The present paper is devoted to the proposal of a theoretical formulation for an isotropic damage model with strain gradient. The approach is based on the non-local estimates of Drugan and Willis (1996), exposed in terms of energetic methods, for the purpose of damage modelling. We ﬁrst focus on the derivation of the non-local constitutive equations for the damage model which is fully analysed from the thermodynamics point of view. It is shown that the positive deﬁniteness of the thermodynamic potential and the intrinsic dissipation are not ensured for every loading paths. The choice of the damage variable is brieﬂy discussed. The equilibrium equation and the boundary conditions are presented. Then, the model is applied to the study of strain gradient torsion problem, for which the axi-symmetric solution is established. This allows us to study the size effect and to evaluate the impact of the non-local term on the damage evolution and the non-linear behaviour of the bar.
C. Oliver-Leblond*, H. Dumontet, D. Kondo
Micro-mechanics Damage model Strain gradient