quantifying the impact of new publications on the knowledge network through metrics like Module Change Rate (∆Modularity), Cluster Linkage (∆Cluster Linkage), and Centrality Dispersion (∆Centrality), this study moves beyond descriptive statistics. It provides measurable evidence of creative recombination, interdisciplinary integration, and paradigm shifts, offering unique insights into the mechanisms driving innovation within the field. The combined analysis of citation bursts and information entropy growth further validates the observed thematic evolution and increasing complexity.

4.

Efficiency and Scope for Researchers

The methodology provides a powerful framework for researchers, especially those new to the field, to efficiently navigate the extensive literature. It systematically identifies core journals (Bradford’s law), foundational papers (high centrality/burst), key research clusters, and emerging frontiers, significantly reducing the time and effort required to grasp the landscape compared to manual review processes. The visualizations (knowledge mapping, time-zone maps, dependency networks) offer intuitive summaries of complex interrelationships.

Despite its strengths, this bibliometric approach has inherent constraints. The reliance on Web of Science and Scopus databases, while ensuring academic rigor, risks excluding significant non-English publications, books, conference proceedings, and emerging preprints. Although litsearchr-optimized searches mitigate terminology gaps, potential mismatches in engineering application terminology may still cause relevant literature omissions, and the focus on peer-reviewed articles may underrepresent industry innovations. Methodologically, co-citation analysis remains susceptible to the “Matthew Effect,” where highly cited works dominate visibility, potentially overlooking niche innovations—even with SVA identifying disruptive newcomers. Finally, while bibliometrics objectively maps knowledge structures, deep technical interpretation within clusters still requires domain expertise, underscoring the need to integrate quantitative mapping with qualitative assessment.

5. Conclusions

Bibliometric network analysis reveals a clear shift in the core driving force within this field, moving from fundamental theoretical exploration towards interdisciplinary technological integration and the construction of intelligent systems.

During the initial phase (2015–2018), research primarily focused on understanding the intrinsic mechanical behavior of materials and establishing methodological foundations. High-frequency keywords such as “negative Poisson’s ratio,” “finite element method,” and “structural dynamics” dominated the discourse. Studies centered on analyzing the deformation mechanisms and characterizing the static performance of auxetic honeycombs and origami structures. The theoretical achievements of this period—notably the fundamental mechanical models of Cluster #7 and the computational frameworks of Cluster #8—laid the essential knowledge groundwork for subsequent applications. Journal dual-map overlay analysis further highlights that knowledge flow from mathematics and systems science to material physics and classical mechanics significantly advanced the development of cross-scale modeling tools.

The intermediate phase (2019–2021) exhibited dual characteristics of technological integration and application expansion. The emergence of keywords like “3D printing” and “gradient design” signaled that innovations in manufacturing processes were driving research from theory towards practical implementation. The research focus shifted towards optimizing structural performance and regulating dynamic responses. In the realm of auxetic structures, this involved enhancing energy absorption efficiency through multi-platform stress design (Cluster #1) and gradient parameterization. Concurrently, origami metamaterials (Cluster #3) leveraged kinematic models to achieve multi-stable switching and programmable deformation. Their geometric programming capabilities (Cluster #4) were further extended to enable collaborative regulation of properties like the thermal expansion coefficient and wave propagation. Application scenarios broadened from fundamental protection mechanisms to engineering domains such as “sandwich panels” and “seismic response.”

In the most recent phase (2022–2025), topic evolution underscores a pronounced trend towards intelligence and system integration. Keyword distribution exhibits increasing information entropy (peaking at 12.56 in 2024), reflecting a significant rise in field complexity. “Geometrically programmable metamaterials” have emerged as a central knowledge integration hub (Cluster #4), deeply incorporating the gradient design concepts of Cluster #1, the protection mechanisms of Cluster #2, and the origami kinematics of Cluster #3. This convergence is propelling materials beyond static configurations towards environment-responsive systems. Key frontier developments include intelligent algorithm-driven inverse design, active regulation strategies, and multifunctional coupling.

Future research efforts must prioritize three critical directions:

• Deepening Integration: Advance the integration of geometric programming with intelligent algorithms to achieve collaborative multi-physics regulation encompassing mechanical response, thermal deformation, and wave propagation.
• Engineering Application: Promote the engineering integration of gradient design, hierarchical design, and multi-stable mechanisms to develop practical, reconfigurable building systems.
• Technical Chain Development: Establish a robust technical chain encompassing “microstructure optimization–multifunctional coupling–building system verification” to accelerate the implementation of applications like impact resistance, vibration isolation, and structural health monitoring.