Stability of non localized responses for damaging materials

Jean-Jacques Marigo (1) , Kim Pham (2)

1 LMS - Laboratoire de mécanique des solides
2 DALEMBERT - Institut Jean le Rond d'Alembert

This work is devoted to the analysis of the stability of the homogeneous states of a bar made of a brittle strain softening material submitted to a tensile loading. We distinguish two types of damage models: local damage models and gradient damage models. We show that a local damage model necessarily leads to the unstability of the homogeneous response once the first damage threshold is reached. On the contrary, in the case of a gradient damage model, viewed as a regularization of the underlying local model, the homogeneous damage states of “sufficiently small” bars are stable.

Domains: Physics [physics]; Mechanics [physics]; Solid mechanics [physics.class-ph]; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Solid mechanics [physics.class-ph]

Jean-Jacques Marigo, Kim Pham. Stability of non localized responses for damaging materials. Vietnam Journal of Mechanics, 2010, 30 (4), pp.1-11. ⟨hal-00490540⟩