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Data-driven micromorphic mechanics for materials with strain localization (2402.15966v3)

Published 25 Feb 2024 in math.NA and cs.NA

Abstract: 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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