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及其无模型数据驱动计算方法在发生应变局部化破坏的固体中的作用。具体而言，我们建立了一种方法，利用数据驱动力学捕捉材料失稳现象，无需预先了解破坏模式。数值结果表明，在涉及应变局部化的问题中，Cauchy/Boltzmann连续介质的标准数据驱动框架无法捕捉材料的长度尺度，这与预期一致。为解决这一不足，我们提出了微形态连续介质的广义数据驱动框架，该框架以无模型方式有效捕捉了材料数据中编码的刚度和长度尺度信息。这些特性在一维软化杆问题中得到系统展示，并通过选定的平面应变问题进一步验证。