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

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.