A constitutive model for interface problems with frictional contact and cohesion

• A new constitutive model for frictional interfaces with cohesion is formulated.
• The macroscopic response is characterized based on the principle of superposition.
• A weak form with regularization of the friction and cohesion terms is derived.
• Results on the representative problem are presented with comparison to experiments.

A numerical approach to modelling contact problems with a unified friction and cohesion interface is formulated. A new nonlinear friction law is suggested for modelling micro-slip of metallic junctions due to contact asperities, and an associated cohesive zone due to adhesion describes the linear portion of the unified total interfacial hysteresis. A variational equality including both the regularized friction and cohesion terms is formulated for the numerical solution of the derived boundary value problem. The suggested modelling technique is readily implementable in the finite element method. There is an application on the representative problem involving the adhesively bonded and significantly normal-stressed contact surface. Macroscopic constitutive relationships between the cyclic tangential load and micro-displacements are established for the set of constant compressive normal loads. The related micromechanical arguments and experimental observations supporting the modelling theory are addressed.