A novel mathematical procedure to evaluate the effects of surface topography on the interfacial state of stress

A mathematical procedure is developed to utilize the complementary energy method, by minimization, in order to find an approximate solution to the 3-D stress distributions in bonded interfaces of dissimilar materials. In order to incorporate the effects of surface topography, the interface is expressed as a general surface in Cartesian coordinates, i.e., F( x, y, z) = 0. The 3-D stress functions are used to produce 3-D stress components in the dissimilar materials. At the interface the internal tractions in each of the coordinate directions are balanced by the mathematic procedure. By using a penalty function method of the optimization theory, the integration of the complementary energy produces the necessary equations to solve the 3-D stress distribute problem on the interface.; In this paper, the fiat interface problem, i.e., y = 0 surface is considered for verification of the method by comparison with the FEA method. Comparison of the results reveals our new mathematical procedure to be a promising method for describing interfacial stress of the bonded materials. Then the results for the interfaces y = x/2, y = x2 and x 2 + (y − 2)2 + z 2 = 4 are presented. A noticeable finding in these results is that the stress jumps at the interface predicted in elasticity theory are presented in each calculation example, but the FEA method used here has difficulty to show the stress jumps on the interfaces.