Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 55, Issue 9, Pages 1932-1963Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2007.02.003
Keywords
homogenization; nonlinear viscoelasticity; elasto-viscoplasticity; variational method; Hashin-Shtrikman estimates
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A new method for determining the overall behavior of composite materials comprised of nonlinear inelastic constituents is presented. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In this first part of the study the variational technique of Ponte Castaneda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains and to linearize the nonlinear thermoelastic problem. The resulting problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained. The accuracy of the proposed scheme is assessed by comparison of the method with exact results. (C) 2007 Elsevier Ltd. All rights reserved.
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