Coupled CANN-DEM simulation in solid mechanics

A general, unified neural network approach as replacement for the finite element method without the need for analytic expressions for material laws is suggested. The complete simulation process from the material characterization to simulations on a structural level takes place in the new neural network framework. The drawback of many conventional analytic expressions of material laws to require large numbers of experiments for parametrization is addressed by an integrated inverse approach. Specifically, an adaptation of the Deep Energy Method is combined with a Constitutive Artificial Neural Network (CANN) and trained on measured displacement fields and prescribed boundary conditions in a coupled procedure. Tests on compressible and incompressible Neo-Hookean solids with up to twelve CANN parameters show high accuracy of the approach and very good generalization of CANNs. A small extent of data is required for robust and reliable training.