The Language of Hyperelastic Materials
arxiv(2024)
摘要
The automated discovery of constitutive laws forms an emerging area that
focuses on automatically obtaining symbolic expressions describing the
constitutive behavior of solid materials from experimental data. Existing
symbolic/sparse regression methods rely on availability of libraries of
material models, which are typically hand-designed by a human expert relying on
known models as reference, or deploy generative algorithms with exponential
complexity which are only practicable for very simple expressions. In this
paper, we propose a novel approach to constitutive law discovery relying on
formal grammars as an automated and systematic tool to generate constitutive
law expressions complying with physics constraints. We deploy the approach for
two tasks: i) Automatically generating a library of valid constitutive laws for
hyperelastic isotropic materials; ii) Performing data-driven discovery of
hyperelastic material models from displacement data affected by different noise
levels. For the task of automatic library generation, we demonstrate the
flexibility and efficiency of the proposed methodology in alleviating
hand-crafted features and human intervention. For the data-driven discovery
task, we demonstrate the accuracy, robustness and significant generalizability
of the proposed methodology.
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