Path independent integrals to identify localized plastic events in two dimensions

Mehdi Talamali (1) , Viljo Petäjä (1) , Damien Vandembroucq (1, 2) , Stéphane Roux (3)

1 SVI - Surface du Verre et Interfaces
2 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)
3 LMT - Laboratoire de Mécanique et Technologie

We use a power expansion representation of plane elasticity complex potentials due to Kolossov and Muskhelishvili, to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first order singularities of quadrupolar and dipolar symmetry which can be associated respectively to pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. Constructing holomorphic functions from the displacement field and its derivatives, it is possible to define path independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations which are believed to be the key mechanisms for plasticity of amorphous materials.

Mots clés: plasticity; amorphous; inclusion; singularity

Domaines: Autre [cond-mat.other]

Mehdi Talamali, Viljo Petäjä, Damien Vandembroucq, Stéphane Roux. Path independent integrals to identify localized plastic events in two dimensions. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78 (1), pp.016109. ⟨hal-00221370v2⟩