Generalized Kelvin model for micro-cracked viscoelastic materials

• We model the viscoelastic properties of micro-cracked materials.
• We base on the homogenization micro–macro approach.
• We propose a technique to avoid the inverse Laplace–Carson transform.

The aim of this paper is to model the viscoelastic properties of micro-cracked materials based on the homogenization micro–macro approach. The isotropic case with random orientation distribution of micro-crack in Burgers nonageing linear viscoelastic solid was previously modeled. This study develops an alternative generalized Kelvin viscoelastic model (GKM) for fractured viscoelastic materials. The use of the same GKM of the non-cracked materials to model the viscoelastic properties of the micro-cracked materials is an approximation. This is a new technique to avoid the complexity of the inverse Laplace–Carson (LC) transform. This approximation is carried out in short and long term behavior in the LC space and is validated in transient situation with exact solution obtained from the inverse LC transform for simple loading condition. This paper focuses on the isotropic case with random orientation distribution of open cracks.