.. _models:

###############
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.

.. There is also a performance section for the model which details how the model is tested for efficiency.

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.

.. toctree::
   :hidden:
   :maxdepth: 1

   models/hypoelastic
   models/hyperelastic
   models/elastic
   models/elastic_3D_ortho
   models/neo_hookean
   models/gent
   models/elastic_plastic
   models/ep_power_law
   models/ductile_fracture
   models/multilinear_ep
   models/multilinear_ep_fail
   models/johnson_cook
   models/j2_plasticity
   models/hosford_plasticity
   models/hill
   models/barlat
   models/plane_stress_rate_plasticity
   models/modular_plane_stress_plasticity
   models/power_law_creep
   models/viscoplastic
   models/md_viscoplastic
   models/hyperfoam
   models/hyperelastic_damage
   models/soil_and_foam
   models/shape_memory_alloy
   models/low_density_foam
   models/foam_plasticity
   models/viscoplastic_foam
   models/foam_damage
   models/orthotropic_crush
   models/orthotropic_rate
   models/universal_polymer
   models/linear_thermoviscoelastic
   models/wire_mesh
   models/viscoplastic_viscoscram
   models/phase_field_fefp
   models/failure
