Nonlinear interfacial contact laws in multi-layer elastic-viscoelastic structural systems

Layered structures are widely used in construction, such as pavement structures consisting of multiple layers of different materials or interfaces between bricks and mortar in masonry structures, etc. In analyzing such structures, understanding the properties of the interface between two layers of materials is essential. If one layer of material contains cracks and layers exhibit viscoelastic behavior, determining the properties of the interface becomes challenging. This study proposes a constitutive mechanical law to model the behavior of the interface between a microcracked viscoelastic medium and an undamaged elastic body based on the homogenization method. The interface is modeled by a layer of zero thickness. The coupling between the homogenization technique and the Griffith’s theory is used to provide the effective behavior of the micro-cracked medium. The interface is modelled as an effective medium (EF) characterized by normal and tangential stiffnesses (CN, CT ). In this work, two viscoelastic models are considered, i.e., Burger and Modified Maxwell. The formulas of CN and CT for two cases of crack distributions (isotropic and transversely isotropic) are obtained by asymptotic techniques where the thickness of the joint tends to zero