Modeling and Numerical Simulations in Materials Mechanics

Dear Colleagues,

Background and Scope

Materials mechanics has emerged as a cornerstone of modern engineering and applied sciences, bridging the gap between fundamental material behavior and real-world applications. The rapid evolution of computational power, coupled with advancements in numerical algorithms and data-driven methodologies, has transformed our ability to predict, design, and optimize materials under complex mechanical, thermal, and environmental conditions. From aerospace alloys to bio-inspired composites, the demand for high-fidelity modeling tools is increasing as industries work to develop materials with tailored properties for extreme performance, sustainability, and multifunctionality.

Despite significant progress, critical challenges persist in the field. Traditional continuum-based models often struggle to capture phenomena at atomic or microstructural scales, while purely atomistic simulations have limitations in scalability and computational cost. Furthermore, the integration of multiphysics interactions, such as thermo-mechanical–electrochemical coupling, remains a formidable task, particularly for dynamic or non-equilibrium systems. The experimental validation of computational predictions is another bottleneck, requiring innovative approaches to reconcile simulations with empirical data across disparate length and time scales. Meanwhile, emerging technologies such as additive manufacturing and machine learning (ML) are reshaping the landscape, introducing both opportunities and complexities in model development.

This Special Issue will address these challenges by curating cutting-edge research at the intersection between computational mechanics, materials science, and applied mathematics. We will highlight novel methodologies that push the boundaries of traditional modeling paradigms while fostering interdisciplinary collaboration. This Special Issue’s scope encompasses theoretical advancements, numerical algorithm development, and practical applications, emphasizing solving industrially relevant problems. Key themes include but are not limited to multiscale and multiphysics frameworks that seamlessly bridge quantum, molecular, mesoscopic, and continuum scales; data-driven and AI-enhanced models leveraging machine learning to accelerate simulations, discover constitutive laws, or reduce dimensionality; uncertainty quantification to improve the reliability of predictions in the presence of material heterogeneity, manufacturing defects, or environmental variability; digital twin technologies enabling the real-time monitoring and adaptive control of material systems; and sustainability-driven modeling for designing recyclable materials, minimizing energy consumption in manufacturing, or predicting long-term degradation.

By showcasing both foundational breakthroughs and applied innovations, this Special Issue will serve as a critical resource for researchers and practitioners seeking to harness computational tools for next-generation material discovery and optimization.

Topics of Interest

This Special Issue invites contributions spanning theoretical, computational, and applied studies in materials mechanics. Submissions should emphasize rigorous methodology development, validation against experiments, and/or translation to engineering applications. The following topics are of particular interest:

• Multiscale and hierarchical modeling, atomistic-to-continuum coupling: hybrid methods (e.g., quasi-continuum, concurrent multiscale), coarse-grained molecular dynamics, and adaptive resolution schemes;
• Microstructure-sensitive models, phase-field simulations, dislocation dynamics, and damage evolution;
• Machine learning-augmented multiscale frameworks, neural network potentials for interatomic interactions, graph-based representations of microstructures, and surrogate models for accelerated property prediction;
• Advanced constitutive modeling, nonlinear material behavior, strain gradient plasticity, viscoplasticity, hyperelasticity, and rate-dependent failure mechanisms;
• Phase-field fracture models, cohesive zone methods, peridynamics, and probabilistic lifetime prediction;
• The service performance of engineering materials, mechanical property simulation, plate and shell models, and material and structural health monitoring for large-scale civil engineering structures;
• Data-driven and AI-enabled simulations and physics-informed machine learning, integrating conservation laws, symmetry principles, and thermodynamic constraints into neural networks;
• Surrogate modeling, generative adversarial networks for high-dimensional parameter spaces, inverse design, and the optimization of material microstructures;
• Finite element/difference/volume innovations: adaptive mesh refinement, isogeometric analysis (IGA), and immersed boundary methods, mesh-free techniques, material point methods, and discrete element methods;
• Multiphysics and environmental interactions, thermo-chemo–mechanical coupling, irradiation effects in extreme environments, and fluid–structure interactions;
• Electroactive materials; piezoelectric, ferroelectric, and dielectric responses under mechanical loading; and additive manufacturing;
• Biomechanics modeling of tissues, bioinspired materials, and medical device performance. 

Prof. Dr. Ping Xiang
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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. Materials 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.