Limitations of the St. Venant–Kirchhoff material model in large strain regimes

Abstract

The St. Venant–Kirchhoff law is a widely used constitutive relation in engineering applications. However, its limitation to small strains is frequently mentioned in the literature but rarely elaborated on. Therefore, we present a comprehensive study discussing the St. Venant–Kirchhoff law and its shortcomings in large stain regimes, focusing on compressive loading based on one-dimensional stress and strain states. The linear stress–strain relation in combination with the associated Green–Lagrange strain yields a nonphysical structural behavior for large compressive strains, which is reflected in instabilities and nonphysical softening. Common misconceptions concerning the St. Venant–Kirchhoff law and alternative constitutive models are presented and evaluated based on a two-bar snap-through problem.