Hadamard’s variational formula in terms of stress and strain tensors

Abstract Starting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function bounded domain and an appropriate stress tensor. By further variation, imposed given vector field, arrive at interior version of Hadamard formula, previously considered P. Garabedian. It gives variation in terms pairing between tensor strain domain, this contrasting classical formula which is expressed as pure boundary variation.