Contents 1. Introduction 2. Overview of computational models at different length scales 2.1 Discrete models 2.2 Continuum-based methods for fracture 3. Hierarchical and semiconcurrent multiscale methods 3.1 Virtual atom cluster model 3.2 Analytical homogenization approaches 3.3 Computational homogenization approaches 3.4 Model generation and RVE design 3.5 Structural reconstruction based on Wang tiles 3.6 Multiscale methods for coupled problems 4. Concurrent multiscale methods for fracture 4.1 Extended bridging scale method 4.2 Extended Bridging domain method 4.3 Fracture criteria 4.4 Coarse graining 4.5 Implementation aspects 5. Conclusions Appendix A.1 Derivation of the internal forces: Fine scale A.2 Derivation of the internal forces: Coarse scale References

Pattabhi Ramaiah Budarapu

Xiaoying Zhuang

Timon Rabczuk

Stephane P.A. Bordas

Advances in Applied Mechanics

应用力学进展汇集了应用力学所有领域的最新重大进展。自 1948 年出版以来，它旨在提供有关机械科学主题的最高质量、权威的评论文章。它是在力学各个分支领域工作的科学家和工程师的主要兴趣所在，对于那些将力学研究结果应用于航空航天、化学、土木、环境、机械和核工程等领域的人来说也很有价值。

Advances in Applied Mechanics brings together the latest significant developments in all areas of applied mechanics. Since its inception in 1948, it has aimed to provide high-quality, authoritative review articles on topics in mechanical science. It serves as a primary interest for scientists and engineers working in various branches of mechanics and is valuable for those applying the results of mechanics research in fields such as aerospace, chemical, civil, environmental, mechanical, and nuclear engineering.

《Advances in Applied Mechanics》汇集了应用力学各领域的最新重大进展。自1948年创刊以来，该期刊旨在提供机械科学主题的高质量、权威的评论文章。它是力学各个分支领域科学家和工程师的主要关注点，对于那些将力学研究成果应用于航空航天、化学、土木、环境、机械和核工程等领域的研究者来说，具有重要的参考价值。

Category	Quartile
工程技术	1
工程技术, 工程机械	1
工程技术, 力学	1

Multiscale modeling of material failure: Theory and computational methods

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