Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors

Author:

Pérez-Escolar A.,Martínez-Frutos J.,Ortigosa R.,Ellmer N.,Gil A. J.

Abstract

AbstractThis paper introduces a metamodelling technique that employs gradient-enhanced Gaussian process regression (GPR) to emulate diverse internal energy densities based on the deformation gradient tensor $$\varvec{F}$$ F and electric displacement field $$\varvec{D}_0$$ D 0 . The approach integrates principal invariants as inputs for the surrogate internal energy density, enforcing physical constraints like material frame indifference and symmetry. This technique enables accurate interpolation of energy and its derivatives, including the first Piola-Kirchhoff stress tensor and material electric field. The method ensures stress and electric field-free conditions at the origin, which is challenging with regression-based methods like neural networks. The paper highlights that using invariants of the dual potential of internal energy density, i.e., the free energy density dependent on the material electric field $$\varvec{E}_0$$ E 0 , is inappropriate. The saddle point nature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of $$\varvec{F}$$ F and $$\varvec{E}_0$$ E 0 (free energy-based GPR), compared to those involving $$\varvec{F}$$ F and $$\varvec{D}_0$$ D 0 (internal energy-based GPR). Numerical examples within a 3D Finite Element framework assess surrogate model accuracy across challenging scenarios, comparing displacement and stress fields with ground-truth analytical models. Cases include extreme twisting and electrically induced wrinkles, demonstrating practical applicability and robustness of the proposed approach.

Funder

Fundación Séneca. Agencia de Ciencia y Tecnologia de la Region de Murcia

Agencia Estatal de Investigación

Publisher

Springer Science and Business Media LLC

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Versatile data-adaptive hyperelastic energy functions for soft materials;Computer Methods in Applied Mechanics and Engineering;2024-10

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