A Review on Modelling Polymer Composites via Anisotropic Viscoelasticity

Polymer composites exhibit not only anisotropic (directional-dependent) but also viscoelastic (time-dependent) behaviors. Modelling via anisotropic viscoelasticity may then provide more accurate information about their mechanical behaviors. In this paper, we present some recent studies on the stress analysis of anisotropic viscoelastic solids solved by the employment of elastic-viscoelastic correspondence principle and time-stepping method. Since both approaches solve the problems of anisotropic viscoelasticity through the associated elastic systems, some analytical solutions and boundary element methods (BEMs) including regular BEM (RBEM), special BEM (SBEM), and boundary-based finite element method (BFEM) developed previously for anisotropic elasticity can now be converted to their corresponding solutions and methods for anisotropic viscoelasticity. After the successful conversion, several analytical solutions and BEMs are re-derived and re-coded for anisotropic viscoelasticity. Implementation of some representative examples shows that the approach with time-stepping method is more general and efficient compared to that with correspondence principle. Moreover, the former is applicable for both time-independent and time-dependent boundary value problems, whereas the latter can only be applied to the cases with time-invariant boundaries.