Thermodynamically consistent neural network plasticity modeling and discovery of evolution laws

Over the past decade, advancements in computational frameworks and processing power have made deep neural networks increasingly viable for material modeling. However, purely data-driven models can yield non-physical predictions due to the lack of physical constraints. While recent works that incorporate physics into the training process partially address this issue, they offer no guarantees beyond the scope of the training data. To tackle this challenge, we propose a novel approach that embeds the neural network within the material model, inherently fulfilling thermodynamic laws. The network represents only the unknown physics allowing us to integrate knowledge accumulated from decades of constitutive modeling research into the data-driven methodology. By analyzing the trained, embedded networks, we recover existing evolution laws from artificial training data and discover new evolution laws from experimental data. The discovered evolution laws for isotropic and kinematic hardening can qualitatively predict an experimentally observed yield strength evolution, which conventional evolution laws cannot describe.