Model-Free Data-Driven Inelasticity

TL;DR

This paper extends Data-Driven elasticity to inelasticity, modeling evolving material data sets over time for various inelastic behaviors, and demonstrates its effectiveness through numerical examples.

Contribution

It introduces three paradigms for representing evolving inelastic material data sets and explores their applicability to different inelastic material classes.

Findings

Effective modeling of inelastic materials with data-driven methods.

Numerical examples show the approach's versatility and performance.

Different paradigms capture various history-dependent behaviors.

Abstract

We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: i) materials with memory, i.e., conditioning the material data set to the past history of deformation; ii) differential materials, i.e., conditioning the material data set to short histories of stress and strain; and iii) history variables, i.e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.