Data-based derivation of material response

Abstract

This paper proposes a method to identify the strain–stress relation of non-linear elastic materials, without any underlying constitutive equation. The approach is based on the concept of Data Driven Computational Mechanics recently introduced by Kirchdoerfer and Ortiz (2016). From a collection of non-homogeneous strain fields, for example measured through Digital Image Correlation, the algorithm builds a database of strain–stress couples that sample the mechanical response of the material for the range of measured strains. The method is first derived for truss structures and then extended to the case of small-strain elasticity. The method accuracy, sensitivity to measurement noise and parameters are discussed using manufactured data.