Multi-scale Modeling and Optimisation of Materials

Topic Information

Dear Colleagues,

More than a century ago, manufactured materials’ fatigue started to be investigated, while material performance evaluation was rethought as a result of the introduction of new technical materials, testing techniques, and computer methodologies. By combining cutting-edge sensor technology with real-time photos of material behavior, it became possible to gain a better understanding of the mechanisms causing damage on a sub-microscale. Meanwhile, incorporating computational methods into multi-scale modeling techniques, continuously enhanced by an ever-increasing computer power, resulted in further insights into the optimization and design of resilient materials. The use of data-driven algorithms allowed for the successful completion of complex structure–property interactions, which would have been computationally costly had physics-based models been used alone. Although substantial research has been conducted on the topic, the materials science community is in even greater need of interdisciplinary methods for multi-scale modeling and optimization. Therefore, we welcome notable and pioneering researchers to participate in our endeavor to advance the current state of the art in this field, within the scope outlined below.

Dr. Mustafa Awd
Prof. Dr. Frank Walther
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Mechanics applmech	1.8	3.5	2020	25.6 Days	CHF 1400
Applied Sciences applsci	2.9	6.1	2011	15 Days	CHF 2400
Materials materials	3.7	7.0	2008	14.4 Days	CHF 2600
Metals metals	3.1	5.7	2011	15.3 Days	CHF 2600
Polymers polymers	5.8	11.0	2009	13.4 Days	CHF 2700
Solids solids	2.1	3.3	2020	17.8 Days	CHF 1200

Preprints.org is a multidisciplinary platform offering a preprint service designed to facilitate the early sharing of your research. It supports and empowers your research journey from the very beginning.

MDPI Topics is collaborating with Preprints.org and has established a direct connection between MDPI journals and the platform. Authors are encouraged to take advantage of this opportunity by posting their preprints at Preprints.org prior to publication:

1. Share your research immediately: disseminate your ideas prior to publication and establish priority for your work.
2. Safeguard your intellectual contribution: Protect your ideas with a time-stamped preprint that serves as proof of your research timeline.
3. Boost visibility and impact: Increase the reach and influence of your research by making it accessible to a global audience.
4. Gain early feedback: Receive valuable input and insights from peers before submitting to a journal.
5. Ensure broad indexing: Web of Science (Preprint Citation Index), Google Scholar, Crossref, SHARE, PrePubMed, Scilit and Europe PMC.

Published Papers (8 papers)

Order results

Content type Publication Date

Result details

Normal Extended Compact

Journals

All Applied Mechanics Applied Sciences Materials Polymers Solids Metals

Show export options expand_more Show export options expand_less

Select all

Export citation of selected articles as:

Plain Text BibTeX BibTeX (without abstracts) Endnote Endnote (without abstracts) Tab-delimited RIS

Error

Oops... you haven't selected anything for export.

Ok

clear

26 pages, 38337 KB  

Open AccessArticle

Physics-Informed Cascaded Learning for Predicting and Optimizing Geometry and Quality in Laser Cladding Repair of Carburized Gear Steel

by Yingjie Xu, Peng Zheng, Zhongming Liu, Linfan Du, Shidang Yan, Miaomiao Xie, Zhanqi Gao and Yangyang Luo

Materials 2026, 19(17), 3793; https://doi.org/10.3390/ma19173793 - 6 Sep 2026

Viewed by 192

Abstract

Laser cladding is promising for use in repairing carburized gear steels, but parameter selection is challenging when clad geometry, substrate thermal disturbance, and morphological quality must be considered. Fifteen tracks of NHT.22.A01 iron-based powder were deposited on carburized-quenched 18CrNiMo7-6 steel with varying laser [...] Read more.

