Lagrangian Methods for Constrained Non-Convex Minimizations and Applications in Fracture Mechanics
Marco Artina · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2015
We address the consistent numerical simulation of quasi-static evolutions of critical points of nonconvex and nonsmooth energy functionals. We focus on the reliable numerical simulation of linearly constrained nonsmooth and nonconvex optimizations. We use these tools as building blocks for the construction of quasi-static evolutions. We apply the machinery on a model of cohesive fractures, giving an alternative and constructive proof of existence. We consider models of brittle fractures and their adaptive anisotropic numerical approximations.