The behavior of a material is said to be elastic when its displacement is linearly proportional to the applied load, and returns to its undeformed state when the load is removed. For elastic materials, stress is directly proportional to the strain as indicated below:

 {s} = [D] {e - et}

where [D] is the elastic (isotropic, anisotropic, or orthotropic) material or material stiffness matrix, {s} is the total stress vector, {e} is the total strain vector, and {et} is the thermal strain vector. The above rule is an approximation that is valid as long as the strains are small for certain types of materials. The above equation is known as constitutive relation. While they take this simple form for linear elastic materials, the constitutive relations can be quite complex for nonlinear materials.

• Linear Elastic Isotropic

• Linear Elastic Orthotropic

• Nonlinear Elastic

• von Mises Plasticiy (Kinematic & isotropic)

• Tresca Plasticity (Kinematic & Isotropic)

• Drucker - Prager Plasticity

Hyperelastic material models can be used for modeling rubber-like materials where solutions involve large deformations. The material is assumed nonlinear elastic, isotropic, and incompressible

The finite element formulation for such materials has numerical difficulties due to incompressibility. A penalty method, based on the introduction of compressibility to the strain energy density function, is used to assemble the additional degrees of freedom into the global stiffness matrix. The introduction of the penalty function modifies the strain energy function from incompressible to nearly incompressible.

All the skills needed for nonlinear analysis apply to the hyperelastic models. The load step, mesh size and distribution,.. etc. require careful considerations. In some cases, especially when no experience with the problem at hand is available, nothing but trial and error will prove successful. Higher order elements (high quality) provides higher numerical stability than lower order elements (draft quality).

• Mooney - Rivlin Hyperelastic

• Ogden Hyperelastic

• Blatz - Ko Hyperelastic