Laser cladding is promising for use in repairing carburized gear steels, but parameter selection is challenging when clad geometry, substrate thermal disturbance, and morphological quality must be considered. Fifteen tracks of NHT.22.A01 iron-based powder were deposited on carburized-quenched 18CrNiMo7-6 steel with varying laser powers, scanning speeds, and powder feed rates. A physics-informed cascaded-learning framework predicted track width, height, Ac₁-boundary depth, and quality. Leave-one-out out-of-fold width predictions were transferred to height and depth models to prevent target leakage. An auxiliary continuous quality index enabled the bi-objective optimization of quality and high-hardness layer depth, while multi-indicator process maps with local sensitivity analysis supported rapid parameter adjustment. Leave-one-out (R²) values for three geometric responses ranged from 0.934 to 0.968, and the maximum relative error at an unseen boundary condition was 4.3%. The fitted HAZ-depth/track width scaling coefficient (0.211) lay within the Rosenthal theoretical range (0.15–0.25), confirming the physical consistency of the cascade relationship. The optimization revealed a trade-off between quality and high-hardness layer depth; maximizing predicted high-hardness layer depth under $(Q_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}}\ge 4.5)$ selected a condition already represented in the training set. Repeatability was supported by an independent batch replicate. By integrating leakage-controlled cascading, physically interpretable validation, constrained optimization, and sensitivity-resolved process mapping, the framework provides a transparent and practically applicable approach to small-sample laser cladding process design. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Figure 1

18 pages, 1399 KB  

Open AccessArticle

A Severity Threshold for Frictional Stability in ZrB₂SiC/ZrO₂ Coatings: Implications for Tool Life in Titanium Machining

by Willian Aperador, Giovany Orozco-Hernández and Julio Cesar Caicedo

Solids 2026, 7(4), 39; https://doi.org/10.3390/solids7040039 - 17 Aug 2026

Viewed by 301

Abstract

Ultra-high-temperature ceramic (UHTC) coatings offer a promising route to extending cutting tool service life under severe conditions. This work evaluates the tribological behaviour and wear regime transitions of ZrB₂–SiC/ZrO₂ coatings, deposited by physical vapour deposition (PVD) onto ASSAB-17 high-speed steel [...] Read more.

Ultra-high-temperature ceramic (UHTC) coatings offer a promising route to extending cutting tool service life under severe conditions. This work evaluates the tribological behaviour and wear regime transitions of ZrB₂–SiC/ZrO₂ coatings, deposited by physical vapour deposition (PVD) onto ASSAB-17 high-speed steel tool bits, during dry turning of Ti-6Al-4V. Structural, microstructural, mechanical, and tribological characterisation was performed by X-ray diffraction (XRD), scanning electron microscopy (SEM), nanoindentation, and pin-on-disc testing under three pressure–velocity (PV) severity levels, with worn surfaces analysed by SEM and profilometry. The coating exhibited a nanostructured ZrB₂/β-SiC/t-ZrO₂ architecture with a hardness (H) of 24 ± 3 GPa, a hardness-to-reduced-elastic-modulus ratio (H/Er) of 0.100, and an elastic resistance to plastic deformation (H³/Er²) of 0.240 GPa. Three tribological regimes were identified: running-in, steady-state sliding, and progressive degradation, with the highest severity (PV = 6.0 N·m/s) triggering degradation beyond approximately 620 m, a more than one-order-of-magnitude rise in wear rate, and the only case exceeding the tool-life criterion of maximum flank wear (VBmax = 0.30 mm) according to ISO 3685. The main advantage of the proposed approach is that it condenses tool-life-relevant behaviour into a single, easily measurable severity parameter, the PV product, directly applicable to coating design and the selection of safe machining-condition windows. The overall behaviour is consistent with a mechanism governed by the stability and regeneration capacity of a protective tribofilm. As the composition of this layer was not directly characterised, this mechanism is proposed as a phenomenological interpretation, from which a PV threshold is derived as a design criterion for UHTC coatings. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Figure 1

22 pages, 5267 KB  

Open AccessArticle

On Ballooning and Burst Behavior of Nuclear Fuel Clad Considering Heating Rate Effect: Development of a Damage Model, a Burst Correlation and Experimental Validation

by Ather Syed and Mahendra Kumar Samal

Solids 2025, 6(4), 56; https://doi.org/10.3390/solids6040056 - 28 Sep 2025

Cited by 1 | Viewed by 2340

Abstract

Nuclear fuel cladding serves as the primary barrier to the release of radioactive fission products and is subjected to high-temperature and high-pressure environments during both normal reactor operation and accident scenarios such as loss of coolant accidents (LOCAs). Predicting the burst behavior of [...] Read more.

