Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity

The adjoint-weighted equation (AWE) formulation is applied to incompressible isotropic plane-stress elasticity for the solution of inverse problems. For the strong form of the problem to have a solution, a restrictive strain compatibility condition must hold. In the AWE variational formulation on the other hand, a much milder sufficient condition is that uniaxial stress states be precluded, making the method more robust to noisy data. We prove that the formulation leads to a stable converging numerical method, and show through computations that the method performs well.