Embedding a Physics-Constrained ML Constitutive Model Into the Finite Element Framework via an Abaqus UMAT

  • He, Yuqing (Institut für Mechanik, Universität Kassel)
  • Heider, Yousef (Institut für Mechanik, Universität Kassel)

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In multiscale material modeling frameworks, artificial neural networks (ANNs) can accurately and effectively map complex microstructural responses to macroscopic stress-strain relationships. For instance, ANNs can directly approximate the stress-strain relationship of complex nonlinear inelastic anisotropic material performance from data such as crystal plasticity, eliminating the need for explicit parameter identification [1]. One challenge that must be addressed in such models is ensuring objectivity and thermodynamic consistency. To address this, Heider et al. [1] introduced a physics-constrained neural network constitutive framework that enforces frame indifference through a spectral tensor representation of stress and strain. Building on these developments and the previous work of the authors [2], this study will embed graph-based neural networks directly into the Abaqus finite element (FE) solver via a UMAT (user-defined material) subroutine to implement mechanical FE simulations involving crystal plasticity materials. Although this approach can also be applied to general elasto-plasticity, crystal plasticity is used here to demonstrate its applicability to the time-dependent and anisotropic performance of materials without any explicit models. To verify the results and effectiveness of the implementation, numerical tests and comparisons with reference boundary-value problems will be performed. REFERENCES [1] Heider, Y., Wang, K., and Sun, W. C., SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials, Comput. Method Appl. Mech. Eng., Vol. 363, pp. 112875, 2020. [2] He, Y., Heider, Y., and Markert, B., Embedding an ANN-Based Crystal Plasticity Model into the Finite Element Framework using an ABAQUS User-Material Subroutine, arXiv preprint arXiv:2410.08214, 2024.