Nuclear fuel cladding serves as the primary barrier to the release of radioactive fission products and is subjected to high-temperature and high-pressure environments during both normal reactor operation and accident scenarios such as loss of coolant accidents (LOCAs). Predicting the burst behavior of cladding is essential for ensuring structural integrity, especially under varying heating rates—an aspect inadequately addressed in existing empirical models. In this study, a finite element-based damage model is developed to simulate the ballooning and burst behavior of Zircaloy-4 cladding. The model incorporates creep deformation, stress triaxiality, and time-dependent damage accumulation. Material behavior is characterized using experimentally determined creep constants and the model is calibrated against burst test data from the literature. A new heating-rate-dependent burst correlation is proposed based on model outputs. The results indicate that increasing the heating rate raises the burst temperature due to reduced exposure time in the temperature regime where creep damage accumulates significantly. The model accurately reproduces burst behavior across a wide range of internal pressures (1–10 MPa) and heating rates (5–100 °C/s). The newly developed correlation improves predictive capability in accident analysis tools and can be directly implemented into safety analysis codes for Indian pressurized heavy water reactors (PHWRs), contributing to enhanced reactor safety evaluations. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Graphical abstract

attachment

Supplementary material:
Supplementary File 1 (ZIP, 360 KB)

17 pages, 2901 KB  

Open AccessArticle

Preliminary Modeling of Single Pulp Fiber Using an Improved Mass–Spring Method

by Yin Liu, Wenhao Shen, Douglas W. Coffin, Tao Song, Jean-Francis Bloch and Jean-Pierre Corriou

Solids 2025, 6(3), 50; https://doi.org/10.3390/solids6030050 - 3 Sep 2025

Viewed by 1922

Abstract

An improved Mass–Spring Model (iMSM) is developed by adding central springs to the conventional Mass–Spring Models (MSMs) of tubular structures. This improvement is necessary to model fibers that have enough stiffness so that they do not collapse under transverse loading. Such is the [...] Read more.

An improved Mass–Spring Model (iMSM) is developed by adding central springs to the conventional Mass–Spring Models (MSMs) of tubular structures. This improvement is necessary to model fibers that have enough stiffness so that they do not collapse under transverse loading. Such is the case with many pulp fibers used in papermaking. Four different types of pulp fibers (Aspen CTMP, Aspen BCTMP, Birch BCTMP, and Spruce BKP) were simulated in the study. A geometric model and iMSM of a single fiber were developed, in which the topological structure of iMSM is explained in detail. The mass of mass points and the elastic coefficient of different springs in iMSM were calculated using axial tensile and torsional responses. A dynamic simulation of transverse bending of the fiber over a rigid cylinder and subjected to a transverse pressure was used to determine the effective elastic modulus for four different single fibers and compared to experimental values with an average relative error of 8.49%. The dynamic simulations were completed in 1.04–2.64 min for the four different paper fibers representing sufficient speeds to meet the needs of most real application scenarios. The acceptable accuracy and the fast simulation speed with the developed iMSM fiber model demonstrate the feasibility of the methodology in analyzing paper structures as well as similar fiber-based materials. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Graphical abstract

31 pages, 8853 KB  

Open AccessArticle

Atomistic-Based Fatigue Property Normalization Through Maximum A Posteriori Optimization in Additive Manufacturing

by Mustafa Awd, Lobna Saeed and Frank Walther

Materials 2025, 18(14), 3332; https://doi.org/10.3390/ma18143332 - 15 Jul 2025

Cited by 4 | Viewed by 1758

Abstract

This work presents a multiscale, microstructure-aware framework for predicting fatigue strength distributions in additively manufactured (AM) alloys—specifically, laser powder bed fusion (L-PBF) AlSi10Mg and Ti-6Al-4V—by integrating density functional theory (DFT), instrumented indentation, and Bayesian inference. The methodology leverages principles common to all 3D [...] Read more.

