Speaker
Description
The numerical simulation of finite strain damage models often faces challenges owing to the non-convexity of the underlying strain energy densities, such as mesh-dependent approximations and stability issues. In this talk, we focus on recent developments in computational relaxation by semiconvexification of a pseudo-time-incremental damage model, including the efficient approximation of polyconvex and rank-one convex envelopes. For the approximation of the polyconvex envelope, a dimension reduction is achieved by employing the signed singular value characterization of isotropic functions, transitioning the convexification from the d x d-dimensional deformation-gradient space to a d-dimensional manifold in the space of signed singular values. The combination of this dimension reduction with well-known algorithms for the resulting convexification process results in a significant increase in computational efficiency. On the other hand, the approximation of the rank-one convex envelope is accelerated by a hierarchical rank-one sequence convexification approach, which computes locally optimal rank-one sequences having the cost of essentially one-dimensional convexification. Although this approach provides only an upper bound on the rank-one convex envelope in general, it yields viable results in the intended application setting. A series of numerical experiments demonstrates the substantial computational speed-up and enhanced stability, thus paving the way for concurrent relaxation in simulations of boundary value problems. The feasibility of the presented approaches is illustrated by application to the isotropic damage model, showcasing mesh-insensitivity in the approximations, the ability to capture strain-softening and the microstructural evolution inherent to the relaxation process.
