https://www.sciencedirect.com/science/article/pii/S0022509623000492

Machine learning (ML) approaches have shown high potential for replacing classical constitutive models for the description of the mechanical behavior of inelastic, heterogeneous materials. However, existing ML aproaches are incremental in time mostly and, therefore, they fail to provide a continuous-time constitutive description that is independent of the time step used for in training data generation.

To deal with this problem we propose a new approach which allows to decouple the material representation from the incremental formulation. Inspired by the Thermodynamics-based Artificial Neural Networks (TANN) and the theory of the internal variables, the evolution TANN (eTANN) are continuous-time and, therefore, independent of time incrementation. Key feature of the proposed approach is the identification of the evolution equations of the internal variables in the form of ordinary differential equations, rather than in an incremental discrete-time form. In this work, we focus attention to juxtapose and show how the various general notions of solid mechanics are implemented in eTANN.

Building on previous works, we propose a methodology that allows to identify, from data and first principles, admissible sets of internal variables from the microscopic fields in complex materials. The capabilities as well as the scalability of the proposed approach are demonstrated through several applications involving a broad spectrum of complex material behaviors, from plasticity to damage, viscoplastitcity and double scale homogenization of heterogeneous inelastic materials.