A homogenization approach for effective viscoelastic properties of porous media

• We model the effective viscoelastic properties of porous materials.
• Generalized Maxwell rheological model is considered.
• This is a new technique to avoid the complexity of the inverse Laplace–Carson 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.
• An application for cement is considered.

The aim of this paper is to model the effective linear non-ageing viscoelastic properties of porous media based on a micromechanical approach. A porous medium is modeled as a mixture of a viscoelastic matrix and pore inclusions. The Generalized Maxwell (GM) viscoelastic model is employed for both the solid matrix and the porous medium. The effective parameters of the viscoelastic GM rheology of the porous medium, which are functions of the porosity and the viscoelastic properties of the solid phase, are derived considering the short and long term behaviors in Laplace–Carson space (LC). They are validated against exact solutions obtained from the inverse LC transform for a simple configuration. The proposed method allows avoiding the complexity of the inverse LC transform in general condition. An application for cement with assumption of spherical pore is considered to illustrate the powerful of this method.