Investigation of the influence of contact interaction conditions on the stress-strain state of an elastic bilayerbody

Abstract

The aim of this work is to investigate the influence of complex contact interaction conditions on the stress-strain state of an elastic bilayer body of finite dimensions. The case of loading the body with a perfectly rigid, smooth, flat indenter is considered. The following variants of contact interaction between the layers are compared: perfect bonding, possible delamination of smooth layers without slip, and slip between layers with friction forces according to the Coulomb-Amontons law with possible delamination. The contact, bonding, and slip planes are not known in advance and are determined as a result of solving the problem. Using the theory of variational inequalities, the problem is formulated as a quasi-variational inequality. The inequalities are associated with a sequence of minimization problems for functionals over the set of admissible displacements. At each step of the sequence, the normal stresses on the contact surface are determined based on the results of the previous iteration. The obtained variational problems are discretized using the finite element method. Quadratic rectangular finite elements are used for the calculations. Characteristic features of the stress-strain state depending on the contact conditions between the layers and the indenter are revealed. The influence of the indenter length and the order of arrangement of layers with different mechanical properties on the stress-strain state is considered. Placing the stiffer layer at the bottom promotes a more uniform stress distribution in the body. The lowest stresses in the body occur in the case of perfect bonding of the layers when the stiffer layer is at the bottom. Increasing the indenter size can eliminate lag and significantly reduce interlayer slip.