# 4. Material Models

This section details the constitutive models that are implemented and supported in LAMÉ. The description of each model has four sections. First, a section discussing the theory of the model is found. This is the mathematical description of the model in a continuum mechanics framework, independent of its implementation in a computational code. As these models are intended for solid mechanics analysis, the following section describes the numerical implementation of the model. This delves into how the model is implemented in the code and any special numerical techniques that are used to integrate the model. The subsequent section presents the verification problems that are run for the model. Through the results of such problems, evidence is provided that, to the best of our understanding, the model is behaving as expected. Finally, documentation of the model user inputs and user outputs are given for analyst reference.

It is our belief that this collection of documentation is important for the use of our constitutive models, and it provides confidence that our models are implemented correctly for the capabilities that are tested.

What this documentation does not provide is guidance on how to use the models. Different materials behave differently, and it is the responsibility of the user to ensure that the material model chosen can accurately model the behavior of a particular material. Furthermore, even with a single material, many models might be capable of modeling the material depending on the loading in a given analysis. It is the responsibility of the analyst to ensure that the model they choose is the best model for their problem. Across the different models, parameters may also vary in value or have slight changes in interpretation. Care needs to undertaken to ensure that material and model parameters used accurately reflect the specific material being investigated (some parameters may vary with simple changes in processing route) and capture the behaviors that of interest. If emphasis needs to be placed on initial yield rather than failure, subtle differences in some parameters may be expected.