A hybrid approach to simulate the homogenized irreversible elastic–plastic deformations and damage of foams by neural networks

Abstract

Classically, the constitutive behavior of materials is described either phenomenologically, or by homogenization approaches. Phenomenological approaches are computationally very efficient, but are limited for complex non-linear and irreversible mechanisms. Such complex mechanisms can be described well by computational homogenization, but respective FE 2 computations are very expensive.As an alternative way, neural networks have been proposed for constitutive modeling, using either experiments or computational homogenization results for training. However, the application of this method to irreversible material behavior is not trivial.The present contribution presents a hybrid methodology to embed neural networks into the established framework of rate-independent plasticity. Both, the yield function and the evolution equations of internal state variables are represented by neural networks. Respective training data for a foam material are generated from RVE-simulations under monotonic loading. It is demonstrated that this hybrid multi-scale neural network approach (HyMNNA) allows to simulate efficiently even the anisotropic elastic-plastic behavior of foam structures with coupled anisotropic evolution of damage and non-associated plastic flow.

Feed-Forward Neural Networks for Failure Mechanics Problems

“…DL has many architectures, especially in mechanics, and research is focused mainly on using the feed-forward neural network (FFNN), recurrent neural network (RNN), and convolutional neural network (CNN). So far, applications of these types of neural networks devoted to the field of mechanics can be seen in the recent works of [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. A detailed description of those approaches is summarized as follows:…”

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

“…When it comes to use NNWs as a surrogate model in FE 2 analyzes, this can be achieved either by approximating the strain energy density surface as suggested by [27,28], the stress-strain responses as achieved by [29][30][31][32], or a function of both the current stress and the plastic dissipation density [22]. Although NNWs have shown to be reliable surrogate models in elasticity and in non-linear elasticity [27], when it comes to irreversible behaviors, the loading history plays an important role in RVE response involving more difficulties both in the NNW architecture definition and in its training.…”

“…In [30], using state variables with the support vector machine as a solution strategy for the decision of loading/unloading, a feed-forward network was used to extract meso-scale resolution for multi-scale failure analysis, but only 1D loading conditions were considered at the macro-scale. In [31], meso-scale plastic strains were used as state variables and were updated at each loading step through an empirical model or in combination with another feed-forward neural network. However, when the RVE has a complex micro-structure, the state variables are not always easy to be defined and their update is also troublesome because of the anisotropy induced by the historical dependent behavior, e.g.…”

A hybrid approach for the multi‐scale simulation of irreversible material behavior incorporating neural networks

“…The latter has been implemented into the commercial FE code Abaqus/Standard via the UMAT interface. Further details on the approach, flow rule, extraction of training data from the RVE simulations and implementation can be found in [5,6].…”

“…Training FEM Simulation Fig. 1: Hybrid Multi-Scale Neural Network Approach (HyMNNA) [5] Considered is for example here a foam made of elastic-plastic bulk material as shown at left-hand side of Fig. 1.…”