A new mesh-independent Rousselier's damage model: Finite element implementation and experimental verification

Abstract

Numerical analyses based on local damage models are often found to depend on the spatial discretisation (i.e., mesh size of the numerical method used). The growth of damage tends to localize in the smallest band that can be captured by the spatial discretisation. As a consequence, increasingly finer discretisation grids can lead to crack initiation earlier in the loading history and to faster crack growth. The reason behind this non-physical behaviour is the loss of ellipticity of the set of partial differential equations, which govern the rate of deformation locally at a certain level of accumulated damage. Displacement discontinuities and damage rate singularities can be avoided by adding nonlocality to the damage model. The enhanced continuum description which is thus obtained results in smooth damage fields, in which the localization of damage is limited to the length scale introduced by the averaging. In this work, a new nonlocal form of Rousselier's damage model has been developed by introducing an additional partial differential equation (diffusion type) for the nonlocal damage variable in terms of the ductile void volume fraction. The diffusion equation has been discretised along with the stress equilibrium equation of the mechanical continuum using finite element (FE) method. The nonlocal damage variable has been used as an additional degree of freedom in the FE model. Several example problems have been solved to demonstrate the mesh-independent nature of the new nonlocal formulation.