Model-free data-driven inelasticity in Haigh–Westergaard space — A study how to obtain data points from measurements

Abstract

Model-free data-driven computational mechanics, first proposed by Kirchdoerfer and Ortiz, replaces phenomenological models with numerical simulations based on sample data sets in strain–stress space. Recent literature extended the approach to inelastic problems using structured data sets, tangent space information, and transition rules. From an application perspective, the coverage of qualified data states and calculating the corresponding tangent space is crucial. In this respect, material symmetry significantly helps to reduce the amount of necessary data. This study applies the data-driven paradigm to elasto-plasticity with isotropic hardening. We formulate our approach employing Haigh–Westergaard coordinates, providing information on the underlying material yield surface. Based on this, we use a combined tension–torsion test to cover the knowledge of the yield surface and a single tensile test to calculate the corresponding tangent space. The resulting data-driven method minimizes the distance over the Haigh–Westergaard space augmented with directions in the tangent space subject to compatibility and equilibrium constraints.