Abstract

Strain localization is one of the most challenging phenomena in solid mechanics. It occurs when strains concentrate in very narrow bands within a solid, typically referred to as localization bands. This behaviour is related to different types of failure mechanisms: fracture, shear bands and slip lines. Being a dissipative process, the modelling of strain localization could seem to preclude the use of variational methods. However, a sound framework to deal with this issue has been developed in the last few decades. In this contribution, we review the modelling of strain localization by means of variational methods systematically, presenting the main underlying theoretical concepts. The issue of irreversibility is approached by means of the theory of generalized standard materials, which constitutes the basis for the variational approach. Then, typical problems occurring in the modelling of strain localization are analyzed: the tendency to localize in a band of zero thickness with no dissipation, the determination of the geometry of the localization band, and the orientation bias of such band with respect to mesh alignment in finite element discretizations. We discuss solutions for these problems, focusing on the approach that tackles the description of the localization band using phase fields.

中文翻译：

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固体中应变局部化的变化模型：一种计算力学的观点

摘要

应变局部化是固体力学中最具挑战性的现象之一。当菌株集中在固体中非常窄的条带（通常称为定位条带）中时，就会发生这种情况。此行为与不同类型的破坏机制有关：断裂，剪切带和滑移线。作为耗散过程，应变局部化的建模似乎排除了变分方法的使用。但是，在过去的几十年中，已经开发出一个解决此问题的合理框架。在这一贡献中，我们通过变分方法系统地回顾了应变局部化的模型，提出了主要的基本理论概念。不可逆性问题是通过通用标准材料理论解决的，它构成了变分方法的基础。然后，分析了在应变局部化建模中出现的典型问题：在零厚度且无耗散的区域中进行局部化的趋势，确定局部化带的几何形状以及该区域相对于有限元网格对齐的方向偏差元素离散化。我们讨论这些问题的解决方案，重点是解决使用相位场描述定位带的方法。