A two-level iterative fem technique for rigorous solution of non-linear interaction problems under large deformations

Various problems arising in applied mechanics involve interaction between two bodies having separation, bonding, re-bonding and slip at the interface. Simple FEM models assume one of the two extremes, "bonded interface" or "smooth interface". Alternative spring models have been developed to model slip, shear strength and dilation. These models are applicable for small deformations and coincident nodes at the interface. The paper describes a rigorous solution for the problem which does not sacrifice the simplicity of the FEM approach. In this study the deformations are assumed to be large enough to change the geometry of the problem and the interface is assumed to be a frictional adhesive one with a coulomb failure criterion. The technique examines the interaction of two bodies, namely the slave and master bodies. It simulates frictional slip, separation, bonding and re-bonding of the slave body with respect to the master allowing for large deformations and non-matching nodes at the interface. The proposed solution is iterative where two levels of iterations are used. The first iteration procedure is used to satisfy equilibrium and to deal with the geometrical non-linearity, while the second is used to satisfy the interaction conditions at the interface. The proposed technique is illustrated with a number of test problems of varying complexity. These demonstrate that the approach performs well for problems involving interaction of two bodies under large deformations.