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Mathematics
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Advanced Computational Mechanics
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Advanced Computational Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 7350

Special Issue Editors

Dr. Lucia Barbu

E-Mail Website
Guest Editor
CIMNE, Centre Internacional de Mètodes Numèrics a l’Enginyeria, C1, Campus Nord, Gran Capità, 08034 Barcelona, Spain
Interests: computational solid mechanics; fatigue; composites; pre-stressed structures; constitutive modelling
Prof. Dr. Riccardo Rossi

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering, Polytechnic University of Catalonia (UPC), c. Gran Capitan s/n, Ed. B0, Campus Nort, UPC, 08034 Barcelona, Spain
Interests: computational solid mechanics; HPC; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue welcomes contributions focused on the nonlinear behavior of structural systems. Aspects involving novel constitutive models, multiscale simulation, topological optimization, failure of composite materials and fatigue failure, as well as fracture mechanics numerical techniques are of interest, both under original research and review articles, are welcome.

Contributions describing the use of novel approaches, such as machine learning in areas or applications demonstrating the applicability of the techniques to large-scale problems, are particularly welcome.

Numerical models that offer high accuracy concerning experimental behavior are kindly welcomed. 

Dr. Lucia Barbu
Prof. Dr. Riccardo Rossi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • constitutive modelling
  • machine learning
  • nonlinear behavior
  • HPC
  • computational solid mechanics
  • numerical simulation

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Published Papers (6 papers)

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Research

Jump to: Review, Other

27 pages, 3589 KiB  
Article
Damage and Failure Modeling of Composite Material Structures Using the Pam-Crash Code
by Eduardo Martin-Santos, Lucia G. Barbu and Pablo Cruz
Mathematics 2024, 12(23), 3847; https://doi.org/10.3390/math12233847 - 6 Dec 2024
Cited by 1 | Viewed by 1222
Abstract
Simulating composite material structures requires complex constitutive models, which normally require fine meshes to obtain an accurate prediction of their behavior. Pam-Crash software has been used for several years in the automotive industry and has been proved to be an efficient tool for [...] Read more.
Simulating composite material structures requires complex constitutive models, which normally require fine meshes to obtain an accurate prediction of their behavior. Pam-Crash software has been used for several years in the automotive industry and has been proved to be an efficient tool for simulating metallic structures, returning good correlations in a fast computational time. However, constitutive models for composite materials in Pam-Crash present some difficulties: some materials are not able to be suitably modeled and the predictive results depend on the mesh refinement. This work proposes a solution for predicting the progressive damage of composite materials in Pam-Crash, which scales the energy dissipated by the damage mechanisms and checks the viability of modeling the material behavior, taking into account the recommended size of finite elements in the automotive industry. The proposed solution is applied for the simulation of Open Hole specimens to evaluate the ultimate strength consistency. After this, it is applied for the simulation of Compact Tension specimens to check the consistency of crack propagation behavior. By considering the target size of the finite elements in the material card definition, the predictions demonstrate great improvement in the equivalence in results between different mesh refinements. Finally, the solution is applied to simulate impact tests on large structures. Good correlations with experimental data are obtained in fast computational times, making this methodology a candidate for application in composite-related automotive simulations. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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23 pages, 4074 KiB  
Article
Efficient Structural Damage Detection with Minimal Input Data: Leveraging Fewer Sensors and Addressing Model Uncertainties
by Fredi Alegría, Eladio Martínez, Claudia Cortés-García, Quirino Estrada, Andrés Blanco-Ortega and Mario Ponce-Silva
Mathematics 2024, 12(21), 3362; https://doi.org/10.3390/math12213362 - 26 Oct 2024
Viewed by 1516
Abstract
In the field of structural damage detection through vibration measurements, most existing methods demand extensive data collection, including vibration readings at multiple levels, strain data, temperature measurements, and numerous vibration modes. These requirements result in high costs and complex instrumentation processes. Additionally, many [...] Read more.
In the field of structural damage detection through vibration measurements, most existing methods demand extensive data collection, including vibration readings at multiple levels, strain data, temperature measurements, and numerous vibration modes. These requirements result in high costs and complex instrumentation processes. Additionally, many approaches fail to account for model uncertainties, leading to significant discrepancies between the actual structure and its numerical reference model, thus compromising the accuracy of damage identification. This study introduces an innovative computational method aimed at minimizing data requirements, reducing instrumentation costs, and functioning with fewer vibration modes. By utilizing information from a single vibration sensor and at least three vibration modes, the method avoids the need for higher-mode excitation, which typically demands specialized equipment. The approach also incorporates model uncertainties related to geometry and mass distribution, improving the accuracy of damage detection. The computational method was validated on a steel frame structure under various damage conditions, categorized as single or multiple damage. The results indicate up to 100% accuracy in locating damage and up to 80% accuracy in estimating its severity. These findings demonstrate the method’s potential for detecting structural damage with limited data and at a significantly lower cost compared to conventional techniques. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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19 pages, 419 KiB  
Article
Rayleigh Waves in a Thermoelastic Half-Space Coated by a Maxwell–Cattaneo Thermoelastic Layer
by Stan Chiriţă and Ciro D’Apice
Mathematics 2024, 12(18), 2885; https://doi.org/10.3390/math12182885 - 16 Sep 2024
Cited by 3 | Viewed by 1085
Abstract
This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the [...] Read more.
This paper investigates the propagation of in-plane surface waves in a coated thermoelastic half-space. First, it investigates a special case where the surface layer is described by the Maxwell–Cattaneo thermoelastic approach, while the half-space is filled by a thermoelastic material described by the classical Fourier law for the heat flux. The contact between the layer and the half-space is assumed to be welded, i.e., the displacements and the temperature, as well as the stresses and the heat flux are continuous through the interface of the layer and the half-space. The boundary and continuity conditions of the problem are formulated and then the exact dispersion relation of the surface waves is established. An illustrative numerical simulation is presented for the case of an aluminum thermoelastic layer coating a thermoelastic copper half-space, highlighting important aspects regarding the propagation of Rayleigh waves in such structures. The exact effective boundary conditions at the interface are also established replacing the entire effect of the layer on the half-space. The general case of the problem is also investigated when both the surface layer and the half-space are described by the Maxwell–Cattaneo thermoelasticity theory. This study helps to further understand the propagation characteristics of elastic waves in layered structures with thermal effects described by the Maxwell–Cattaneo approach. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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27 pages, 552 KiB  
Article
Thermostatistics, Information, Subjectivity: Why Is This Association So Disturbing?
by Didier Lairez
Mathematics 2024, 12(10), 1498; https://doi.org/10.3390/math12101498 - 11 May 2024
Cited by 1 | Viewed by 1014
Abstract
Although information theory resolves the inconsistencies (known in the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This article supports the idea that this is mainly due to epistemological rather [...] Read more.
Although information theory resolves the inconsistencies (known in the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This article supports the idea that this is mainly due to epistemological rather than scientific reasons: the subjectivity introduced into physics is perceived as a problem. Here is an attempt to expose and clarify where exactly this subjectivity lies: in the representation of reality and in probabilistic inference, two aspects that have been integrated into the practice of science for a long time and which should no longer frighten anyone but have become explicit with information theory. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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Review

