Elastic potentials as yield surfaces for homogeneous materials

TL;DR

This paper introduces a novel approach to defining yield surfaces in elasto-plastic models using elastic potentials, enhancing flexibility and accuracy in representing material behavior, including tension-compression asymmetry and non-linear elasticity.

Contribution

It proposes using elastic potentials as the basis for yield surfaces, incorporating non-linear elasticity and asymmetry, which advances the modeling of homogeneous materials under isothermal conditions.

Findings

Elastic potentials can serve as yield surfaces for materials.

The approach captures tension-compression asymmetry.

Correlation between Poisson's ratio and yield surface shape is identified.

Abstract

This paper proposes that elastic potentials, which may be rigorously formulated using the negative Gibbs free energy or the complementary strain energy density, should be used as the basis for the plastic part of elasto-plastic constitutive models. Thus, the yield surface may be assumed as an elastic potential surface for a specific level of critical complementary strain energy density. Here, rate-independent homogenous continuous materials under isothermal conditions are considered. Visualization of elastic potentials using principal stresses is presented. The proposed approach improves the total strain energy criterion because: (1) the elastic potential does not have to be centred at the current stress state and, consequently, is able to reproduce a tension-compression asymmetry; (2) the corresponding correlation between the Poisson's ratio and the shape of the yield surface is found for soils and metallic glasses; (3) non-linear elasticity is considered, which notably increases the flexibility and capabilities of the proposed approach. Ultimately, and similarly to hyperelasticity, the proposed framework for deriving (associated) yield surfaces may be considered just as a classifying criterion and a possible approach to formulate yield surfaces. Finally, if an associated flow rule is also assumed, the elastic potential, yield and plastic potential surfaces coincide.