Multidimensional rank-one convexification of incremental damage models at finite strains

Abstract This paper presents computationally feasible rank-one relaxation algorithms for the efficient simulation of a time-incremental damage model with nonconvex incremental stress potentials in multiple spatial dimensions. While standard suffers from numerical issues due to lack convexity, our experiments showed that by convexification delivering an approximation quasiconvex envelope prevents mesh dependence solutions finite element discretizations. By combination, modification and parallelization underlying algorithms, novel approach becomes feasible. A descent method Newton scheme enhanced step-size control prevent stability related local minima energy landscape computation derivatives. Numerical techniques construction continuous derivatives approximated convex are discussed. series demonstrates ability relaxed capture softening effects independence computed approximations. An interpretation terms microstructural evolution is given, based on lamination process.