Gradient-enhanced Gurson-type modelling of ductile fracture

A nonlocal ductile damage is constructed on the basis of the yieldcriterion proposed by Gurson (1977). The nonlocality is introduced byreleasing the kinematic constraint which relates the porosity growthto the overall plastic flow. Instead of relating these quantitiespointwise, the pore growth is linked to a spatially averaged plasticdeformation field, which follows from an additional boundary valueproblem. The nonlocality which thus enters the constitutive modellingregularises the pathological localisation of deformation and damagewhich is sometimes observed in ductile damage models and removes theresulting mesh sensitivity of numerical analyses. In crack growthproblems, the non-standard boundary condition associated to theadditional partial differential equation allows to separate the crackregion from the rema! ining material, so that the nonphysicaldeformations which may be computed in the crack region do notinfluence the growth of damage.