We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following interior point method coupled with a Mehrotra's predictor-corrector approach is proposed. Implementations based on direct methods are theoretically and numerically investigated taking into account tensors C arising in the modelling of masonry-like materials.
CALCOLO, pp. 1-28, 2022 (doi:10.1007/s10092-022-00478-1)
View A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics