A non-local finite element based on volumetric strain gradient: Application to ductile fracture

The aim of this work is to propose a finite element formulation adapted to ductile fracture simulation using Continuum Damage Mechanics and unravelling two main encountered difficulties. First, as ductile damage represents voids nucleation and growth, constitutive behaviors constrain the plastic volumetric strain through damage evolution laws, leading to volumetric locking. A specific formulation is consequently needed. A three-field formulation is defined, in which volume change is treated as a new unknown; its relation to the displacement field is weakly enforced by mean of a Lagrange multiplier. Then, strain and damage localisation occurs due to softening, and leads to spurious mesh dependent solutions. A coupling between neighbouring material points is thus introduced through a volume change gradient term added in the three field formulation. First results show that this formulation permits to control localisation and to unravel mesh dependency.