  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.
