J. Phys. IV France
Volume 105, March 2003
Page(s) 231 - 238

J. Phys. IV France
105 (2003) 231
DOI: 10.1051/jp4:20030192

New self-consistent approach for inelastic materials based on translated fields

V. Favier1, H. Sabar2, M. Berveiller1 and S. Berbenni1

1  Laboratoire de Physique et Mécanique des Matériaux, ENSAM, 4 rue Augustin Fresnel, 57078 Metz cedex 3, France
2  Laboratoire de Physique et Mécanique des Matériaux, ISGMP, Ile de Saulcy, 57045 Metz cedex 1, France

In real heterogeneous materials, the simultaneous presence of instantaneous mechanisms (elasticity) and time dependent ones (non linear visco-plasticity) leads to a complex space-time coupling between the mechanical fields, difficult to represent in a simple and efficient way. In this work, a new micro-macro model is proposed, starting from the integral equation and translated strain rate fields. The chosen translated field is the (compatible) viscoplastic strain rate of the (fictitious) viscoplastic heterogeneous medium submitted to a uniform (unknown) boundary condition. The self-consistency condition allows to define these boundary conditions so that a relative simple and compact strain rate concentration equation is obtained. The model is first applied to the case of a twophase composite with isotropie, linear and incompressible visco-elastic properties. In that case, an exact selfconsistent solution using the Laplace-Carson transform is available. The agreement between both approaches appears quite good. Results for elastic-viscoplastic FCC polycrystals are also presented and compared with those obtained from other models.

© EDP Sciences 2003