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42 pages, 3989 KiB  
Review
Numerical Analysis of Damage in Composites: From Intra-Layer to Delamination and Data-Assisted Methods
by Alireza Taherzadeh-Fard, Alejandro Cornejo, Sergio Jiménez and Lucia G. Barbu
Mathematics 2025, 13(10), 1578; https://doi.org/10.3390/math13101578 - 10 May 2025
Viewed by 725
Abstract
The simulation of damage in composite materials is an important research area that impacts different engineering applications from aerospace structures to renewable energy systems. This review provides a comprehensive analysis of current damage modeling approaches, including intra-layer and inter-layer failures. Various numerical strategies, [...] Read more.
The simulation of damage in composite materials is an important research area that impacts different engineering applications from aerospace structures to renewable energy systems. This review provides a comprehensive analysis of current damage modeling approaches, including intra-layer and inter-layer failures. Various numerical strategies, such as continuum damage mechanics (CDM), cohesive zone models (CZM), extended finite element methods (XFEM), phase-field models (PFM), and peridynamics (PD), are examined to assess their efficiency in predicting crack initiation, propagation, and interaction. Additionally, the role of data-assisted (driven) techniques, such as machine learning, in enhancing predictive capabilities is explored. This review highlights the strengths and limitations of each approach, underscoring the need for further advancements in computational efficiency, multiscale modeling, and integration with experimental data. The findings serve as a foundation for future research into optimizing damage prediction techniques to improve the reliability and durability of composite structures. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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Other

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40 pages, 2903 KiB  
Systematic Review
Physics-Informed Neural Networks for the Structural Analysis and Monitoring of Railway Bridges: A Systematic Review
by Yuniel Martinez, Luis Rojas, Alvaro Peña, Matías Valenzuela and Jose Garcia
Mathematics 2025, 13(10), 1571; https://doi.org/10.3390/math13101571 - 10 May 2025
Viewed by 829
Abstract
Physics-informed neural networks (PINNs) offer a mesh-free approach to solving partial differential equations (PDEs) with embedded physical constraints. Although PINNs have gained traction in various engineering fields, their adoption for railway bridge analysis remains under-explored. To address this gap, a systematic review was [...] Read more.
Physics-informed neural networks (PINNs) offer a mesh-free approach to solving partial differential equations (PDEs) with embedded physical constraints. Although PINNs have gained traction in various engineering fields, their adoption for railway bridge analysis remains under-explored. To address this gap, a systematic review was conducted across Scopus and Web of Science (2020–2025), filtering records by relevance, journal impact, and language. From an initial pool, 120 articles were selected and categorised into nine thematic clusters that encompass computational frameworks, hybrid integration with conventional solvers, and domain decomposition strategies. Through natural language processing (NLP) and trend mapping, this review evidences a growing but fragmented research landscape. PINNs demonstrate promising capabilities in load distribution modelling, structural health monitoring, and failure prediction, particularly under dynamic train loads on multi-span bridges. However, methodological gaps persist in large-scale simulations, plasticity modelling, and experimental validation. Future work should focus on scalable PINN architectures, refined modelling of inelastic behaviours, and real-time data assimilation, ensuring robustness and generalisability through interdisciplinary collaboration. Full article
(This article belongs to the Special Issue Advanced Computational Mechanics)
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