面向应变局部化材料的数据驱动微形态力学
Data-driven micromorphic mechanics for materials with strain localization
AI总结：
本文提出一种适用于微形态连续体的广义无模型数据驱动计算框架，解决了标准数据驱动方法无法捕捉应变局部化材料长度尺度的问题，并通过一维软化杆和平面应变问题验证了其有效性。
摘要：
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经历应变局部化破坏的固体中的作用与可行性。具体而言，我们提出了一种在缺乏失效模式先验信息的情况下，利用数据驱动力学捕捉材料不稳定性的方法。我们通过数值计算表明，在涉及应变局部化的问题中，针对Cauchy/Boltzmann连续体的标准数据驱动框架如预期般无法捕捉材料的长度尺度。我们通过为微形态连续体制定广义数据驱动框架来解决这一缺陷，该框架以无模型方式有效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系统展示，并通过选定的平面应变问题得到进一步验证。
英文摘要：
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.
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