Advances in the application of non-local damage models in the simulation of ductile crack-extension

Local damage models usually have the disadvantage that results are strongly mesh dependent. The reason is that the type of the underlying partial differential equations changes under quasi-static conditions from elliptic to hyperbolic. Non-local damage models do not exhibit such behaviour under certain conditions. The usage of such nonlocal damage models in finite element analyses opens the possibility for preserving the ellipticity of the partial differential equations and thus avoiding mesh dependence of numerically obtained results. The loss of ellipticity for local models and its preservation for non-local models are demonstrated for a wide variety of examples enclosing ductile damage. In the present investigation, the non-local damage model is applied to the simulation of ductile crack extension in fracture mechanics specimens. The type of the underlying differential equations is permanently analysed and controlled. Non-local extension of Gurson s model The basic equations of the local Gurson model in the formulation of Tvergaard and Needleman include the yield condition ( ) ( ) ( ) 0 1 2 tr cosh 2 , , 2 1 2 1 2 = − − ⎟⎠ ⎞ ⎜⎜ ⎝ ⎛ + = Φ ∗ ∗ f q q f q f M M v M σ σ σ σ σ σ , (1) the evolution equation for the modified void volume fraction