Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials |
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Authors: | A Paquin H Sabar M Berveiller |
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Institution: | (1) Laboratoire de Physique et Mécanique des Matériaux, URA CNRS 1215 ISGMP, Ile du Saulcy, F-57045 Metz Cedex 01, France, FR |
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Abstract: | Summary Based on projection operators, an integral formulation is proposed for elastoviscoplastic heterogeneous materials. The problem
requires a complete mechanical formulation, including the static equilibrium property concerning the known field σ, in addition to the classical field equations concerning the unknown fields ɛ˙ and σ˙. The formulation leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous
elastoviscoplastic medium with elastic moduli C and viscoplastic moduli B.
To approximate the integral equation, the self-consistent scheme is followed. In order to obtain consistent approximation
conditions, we introduce fluctuations of elastic and viscoplastic strain rate fields with respect to known kinematically compatible
fields. It results in a strain rate concentration relation connecting the strain rate at each point to the macroscopic loading
conditions and the local stress field. The results are presented and compared with other models and with experimental data
in the case of a two-phase material.
Received 26 August 1997; accepted for publication 2 July 1998 |
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Keywords: | heterogeneous material elastoviscoplasticity integral equation projection operator self-consistent approximation |
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