Constitutive model characterization and discovery using physics-informed deep learning

Abstract

Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have very limited number of parameters, yet, they are extremely efficient in reproducing complex responses observed in experiments. Additionally, in their discretized form, they are computationally very efficient, often resulting in a simple algebraic relation, and therefore they have been extensively used within large-scale explicit and implicit finite element models. However, it is very challenging to formulate new constitutive models, particularly for materials with complex microstructures such as composites. A recent trend in constitutive modeling leverages complex neural network architectures to construct complex material responses where a constitutive model does not yet exist. Whilst very accurate, they suffer from two deficiencies. First, they are interpolation models and often do poorly in extrapolation. Second, due to their complex architecture and numerous parameters, they are inefficient to be used as a constitutive model within a large-scale finite element model. In this study, we propose a novel approach based on the physics-informed learning machines for the characterization and discovery of constitutive models. Unlike data-driven constitutive models, we leverage foundations of elastoplasticity theory as regularization terms in the total loss function to find parametric constitutive models that are also theoretically sound. We demonstrate that our proposed framework can efficiently identify the underlying constitutive model describing different datasets from the von Mises family.

Neural Networks for Constitutive Modeling: From Universal Function Approximators to Advanced Models and the Integration of Physics

“…The presented model was analyzed by training the network on simulation data of an Oldroyd-B-fluid and a hyper-elastic tyre. A different approach was described in Haghighat et al [179], which uses PINNs [180] as the basis for a framework to solve material-related differential equations. A boundary value problem solver incorporating elastoplastic material behavior and damage formulations was developed and applied to a plate deformation problem.…”

“…A boundary value problem solver incorporating elastoplastic material behavior and damage formulations was developed and applied to a plate deformation problem. In [179], the authors stated that their approach can be applied to stress-strain data from meso-or micro-mechanical as well as molecular dynamics simulations. However, the PINNbased framework is only applicable to homogeneous stress and strain distributions.…”