Constitutive Laws

A constitutive law defines how a material responds to deformation. It connects strain to stress and is a central part of any structural simulation.

For linear elastic analysis, the constitutive relationship is:

sigma = D epsilon

The matrix D depends on the material model and required engineering constants. For isotropic linear elastic materials, the required constants are commonly Young's modulus and Poisson's ratio. For orthotropic materials, stiffness depends on direction and requires additional material constants.

The constitutive law must be consistent with the analysis assumptions. Using a linear elastic law for a material that yields, cracks, creeps, or undergoes large deformation can produce misleading results.