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An established method for incorporating inelastic constitutive equations into finite element software is the use of rheological elements, assembled in series or in parallel, to describe the constitutive response at each material point. This approach can be extended to finite strains by exploiting the multiplicative decomposition of the deformation gradient. In this study, we propose an hybrid approach that integrates traditional elements with elements, with constitutive equations defined through deep neural networks (DNNs), into an assemblage of standard rheological elements. We formulate DNNs to guarantee thermodynamic consistency, enabling us to model the time-dependent, large strain response of elastomers and predict the Payne effect in filled rubber. This effect, characterized by deformation-enhanced shear thinning, poses unique modeling challenges. Additionally, we discuss data augmentation procedures to address the data-intensive nature of training neural networks, showcasing the effectiveness of utilizing ordinary dynamic mechanical analysis (DMA) tests for this purpose.
Califano et al. (Thu,) studied this question.