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arXiv · 2208.01947

A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics

Cristina Padovani·Margherita Porcelli
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Abstract

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.

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Cristina Padovani, Margherita Porcelli. 2022-08-03. A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics. https://arxiv.org/abs/2208.01947

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