A Mixed Variational Framework for Eigenstrain and Residual Stress Reconstruction

Abstract

This paper proposes an inverse eigenstrain analysis procedure to estimate full-field residual stress from an incompletely measured residual elastic strain or stress field. The inverse problem is solved by minimizing the linear elastic constitutive relation discrepancy that arises from different admissible stress and strain fields within an alternating minimization framework. First, a standard forward thermoelastic problem is solved to obtain a statically admissible total strain field. Then, full-field residual stress (or elastic strain) that satisfies partial measurement is obtained by minimizing a Hellinger-Reissner-type energy functional under a mixed variational framework. We have used standard two and three-dimensional hybrid finite elements to obtain a stress field. Finally, a full-field eigenstrain field is obtained by minimizing constitutive disparity due to dissimilar elastic strain and total strain fields. We show the efficacy of the proposed procedure with some numerically obtained and experimentally reported data.