A Hybrid Approach Employing Neural Networks to Simulate the Elasto−Plastic Deformation Behavior of 3D‐Foam Structures

Herein, a general methodology to describe the complex inelastic macroscale behavior of cellular media is presented. It is an important contribution toward establishing predictive computational tools to study the structure−property−performance relations in such materials. A particular challenge is given by the possible complexity of the inelastic macroscopic response, which makes it difficult to capture with classical phenomenological approaches. Numerical micro−macro transitions schemes, such as the FE² method, have recently been used to address this problem but are computationally very costly. Building on earlier work, a 3D extension of an efficient hybrid scale‐bridging approach is therefore proposed that comprises the following key elements: 1) spatially fully resolved finite element analysis (FEA) of representative volume element (RVEs) approximating technologically relevant foam morphologies, with an associated plasticity model describing the bulk behavior at the microscale; 2) a hybrid material model for the macroscopic material behavior, which incorporates neural networks (NN) representing complex yield surfaces and flow directions into a nonassociative plasticity formulation; and 3) NN training via numerical homogenization involving off‐line RVE computations. A 3D Wheire−Phelan structure with elasto−plastic microscale behavior is chosen as an exemplary application. The requirements on training data sets and NN properties regarding approximation accuracy and numerical effort of the hybrid approach are carefully investigated.