Contents 153Appendix A. A brief recount on variational calculus 153 Appendix B. Positive/negative projection and its application to phase-field fracture models 155 B.1 General definition of the positive/negative projection 155 B.2 Miehe's strain energy decomposition 156 B.3 Wu and Cervera's strain energy decomposition 157 Appendix C. Thermodynamics 157 Appendix D. Comparison with other gradient-damage models 160 Appendix E. Arc-length (path following) methods 162 References 164

Jian-Ying Wu

Vinh Phu Nguyen

Chi Thanh Nguyen

Danas Sutula

Sina Sinaie

Stéphane 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

Phase-field modeling of fracture

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