Methods appropriate for the dynamic analysis and interaction of structures with adhesive and contact effects along interfaces will be developed. A time domain formulation with the direct Boundary Element Method (BEM) and an incremental stepwise holonomic technique will be used for the nonlinear dynamic problem.
Within each step a holonomic nonlinear elastic analysis problem which leads to a hemivariational inequality arises. For monotone possibly multivalued interface laws it is a variational inequality. For nonmonotone, possibly multivalued adhesive interface laws a monotone decomposition technique will be applied. Difference of monotone laws or equivalently of convex potentials lead to a system of variational inequalities or multilevel optimisation techniques which fully utilise the convex analysis results. In a more general setting quasidifferentiable optimisation techniques will be applied. The arising highly nonlinear dynamic interaction effect will be modelled in this way by means of methods based on up to date nonsmooth analysis and optimisation, and computational mechanics methods.
The development of the theory, the algorithmic implementation and the demonstration of the features of the model by means of extensive numerical experiments lie within the objectives of the proposed work.