Component-based machine learning paradigm for discovering rate-dependent and pressure-sensitive level-set plasticity models

Abstract

Conventionally, neural network constitutive laws for path-dependent elasto-plastic solids are trained via supervised learning performed on recurrent neural network, with the time history of strain as input and the stress as input. However, training neural network to replicate path-dependent constitutive responses require significant more amount of data due to the path dependence. This demand on diverse and abundance of accurate data, as well as the lack of interpretability to guide the data generation process, could become major roadblocks for engineering applications. In this work, we attempt to simplify these training processes and improve the interpretability of the trained models by breaking down the training of material models into multiple supervised machine learning programs for elasticity, initial yielding and hardening laws that can be conducted sequentially. To predict pressure-sensitivity and rate dependence of the plastic responses, we reformulate the Hamliton-Jacobi equation such that the yield function is parametrized in the product space spanned by the principle stress, the accumulated plastic strain and time. To test the versatility of the neural network meta-modeling framework, we conduct multiple numerical experiments where neural networks are trained and validated against (1) data generated from known benchmark models, (2) data obtained from physical experiments and (3) data inferred from homogenizing sub-scale direct numerical simulations of microstructures. The neural network model is also incorporated into an offline FFT-FEM model to improve the efficiency of the multiscale calculations.

FE${}^\textbf{ANN}$ $-$ An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

“…For instance, an extension to further material symmetry groups [68] have to be made by integrating appropriate invariant sets into the implementation. Finally, an extension to dissipative constitutive behavior [41,56,55] is needed.…”

“…Based on this, [55,42] show an extension to elastoplasticity, whereby ANNs are used for the description of the yield surface and the stress within a hybrid modeling approach. Similarly, the simulation of the elastic-plastic deformation behavior of open-cell foam structures is shown in [33,34].…”

A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity

“…Vlassis and Sun (28,29) presented an ANN-based framework for conventional elasto-plastic materials that incorporates a yield surface and plastic flow rule. The yield surface is recast as a level-set function that can evolve in the stress space (representing hardening/softening) following a prescribed rule.…”

“…The EPNN's prediction and the ground truth are compared in Figs. [28][29][30] for three different values of α, but the same initial condition of p in = 375 kPa and e in = 0.64. The results further validate the predictive capabilities of the proposed EPNN in this work in arbitrary monotonic loading paths.…”

Modular machine learning-based elastoplasticity: generalization in the context of limited data

“…Other models used feedforward neural networks to update the stress and make explicit use of internal variables that are inaccessible from an experiment (for example from simulations of microstructure representative volumes), which restricts the use of such approaches [39,40]. As an alternative, [31,41,42] recently proposed a modular approach for elastoplastic modeling where the elastic law and the yield function evolution are treated as separately trainable data-driven models, inspired by traditional modeling of elastoplasticity. In their approach, beyond training the elastic law which we discussed previously, a neural network-based yield function is trained using a level-set hardening framework that is dependent on the internal variables.…”