Contact interaction of machine elements with non–linear elastic intermediate layer

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The work presents a variational formulation of a contact problem for elastic bodies with an intermediate nonlinear contact layer. The layer is introduced in order to model compliant gaskets, coatings and roughness between or on the surface of the machine parts. The contact conditions in this case incorporate not only the elastic displacements but the local deformations attributed to the contact layer. This additional deformation is determined at every point of the contact surface as a function of the acting normal tractions. This relation is in general nonlinear and can be accounted for by a special term in the complementary energy updating the original Kalker’s variational principle. As an outcome the problem acquires besides the structural nonlinearity (i.e. contact) as well the physical nonlinearity. This means that one needs to solve a system comprising both the inequalities and nonlinear equations. This is done by computing consecutive approximations from problem linearizations. The two particular variants of this procedure comprise the method of augmented gap and the method of variable compliance. Newton-Raphson iterations are also considered as an option. With this model and the numerical analysis method at hand one can solve certain inverse problems. The goal is to justify the the geometrical shape of the contacting bodies as well as the physical parameters of the contact layers. The objective criteria enforcing strength and durability in terms of the contact loads are proposed for the optimization. Furthermore deformation components arising from the applied external loads and the corresponding correction of the contact geometry are introduced as an additional design factor.