Generalized Maxwell model for micro-cracked viscoelastic materials

This paper aims to model the effective viscoelastic properties of micro-cracked materials based on the homogenization micro-macro approach. The isotropic case with random orientation and parallel distribution of micro-cracks in Burger and generalized Kelvin non-ageing linear viscoelastic solids was recently considered. To complete these works, this paper develops a model to estimate viscoelastic properties of materials that are constituted of two phases: a non-cracked phase described by Generalized Maxwell model and micro-cracks. The methodology consists in an approximation by using the same Generalized Maxwell model of the non-cracked phase for the overall cracked material. The crucial advantage of this technique is to avoid the complexity of the inverse Laplace–Carson (LC) transform. The approximation is carried out in short- and long-term behaviors in the LC space and validated in transient situation with exact solution obtained from the inverse LC transform in simple loading condition. Useful explicit formulas are provided for calculation of effective viscoelastic properties of isotropic micro-cracked media.