This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for capturing material instabilities using data-driven mechanics without prior information regarding the failure mode. We show numerically that, in problems involving strain localization, the standard data-driven framework for Cauchy/Boltzmann continua fails to capture the length scale of the material, as expected. We address this shortcoming by formulating a generalized data-driven framework for micromorphic continua that effectively captures both stiffness and length-scale information, as encoded in the material data, in a model-free manner. These properties are exhibited systematically in a one-dimensional softening bar problem and further verified through selected plane-strain problems.

翻译：本文探讨了广义连续介质力学在因应变局部化而发生破坏的固体中的作用，以及其无模型数据驱动计算方法的可行性。具体而言，我们提出了一种方法，可在无需先验失效模式信息的情况下，利用数据驱动力学捕捉材料的不稳定性。我们通过数值计算表明，在涉及应变局部化的问题中，标准的Cauchy/Boltzmann连续体数据驱动框架无法捕捉材料的长度尺度，这与预期一致。我们通过为微形态连续体构建一个广义的数据驱动框架来解决这一不足，该框架以无模型的方式有效地捕捉了材料数据中编码的刚度与长度尺度信息。这些特性在一维软化杆问题中得到了系统展示，并通过选定的平面应变问题进一步验证。