Graph-based representation of history-dependent material response in the Data-Driven Computational Mechanics framework

Abstract

This work develops an extension of the Data-Driven Computational Mechanics approach introduced by Kirchdoerfer and Ortiz (2016) to history-dependent behaviour. The material database is replaced by a material directed graph, where vertices represent strain–stress pairs and arcs encode thermomechanically admissible transitions between them. A graph search algorithm is used to select local material databases representative of the incremental material behaviour. This study thus gives the mathematical tools for a structured data-driven representation of the material behaviour, designed to minimise the increase of the problem dimensionality. The performances of the proposed approach applied to elastoplasticity are studied on a single-element structure and a larger truss structure. A two-step solver is proposed to address numerical accuracy issues in the latter case.