Adhesive Contact : a Survey and a Unified Formulation
Résumé
A brief survey of the most widely used Cohesive Zone Models is first presented and discussed. Then, a general framework for these laws is given under the form of a unified formulation recently proposed by Del Piero and Raous (Del Piero, Raous [1]). This unified formulation is based on : – general laws, typically, energy conservation and dissipation principles, that is, mechanical versions of the first two laws of thermodynamics, – a set of state variables, that is, an array of independent variables which fully determine the response to all possible deformation processes, – a set of elastic potential and dissipation potentials, which are functions of state in terms of which the general laws take specific forms, – a set of constitutive assumptions. The behavior of the interface is first characterized by two given loading curves f n (u n) and f t (u t) , which are supposed to be star-shaped with respect to the origin, where u n and u t are the normal and tangential components of the relative displacement on the interface and R n and R t are respectively the components of the contact force. A state variable α is introduced to measure the current intensity of damage. The variables {u n , u t , α} have to satisfy a set of inequalities which defines the state space. To exemplify this, for the special case where there is no viscosity, the loading curve R n =f n (u n) and the state space are given for the normal components in Fig.1 (a) and (b). The response due to a deformation process of loading-unloading starting from the origin is represented by the dashed line in the force-displacement plane (a) and in the state space (b). As described in [1], the strain energy is then given by : Ψ(u n , u t , α) = 1 2 g n (α)u
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