Incremental variational principles. Application to the homogenization of nonlinear dissipative composites.
Résumé
This study is devoted to the overall response of nonlinear composites comprised of phases which have a partly reversible and partly irreversible behavior. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases are reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a nonuniform transformation field. Two different techniques for approximating the nonuniform eigenstrains by piecewise uniform eigenstrains and for linearizing the nonlinear thermoelastic problem will be presented.