Self-consistent estimates for nonlinear viscoelastic polycrystals: a simplified resolution of the affine formulation adapted to monotonic loading paths

Rénald Brenner (1, 2) , Olivier Castelnau (1) , Renaud Masson (3) , Brigitte Bacroix (1) , André Zaoui (3)

1 LPMTM - Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux
2 SRMA - Service des Recherches Métallurgiques Appliquées
3 LMS - Laboratoire de mécanique des solides

A simplified resolution of the self-consistent model for non-linear viscoelastic polycrystals is presented. The formulation is based on an affine linearization of the constitutive relations as recently proposed by Masson and Zaoui [4], which adapts Hill's conception of self-consistent modelling to nonlinear viscoelastic behaviours. The approximation of the inverse Laplace-Carson transform introduced here, which is believed to be well adapted to monotonic loading paths, makes the resolution of the whole self-consistent problem possible in the direct time space. This results in a largely simplified numerical algorithm. Comparisons with the predictions of a model treating accurately the inverse Laplace-Carson transform are presented, and very good results are obtained for creep of FCC and HCP polycrystals.

Mots clés: Non Linear Viscoelasticity; Polycrystals; Self-Consistent Scheme

Domaines: Mécanique [physics.med-ph]

Rénald Brenner, Olivier Castelnau, Renaud Masson, Brigitte Bacroix, André Zaoui. Self-consistent estimates for nonlinear viscoelastic polycrystals: a simplified resolution of the affine formulation adapted to monotonic loading paths. Key Engineering Materials, 2002, 177-180, pp.153-158. ⟨10.4028/www.scientific.net/KEM.177-180.153⟩. ⟨hal-00111367⟩