This work presents a multiscale, microstructure-aware framework for predicting fatigue strength distributions in additively manufactured (AM) alloys—specifically, laser powder bed fusion (L-PBF) AlSi10Mg and Ti-6Al-4V—by integrating density functional theory (DFT), instrumented indentation, and Bayesian inference. The methodology leverages principles common to all 3D printing (additive manufacturing) processes: layer-wise material deposition, process-induced defect formation (such as porosity and residual stress), and microstructural tailoring through parameter control, which collectively differentiate AM from conventional manufacturing. By linking DFT-derived cohesive energies with indentation-based modulus measurements and a MAP-based statistical model, we quantify the effect of additive-manufactured microstructural heterogeneity on fatigue performance. Quantitative validation demonstrates that the predicted fatigue strength distributions agree with experimental high-cycle and very-high-cycle fatigue (HCF/VHCF) data, with posterior modes and 95 % credible intervals of ${\widehat{\sigma }}_f^{\mathrm{AlSi}10\mathrm{Mg}}={86}_{-7}^{+8}\mathrm{MPa}$ and ${\widehat{\sigma }}_f^{\mathrm{Ti}–6\mathrm{Al}–4\mathrm{V}}={115}_{-9}^{+10}\mathrm{MPa}$, respectively. The resulting Woehler (S–N) curves and Paris crack-growth parameters envelop more than 92 % of the measured coupon data, confirming both accuracy and robustness. Furthermore, global sensitivity analysis reveals that volumetric porosity and residual stress account for over 70 % of the fatigue strength variance, highlighting the central role of process–structure relationships unique to AM. The presented framework thus provides a predictive, physically interpretable, and data-efficient pathway for microstructure-informed fatigue design in additively manufactured metals, and is readily extensible to other AM alloys and process variants. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Figure 1

attachment

Supplementary material:
Supplementary File 1 (ZIP, 2006 KB)

27 pages, 4124 KB  

Open AccessArticle

Evaluating Binary Molybdenum Alloys as Strong and Ductile High-Temperature Materials

by Cheng Fu, Jiayi Yan, Jiang Yu, Yuhong Ren and Sha Li

Materials 2025, 18(14), 3329; https://doi.org/10.3390/ma18143329 - 15 Jul 2025

Cited by 2 | Viewed by 1989

Abstract

Molybdenum alloys as refractory alloys can provide strength levels at operating temperatures higher than that of Ni-base superalloys, yet their ductility is usually inferior to Ni-base alloys. Currently, commercialized Mo alloys are much fewer than Ni alloys. The motivation of this work is [...] Read more.

Molybdenum alloys as refractory alloys can provide strength levels at operating temperatures higher than that of Ni-base superalloys, yet their ductility is usually inferior to Ni-base alloys. Currently, commercialized Mo alloys are much fewer than Ni alloys. The motivation of this work is to explore opportunities of discovering useful alloys from the usually less investigated binary Mo-X systems (X = alloying element). With computational thermodynamics (CALPHAD), first-principles calculation, and mechanistic modeling combined, in this work a large number of Mo-X binary systems are investigated in terms of thermodynamic features and mechanical properties (yield strength, ductility, ductile-brittle transition temperature, creep resistance, and stress-strain relationship). The applicability of the alloy systems as solution-strengthened or precipitation-strengthened alloys is investigated. Starting from 92 Mo-X systems, a down-selection process is implemented, the results of which include three candidate systems for precipitation strengthening (Mo-B, Mo-C, Mo-Si) and one system (Mo-Re) for solid-solution strengthened alloy. In a composition optimization of Mo alloys to reach the properties of Ni-base superalloys, improving ductility is of top priority, for which Re plays a unique role. The presented workflow is also applicable to other bcc refractory alloy systems. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Graphical abstract

