where σi is the initial stress. The integration can then be carried out analytically and the result is
For a Nonlinear Elastic Material, the strain energy density is computed in different ways depending on the material model selected. If the integration in Equation 3-204 can be performed analytically, then a closed form expression is used, similar to what is done in the linear elastic material. If not, then the integral is actually computed using the
integrate() operator.