On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles.

Noël Lahellec (1) , Pierre Suquet (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

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.

Mots clés: Homogenization; Nonlinear viscoelasticity; Elasto-viscoplasticity; Variational method; Hashin–Shtrikman estimates

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Noël Lahellec, Pierre Suquet. On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles.. Journal of the Mechanics and Physics of Solids, 2007, 55 (9), pp.1932-1963. ⟨10.1016/j.jmps.2007.02.003⟩. ⟨hal-00214209⟩