Effective viscoelastic properties of micro-cracked heterogeneous materials

The aim of this paper is to model the effective viscoelastic properties of micro-cracked masonry based on a homogenization approach. The masonry is modeled as a mixture of a micro-cracked viscoelastic mortar matrix and isotropic elastic brick inclusions. Firstly, the effect of micro-cracks on the effective viscoelastic properties of mortar is considered at micro-scale. Secondly, brick inclusions are added in the micro-cracked mortar matrix at mesoscale to simulate effective viscoelastic properties of masonry. The modified Maxwell viscoelastic model is employed for noncracked, micro-cracked mortar matrix and micro-cracked masonry. The use of the same modified Maxwell model of the noncracked mortar to model the viscoelastic properties of the micro-cracked mortar is an approximation. This approximation is carried out in the short- and the long-term behaviors in the Laplace–Carson space. It is validated in transient situation with exact solutions obtained from the inverse Laplace–Carson transform for simple loading conditions. This technique allows avoiding the complexity of the inverse Laplace–Carson transform. The isotropic case with random orientation distribution of open micro-cracks in mortar and with spherical brick inclusions is considered.