37 pages, 11657 KB  

Open AccessArticle

Experimental Evaluation of Temperature and Strain-Rate-Dependent Mechanical Properties of Austenitic Stainless Steel SS316LN and a New Methodology to Evaluate Parameters of Johnson–Cook and Ramberg–Osgood Material Models

by Sanjay Kumar Pandey and Mahendra Kumar Samal

Solids 2025, 6(1), 7; https://doi.org/10.3390/solids6010007 - 11 Feb 2025

Cited by 5 | Viewed by 6805

Abstract

Austenitic stainless steel SS316LN is used as the material of construction of the vessel and core components of fast breeder reactors, which operate at an elevated temperature of 550 °C. For design and integrity analysis using the finite element method, material models, such [...] Read more.

Austenitic stainless steel SS316LN is used as the material of construction of the vessel and core components of fast breeder reactors, which operate at an elevated temperature of 550 °C. For design and integrity analysis using the finite element method, material models, such as Johnson–Cook and Ramberg–Osgood, are widely used. However, the temperature- and strain-rate-dependent plasticity and damage parameters of these models for this material are not available in the literature. Moreover, the method of evaluation of temperature and strain-rate-dependent plasticity parameters, in literature, has some major shortcomings, which have been addressed in this work. In addition, a new optimization-based procedure has been developed to evaluate all nine plasticity and damage parameters, which uses results of combined finite element analysis and experimental data. The procedure has been validated extensively by testing tensile specimens at different temperatures, by testing notched tensile specimens of different notch radii, and by carrying out high strain-rate tests using a split Hopkinson pressure bar test setup. The parameters of the Johnson–Cook material model, evaluated in this work, have been used in finite element analysis to simulate load-displacement behavior and fracture strains of various types of specimens, and the results have been compared with experimental data in order to check the accuracy of the parameters. The procedure developed in this work shall help the researchers to adopt such a technique for accurate estimation of both plasticity and damage parameters of different types of material models. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Figure 1

23 pages, 9957 KB  

Open AccessArticle

Multi-Objective Optimization of Three-Stage Turbomachine Rotor Based on Complex Transfer Matrix Method

by Hüseyin Tarık Niş and Ahmet Yıldız

Appl. Sci. 2024, 14(22), 10445; https://doi.org/10.3390/app142210445 - 13 Nov 2024

Cited by 5 | Viewed by 2219

Abstract

This study presents the complex transfer matrix method (CTMM) as an advanced mathematical model, providing significant advantages over the finite element method (FEM) by yielding rapid solutions for complex optimization problems. In order to design a more efficient structure of a three-stage turbomachine [...] Read more.

This study presents the complex transfer matrix method (CTMM) as an advanced mathematical model, providing significant advantages over the finite element method (FEM) by yielding rapid solutions for complex optimization problems. In order to design a more efficient structure of a three-stage turbomachine rotor, we integrated this method with various optimization algorithms, including genetic algorithm (GA), differential evolution (DE), simulated annealing (SA), gravitational search algorithm (GSA), black hole (BH), particle swarm optimization (PSO), Harris hawk optimization (HHO), artificial bee colony (ABC), and non-metaheuristic pattern search (PS). Thus, the best rotor geometry can be obtained fast with minimum bearing forces and disk deflections within design limits. In the results, the efficiency of the CTMM for achieving optimized designs is demonstrated. The CTMM outperformed the FEM in both speed and applicability for complex rotordynamic problems. The CTMM was found to deliver results of comparable quality much faster than the FEM, especially with higher element quality. The use of the CTMM in the iterative optimization process is shown to be highly advantageous. Furthermore, it is noted that among the different optimization algorithms, ABC provided the best results for this multi-objective optimization problem. Full article

(This article belongs to the Topic Multi-scale Modeling and Optimisation of Materials)

►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less

Select all

Export citation of selected articles as:

Plain Text BibTeX BibTeX (without abstracts) Endnote Endnote (without abstracts) Tab-delimited RIS

 

Error

Oops... you haven't selected anything for export.

Ok

clear

Displaying articles 1-8