Automatic Differentiation in PyTorch as a Tool for Robust Implementation of Elasto-Plastic Constitutive Model

The paper presents a simple and robust approach to an implementation of the hardening soil model into finite element calculations.The implementation of the return stress mapping exploits the automatic differentiation of tensor variables provided by the Py-Torch framework.The automatic differentiation allows for a succinct implementation despite the relatively complex structure of the nonlinear equations in the stress return algorithm.The presented approach is not limited to the hardening soil model.It can be utilised in the development and verification of other elasto-plastic constitutive models where expressing and maintaining the Jacobian matrix over different versions of a material model is time-consuming and error-prone.