A time-incremental Eshelby-based homogenization scheme for viscoelastic heterogeneous materials

Stéphane Berbenni (1) , Hafid Sabar (2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 LaBPS - Laboratoire de mécanique Biomécanique Polymère Structures

A time-incremental Eshelby-based homogenization scheme for Maxwellian heterogeneous materials is proposed and discussed. This is based on the exact solution of the heterogeneous Eshelby ellipsoidal inclusion problem obtained in the time domain. In contrast with hereditary methods, the effective behavior as well as the evolution laws of the averaged stresses per phase are solved incrementally in the time domain without need to inverse Laplace or Laplace-Carson transforms. This is made through a time-differential equation to exactly solve a volume term in the integral equation that was generally approximated in previous internal variable methods. The present formulation works for any arbitrary anisotropic ellipsoidal Maxwellian inclusion embedded in an isotropic Maxwellian matrix without any other restrictive assumptions. In order to show the interest of the present approach, a Mori-Tanaka homogenization scheme is applied to two-phase composites using the developed strain rate concentration equations. The results are reported and discussed in comparisons with other existing methods, including hereditary approaches and more recent internal variable approaches, in order to show the efficiency of the present time-incremental homogenization scheme.

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

Stéphane Berbenni, Hafid Sabar. A time-incremental Eshelby-based homogenization scheme for viscoelastic heterogeneous materials. Micromechanics and Nanomechanics of Composite Solids, 2017, 978-3-319-52793-2. ⟨hal-02360507⟩