A circular inclusion with circumferentially inhomogeneous non-slip interface in plane elasticity (Q2743623)

Using the plane elasticity, the authors study a circular inclusion with circumferentially inhomogeneous non-slip interface. At the inclusion-matrix interface, the bonding is assumed to be imperfect; especially, the jump in normal displacement is assumed to be proportional to normal traction with proportionality parameter taken to be circumferentially inhomogeneous. Besides, the authors assume that tangential displacements are continuous at the interface. Then, using the principle of analytic continuation, the basic boundary value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function defined inside the circular inclusion. The resulting closed-form solutions include a finite number of unknown constants determined by analyticity requirements and by other supplementary conditions. The authors illustrate the method by some example problems comparing the results with existing solutions. They point out that the circumferential variation of interface damage has a significant effect even on average stresses induced within the circular inclusion.