Effective behavior of linear viscoelastic composites: A time-integration approach

A new method for determining the overall behavior of composite materials comprised of linear viscoelastic constituents is presented. Unlike classical methods which are based on the Laplace transform, the present method operates directly in the time-domain. 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 linear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). The variational technique of Ponte Castan˜eda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains. The latter 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 obtained either by full finite element simulations in time-domain or by available analytical results obtained by the Laplace transform.