1. Introduction

Constitutive modeling is a fundamental aspect of solid mechanics modeling and simulation. The wide range of behaviors of solid materials requires a vast number of models capable of modeling all (or even some of) the different responses. This is in contrast to fluid mechanics, for example. As such, constitutive modeling is arguably the major problem in solid mechanics. A constitutive model is necessary for accurately predicting the state of a material. This determination includes both the stress state whose resolution is essential for many phenomena of interest like fracture and failure as well as capturing inelastic responses like damage or multiphysics couplings.

One aspect of obtaining an accurate resolution of the stress field is, in one sense, easy to understand. It is mesh discretization. More degrees of freedom in a simulation enables better resolution and results in a more accurate stress field if we look just at the mathematics. If all materials followed an elastic law, then mesh resolution on its own would be all that is needed to resolve the stress field. In reality, however, materials do not exhibit elastic responses except in very limited cases.

This leads us to a second aspect of calculating accurate stress fields, which is much harder to understand. This one concerns the physics. The specific behavior of a material depends on the physical processes specific to that material, and this must be included in a constitutive model in some form or another. The main goal of the Library of Advanced Materials for Engineering - LAMÉ - is to provide a simple means to implement the wide variety of models in a library that can be used by our solid mechanics application codes.