A micro/macro homogenization approach for viscoelastic creep analysis with dissipative correctors for heterogeneous woven-fabric layered media

Abstract

The analysis of heterogeneous structures containing micromechanical details is an active area of interest in composite materials. The present investigation proposes a novel finite-element approach for studying the viscoelastic creep problem in dual length-scale heterogeneous materials. To illustrate the approach, constituents at the micro-level are assumed to be isotropic single-parameter Kelvin–Voigt viscoelastic solids. Of the various homogenization approaches, because of its inherent advantages, the asymptotic expansion homogenization (AEH) approach is employed to resolve the multi-scale issue. Of key interest is the observation of the so-called dissipative corrector, a direct result of the mathematical derivation of the homogenized constitutive equation. Physically, it is due to the junction of dissimilar dissipative materials at the micro-level but it is required to ensure satisfaction of the equilibrium equations at both length scales. The analytical and computational developments employ existing material properties and constants to determine all relevant homogenized properties. A closed-form solution is employed to verify the present formulations for a degenerated case of a homogeneous viscoelastic material subject to constant creep. Several test cases are also presented to illustrate the observations for a microstructure resembling layered woven fabric composites.