A deep learning energy method for hyperelasticity and viscoelasticity

TL;DR

This paper introduces a deep energy method that combines potential energy formulation with deep learning to efficiently solve PDEs in hyperelastic and viscoelastic materials, providing accurate 3D responses without extensive data or meshing.

Contribution

The deep energy method (DEM) is a novel, meshfree, self-contained approach that accurately models material deformation directly from energy principles using deep learning.

Findings

Accurately captures 3D mechanical responses.

Eliminates need for extensive training data.

Provides instant response after training.

Abstract

The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and meshfree. It can accurately capture the three-dimensional (3D) mechanical response without requiring any time-consuming training data generation by classical numerical methods such as the finite element method. Once the model is appropriately trained, the response can be attained almost instantly at any point in the physical domain, given its spatial coordinates. Therefore, the deep energy method is potentially a promising standalone method for solving partial differential equations describing the mechanical deformation of materials or structural systems and other physical phenomena.