Finite element formulation of a new nonlocal damage model

It is now widely recognized in literature that the results of the local damage model are mesh dependent. Regularization methods which use gradients of equivalent plastic strain in the material yield function are also popularly known as gradient plasticity models. Many times, these nonlocal forms of equivalent plastic strain have been used as a measure of material damage in the integral and gradient enhanced formulations. Regularization methods based on nonlocal forms of ductile void volume fraction are limited in literature, especially for the Rousselier's model. Moreover, the mesh independent nature of the nonlocal solutions are usually demonstrated with the help of 1D bar, shear band and notched tensile specimens, etc. Comparisons of the nonlocal solutions with those of experiment are hardly done, especially, for problems involving prediction of the fracture resistance behaviour of cracked specimens. In this work, the Rousselier's damage model has been extended to a nonlocal form using the nonlocal damage parameter ‘d’ as an additional degree of freedom of the finite element (FE) model. The FE equations have been derived using the weak forms of the governing equations for both mechanical stress equilibrium and the damage equilibrium. The mesh independent nature of the model has been demonstrated through various examples, such as an axisymmetric tensile specimen and a standard fracture mechanics specimen (for which predicted results have been compared with those of experiment) using different mesh sizes. The ability of the new model to predict the effect of crack tip constraint on the fracture resistance behaviour has been demonstrated by analysing two different types of standard fracture mechanics specimens.