Constitutive modeling of plastic deformation behavior of open-cell foam structures using neural networks

This article presents an approach to use neural networks as a constitutive model for the inelastic deformation behavior of open-cell foams or other porous materials. The inelastic deformation behavior of highly porous materials can be very complex and makes the formulation of a closed form constitutive model a very challenging or even impossible task. The presented methods include the creation of a periodic representative volume element (RVE) of the porous structure, the supply of training data by means of finite element simulations using the RVE and the use of trained neural networks within a user material routine (UMAT) for the finite element code ABAQUS. As a proof of concept this approach is applied to relatively simple two dimensional porous structures, where both the homogenized material behavior and a fully resolved porous structure are simulated and compared. The computational effort for simulating a simple foam structure can be reduced by a factor of more than 10,000 using the proposed homogenization approach.