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Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold
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DOI：10.1016/j.taml.2021.100289.png)
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摘要
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Data-driven computing in elasticity attempts to directly use experimental data on material, without con-structing an empirical model of the constitutive relation, to predict an equilibrium state of a structure subjected to a specified external load. Provided that a data set comprising stress-strain pairs of material is available, a data-driven method using the kernel method and the regularized least-squares was devel-oped to extract a manifold on which the points in the data set approximately lie (Kanno 2021, Jpn. J. Ind. Appl. Math.). From the perspective of physical experiments, stress field cannot be directly measured, while displacement and force fields are measurable. In this study, we extend the previous kernel method to the situation that pairs of displacement and force, instead of pairs of stress and strain, are available as an input data set. A new regularized least-squares problem is formulated in this problem setting, and an alternating minimization algorithm is proposed to solve the problem. (C) 2021 The Author. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.
Keyword:
Alternating minimization
Regularized least-squares
Kernel method
Manifold learning
Data-driven computing
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