Efficient numerical integration of an elastic–plastic damage law within a mixed velocity–pressure formulation

R. El Khaoulani (1) , Pierre-Olivier Bouchard (1)

1 CEMEF - Centre de Mise en Forme des Matériaux

This study focuses on numerical integration of constitutive law in numerical modeling of cold materials processing involving large plastic strain together with ductile damage. A mixed velocitypressure formulation is used to handle the incompressibility of plastic deformation. A Lemaitre damage model where dissipative phenomena are coupled is considered. Numerical aspects of the constitutive equations are addressed in details. Three integration algorithms with different levels of coupling of damage with elastic-plastic behavior are presented and discussed in terms of accuracy and computational cost. The implicit gradient formulation with a non-local damage variable is used to regularize the localization phenomenon and thus to ensure the objectivity of numerical results for damage prediction problems. Tensile test on a plane plate specimen, where damage and plastic strain tend to localize in well-known shear bands, shows successfully both objectivity and effectiveness of the developed approach.

Mots clés: numerical integration of constitutive law; Ductile damage; numerical coupling; consistent tangent matrix; mixed finite element method; stabilized discretization P 1+ /P

Domaines: Mécanique des solides [physics.class-ph]; Physique mathématique [math-ph]

R. El Khaoulani, Pierre-Olivier Bouchard. Efficient numerical integration of an elastic–plastic damage law within a mixed velocity–pressure formulation. Mathematics and Computers in Simulation, 2013, 94, pp.145-158. ⟨10.1016/j.matcom.2013.06.004⟩. ⟨hal-03605099⟩