On a geometrically nonlinear damage model based on a multiplicative decomposition of the deformation gradient and the propagation of microcracks
The aim is to derive a damage model for materials damaged by microcracks. The damage evolution equations are based on micromechanical considerations. The aim is to describe the brittle damage, when no macroscopic plastic deformation occurs. The micromechanics of crack propagation in a unit cell containing a crack is purely based on a variational principle for elastic body containing a crack in equilibrium, leading to the principle of maximum energy release rate. From this it follows the path of a growing crack by introducing a series of thermodynamically equivalent straight cracks. The equivalence of the energy dissipated by microcrack growth and the damage dissipation leads to a damage evolution law. This evolution law is embedded in a finite deformation framework based on a multiplicative decomposition into elastic and damage parts. As a consequence, an anisotropic damaged elasticity tensor is presented with the help of push and pull operations. The connection of the approach to other well-known damage theories is shown, and the advantages of a finite element framework are discussed. Numerical excamples show the possibilities of the proposed model.
scientific article; zbMATH DE number 1761043
scientific article