For analyses that include displacement degrees of freedom, the input is a function of deformation such as strain or displacement, and the response is given force-like quantities such as stress or normal and tangential forces. The following general material types are available:
| Type | Behavior | Application |
|---|---|---|
| Linear elastic | The response is the stresses that are directly proportional to the strains and the material will fully recover the original shape when unloaded. For isotropic materials, the relationship is given by Hooke's law and this relationship can be generalized to define anisotropic behavior. | Many metals are linear elastic at room temperature when the strains are small. |
| Plastic and elastic-plastic | The deformation of the material includes a permanent, or plastic, component that will not return to the original configuration if the load is removed and evolves in response to the deformation history. These materials also typically have an elastic behavior so that the combined deformation includes a part that is recoverable upon unloading. | Plastic deformation is observed in many materials such as metals, alloys, soils, rocks, concrete, and ceramics. |
| Hyperelastic | The behavior of these models is defined by a strain-energy potential, which is the energy stored in the material due to strain. The mathematical formulation is convenient for large-deformation analyses. | Hyperelastic models are often used for materials that undergo large elastic deformation, such as polymers and biological materials. |
| Rate effects and time dependency | This is a general behavior in which the response of the material depends on the rate of deformation, and therefore also the time. Examples include viscoelasticity, viscoplasticity, creep and damping. | Metal alloys that show significant creep deformation under elevated temperature, rate-dependent metal forming applications, polymers which typically get stiffer for increased deformation rate, and structures that damp out high frequency waves under dynamic loading. |
| Expansion and swelling | Materials often respond to changes in the physical environment and this response affects the structural behavior. Examples include thermal expansion in which changes in material volume depend on changes in temperature and swelling behaviors that depend on hygroscopic effects or neutron flux. | Radiation environments, bonded materials with thermal strain mismatch, and soils that absorb water. |
| Interaction | These models produce a response based on the interaction of structures. | Gasket and joint materials and also models of bonded and separating surfaces along interfaces or material cleavage. |
| Shape memory alloy | An elastic constitutive model with an internal phase transformation. | The phase transformation depends on the stress and temperature that cause an internal transformation strain. |