Locally-exact homogenization of viscoelastic unidirectional composites

Abstract

The elasticity-based, locally-exact homogenization theory for periodic materials with hexagonal and tetragonal symmetries is extended to accommodate linearly viscoelastic phases via the correspondence principle. The theory employs Fourier series representations for fiber and matrix displacement fields in the cylindrical coordinate system that satisfy exactly equilibrium equations and continuity conditions in the interior of the unit cell. The inseparable exterior problem requires satisfaction of periodicity conditions efficiently accomplished using previously introduced balanced variational principle which ensures rapid displacement and stress field convergence in the presence of linearly viscoelastic phases with relatively few harmonic terms. The solution’s stability and efficiency, with concommitant simplicity of input data construction, facilitate rapid identification of the impact of phase viscoelasticity and array type on homogenized moduli and local fields in wide ranges of fiber volume fraction. We illustrate the theory’s utility by investigating the impact of fiber array type and matrix viscoelastic response (constant Poisson’s ratio vs constant bulk modulus) on the homogenized response and local stress fields, reporting previously undocumented differences. Specifically, we show that initially small differences between hexagonal and square arrays are magnified substantially by viscoelasticity. New results on the transmission of matrix viscoelastic features to the macroscale are also generated in support of construction of homogenized viscoelastic functions from experimental data.