Bifurcation and stability issues in gradient theories with softening

Ahmed Benallal (1) , Jean-Jacques Marigo (2)

1 LMT - Laboratoire de Mécanique et Technologie
2 DALEMBERT - Institut Jean Le Rond d'Alembert

A bifurcation and stability analysis is carried out here for a bar made of a material obeying a gradient damage model with softening. We show that the associated initial boundary-value problem is ill posed and one should expect mesh sensitivity in numerical solutions. However, in contrast to what happens for the underlying local damage model, the damage localization zone has a finite thickness and stability arguments can help in the selection of solutions.

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

Ahmed Benallal, Jean-Jacques Marigo. Bifurcation and stability issues in gradient theories with softening. Modelling and Simulation in Materials Science and Engineering, 2007, 15 (1), pp.S283-S295. ⟨10.1088/0965-0393/15/1/S22⟩. ⟨hal-00551073⟩