Stochastic Deep Material Networks as efficient surrogates for composites & Deep Material Networks performance for damaging processes

Deep Material Network (DMN) is a homogenisation method that incorporates analytical homogenisation solutions and material constitutive relations into a neural network model yielding mechanistic building blocks [1]. DMN was reformulated from the interaction view point [2] in order to improve its training performance. In this work, on the one hand, the phase volume fraction is decoupled from the topological parameters of the Interaction-Based DMN (IB-DMN). Since the phase volume fraction is no longer influenced by the topological parameters, a stochastic IB-DMN is constructed by introducing uncertainties to the topological parameters of a general IB-DMN trained with linear elastic homogenization data. The nonlinear predictions of the proposed stochastic IB-DMN are compared to those from Direct Numerical Simulations (DNSs) on 2D Stochastic Volume Elements (SVEs) of unidirectional fiber-reinforced matrix composites under a finite strain setting. On the other hand, damage is introduced in the matrix constituent phase in order to test the performance of the IB-DMN upon softening.