Application Of Homogenization Method In Continuum Micromechanics To Viscoelastic Composites

Micro-mechanics homogenization theory uses a homogenous macro structure together with a heterogeneous micro one to describe the composite structure considered. The mechanics variables are represented as functions of macro and micro-coordination and are developed in terms of the ratio of the micro and macro coordination. Then the original problem can be described as the combination of micro homogenization problems and a macro one. The solution of these problems provides answers to the prediction of effective properties and the determination of the micro stress field in them.In this paper, based on the asymptotic homogenization, the periodic boundary conditions for the unit cell are established by using the ANSYS Parametric Design Language, and the problem of the unit cell is solved by finite element method. The effect of microstructure on elastic properties of composites is examined, comparisons with experimental results and other results are presented, and the effective modulus and Poisson's ratio for different cubic fiber orientations are analyzed.The problem of viscoelastic multi-layered media is studied, the matrix is assumed linear and isotropic viscoelastic and the reinforcement is assumed linear and isotropic elastic. Based on the homogenization of linear elastic multi-layered media, the correspondence principle in viscoelasticity is applied and the problem in the Carson domain is solved. The inversion to the time domain of the effective relaxation moduli and the effective Poisson coefficients of multi-layered media is carried out when the Burgers model is used to represent the viscoelastic behavior of the matrix. Finally, comparisons with experimental results and other results are presented.The formulas of the relaxation functions of a kind of unidirectional reinforced composites are obtained by using the homogenization method twice. The inversion to the time domain of the effective relaxation modulus of this kind of composites is carried out. Finally, comparisons with other results are presented.