A Variational Justification of Linear Elasticity with Residual Stress

We consider a residually-stressed, uniform hyperelastic body whose stored energy is quadratic with respect to the Green-St. Venant strain. We show that, in the limit of vanishing loads, suitable minimizing sequences converge to the unique minimizer of the energy functional of linear elasticity. We also deduce the standard stress-strain relations for linear elasticity with residual stress.