Modeling and design optimization of adhesion between surfaces at the microscale

A methodology is introduced for designing adhesive interfaces between structures through topology optimization. Design problems involving delaminating structures undergoing small displacements and deformations are studied. Only the effects of adhesive forces acting normal to the surfaces are considered. An interface finite element is presented that couples a penalty contact formulation and a Lennard-Jones model of van der Waals adhesive forces. 2D and 3D design optimization problems are presented in which load-displacement curves of delaminating structures are matched to target responses. The design variables are the adhesive energy per area of interface elements between surfaces as well as the geometry of the delaminating structure. The resulting design problem is solved by gradient based optimization algorithms evaluating the design sensitivities by the adjoint method. The results show that the delamination response can be effectively manipulated by the method presented. Varying simultaneously both adhesive and geometric parameters yields a wider range of reachable target loading curves than in the case varying adhesive energy alone.