Investigation of Large Deformations of Composite Plane with Interface Crack Loaded by Uniform Pressure - Mal’kov, V. M.; Mal’kova, Yu. V. (Vestnik, St. Petersburg University. Mathematics, 2020)
The analytical solution to the nonlinear problem of the theory of elasticity for a composite plane formed by the joining of two half-planes of different materials with an interface crack is obtained in this paper. The elastic properties of half-planes are modelled by the semi-linear material. The follower normal pressure orthogonal to the deformed surfaces of the crack is the external load, and the stresses vanish at infinity. The methods of the theory of functions of a complex variable are applied to solve the problem. It is established that critical values of pressure exist, whose excess leads to large displacements, strains, and stresses in the neighborhood of the crack. The critical pressures are on the order of the shear modulus of material and are possible for low-modulus rubber-like materials (elastomers). For rigid materials with large shear modulus, for instance, for metals, the critical pressures are usually not achieved. The formulas for the crack opening are obtained depending on the pressure value and material parameters. Based on the general solution, the asymptotics of the nominal (Piola) stresses and of the Cauchy stresses are constructed in the neighborhood of the crack tip. It is demonstrated that the nominal stresses have the root singularity and the Cauchy stresses have no singularity at the crack tip.