Mathematical Models of Material Science: Symmetry and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 1269

Special Issue Editors

School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
Interests: multiscale analysis methods; computational material science; machine learning methods in materials science

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Guest Editor
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
Interests: finite element method; numerical analysis; multiscale analysis methods; computational material science
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
Interests: machine learning; deep neural network; optimization theory and methods

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Guest Editor
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Interests: multiscale computation; deep learning method and application

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Guest Editor
School of Highway, Chang’an University, Xi’an 710064, China
Interests: structural mechanics; multifunctional composites/structures; micro-nano materials/structures

Special Issue Information

Dear Colleagues,

Materials are the physical basis for human survival and development and constitute one of the three pillars of modern civilization, together with energy and information. Numerous materials have spatially symmetric configuration in the microscale, such as crystalline material, carbon nanotubes, composite material, etc. Research on material science is one of the core scientific issues in modern science and technology. In recent years, scientific computing and data-driven modeling based on mathematical models and theories have shown prominent advantages in material science research. In order to provide a solid theoretical basis and advanced algorithm for predicting and simulating the physical behaviors of materials, especially with spatially geometric symmetry, it is of great practical value and theoretical significance to study mathematical models and methods in material science. The aim of the present Special Issue is to provide an exchange platform for experts and scholars engaged in interdisciplinary research in mathematics and material science.

Dr. Hao Dong
Prof. Dr. Yufeng Nie
Dr. Xixi Jia
Dr. Yating Wang
Dr. Xiaojian Xu
Guest Editors

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Keywords

  • numerical simulation of partial differential equations in materials science
  • multiscale methods and their mathematical theories in material science
  • multiscale modeling and computation of composite materials and structures
  • machine learning methods in materials science
  • uncertainty quantification for random models in material science
  • multiphysical modeling and computation in material science
  • nonlocal models and their application in material science
  • nonlinear models and their application in material science

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Published Papers (1 paper)

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Research

25 pages, 4330 KiB  
Article
Multiscale Asymptotic Computations for the Elastic Quadratic Eigenvalue Problem in Periodically Composite Structure
by Qiang Ma, Hongyu Wang, Lin Bi, Junzhi Cui, Tingyan Chen and Yuting Wu
Symmetry 2023, 15(7), 1299; https://doi.org/10.3390/sym15071299 - 22 Jun 2023
Viewed by 1675
Abstract
A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of [...] Read more.
A multiscale analysis and computational method based on the Second-Order Two-Scale (SOTS) approach are proposed for the elastic quadratic eigenvalue problems in the periodic composite domain. Two typical quadratic eigenvalue problems with different damping effects are considered, and by the asymptotic expansions of both the eigenfunctions and eigenvalues, the first- and second-order cell functions, the microscale features of this heterogeneous materials are defined successively. Then, the homogenized quadratic eigenvalue problems are derived and the second-order expansions of the eigenfunctions are formed. The eigenvalues are also broadened to the second-order terms by introducing proper auxiliary elastic functions defined in the composite structure, and the nonlinear expressions of the correctors of the eigenvalues are derived. The finite element procedures are established, linearized methods are discussed for solving the quadratic eigenvalue problems and the second-order asymptotic computations are performed. Effectiveness of the asymptotic model is demonstrated by both the qualitative and quantitative comparisons between the computed SOTS approximations and the reference solutions, and the converging behavior of the eigenfunctions are numerically verified. It is also indicated that the second-order correctors are of importance to reconstruct the detailed information of the original eigenfunctions within the micro cells. Full article
(This article belongs to the Special Issue Mathematical Models of Material Science: Symmetry and Applications)
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