NONSYMMETRIC CAVITY FORMATION AT A CIRCULAR INCLUSION UNDER REMOTE EQUIBIAXIAL LOAD

This paper examines the phenomenon of cavity formation through an anal ysis of the problem of a plane circular elastic inclusion embedded in an unbounded elastic matrix subject to a remote equibiaxial load. Cons istent with infinitesimal strain kinematics, nonlinear behavior is con fined to a cohesive zone so that inclusion-matrix interaction is chara cterized by a nonlinear interface force-interface separation law requi ring a characteristic length for its prescription. Equilibrium solutio ns for both rotationally symmetric and nonsymmetric cavity shapes are sought based on an integral equation formulation together with known e lasticity solutions for circular domains. For values of remote load, i nterface strength and elastic moduli within certain bounds only rotati onally symmetric cavities occur under decreasing characteristic length -inclusion radius ratio. At other parameter values the existence of no nsymmetric cavities is studied by performing a linearized bifurcation analysis about the rotationally symmetric equilibrium state. A post bi furcation analysis is carried out by reducing the governing integral e quations to a truncated set of nonlinear algebraic equations and analy sing those. Stability of equilibrium states is assessed with the Hadam ard stability definition. Calculations for the interfacial tractions a re carried out as well. The study reveals that rotationally symmetric cavities must give way to the abrupt formation of stable nonsymmetric cavities when the interface force attains its maximum value. Thus, the phenomenon of ductile decohesion, or the gradual opening of a cavity coincident with an unloading of the interface, cannot occur (for the s ystem being studied) without artificially constraining the inclusion a gainst rigid displacement.