A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics

Abstract

This manuscript introduces a novel neural network-based computational framework for constitutive modeling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as ¿nn(F, E0, ¿), enn(F, D0, n), Ynn(F, E0, n), or Tnn(F, D0, o), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, o and n, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy n is typically unmeasurable. (iii) The framework accommodates models like e(F, D0, n), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electromechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics.

R. Ortigosa, J. Martínez-Frutos and I. Castañar acknowledge the support of grant PID2022-141957OA-C22 funded by MI CIU/AEI/10.13039/501100011033 and by ‘‘ERDF A way of making Europe’’. R. Ortigosa and J. Martínez-Frutos also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia 𝑦 Tecnologia de la Region de Murcia. N. Ellmer and A. J. Gil acknowledge the support provided by the defence, science and technology labora

Peer Reviewed

Postprint (published version)