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Learning nonlinear constitutive models in finite strain electromechanics with Gaussian process predictors
Computational Mechanics
Swansea University Authors:
Rogelio Ortigosa Martinez, Antonio Gil
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© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License.
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DOI (Published version): 10.1007/s00466-024-02446-8
Abstract
This 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 F and electric displacement field D0. The approach integrates principal invariants as inputs for the...
| Published in: | Computational Mechanics |
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| ISSN: | 0178-7675 1432-0924 |
| Published: |
Springer Science and Business Media LLC
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa65822 |
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| Abstract: |
This 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 F and electric displacement field D0. 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 E0, is inappropriate. The saddle pointnature of the latter contrasts with the convexity of the internal energy density, creating challenges for GPR or Gradient Enhanced GPR models using invariants of F and E0 (free energy-based GPR), compared to those involving Fand D0 (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. |
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| Keywords: |
Kriging, Machine Learning, Constitutive Modelling, Electro Active Polymers, Electromechanics |
| College: |
Faculty of Science and Engineering |
| Funders: |
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. |