Singular elastostatic fields near the notch vertex of a Mooney–Rivlin hyperelastic body

Abstract

Within the framework of fully nonlinear fracture mechanics under plane deformation conditions, boundary value problem equations for the V-notch vertex problem in an incompressible Mooney–Rivlin material are deduced. Using an asymptotic procedure, the deformation, the Lagrange multiplier and stress fields near the notch vertex are computed and their principal properties are illustrated. First, it is shown that the singularity order depend on the V-notch angle. Second, a change of the singular term for a critical angle was revealed and a logarithmic singular term appears. Based on the results obtained, the deformed V-notch vertex lips near the tip was drawn. The V-notch vertex is shown to open, but not necessary in a symmetric manner. Analysis of the Cauchy stress tensor shows that the component σ 22 dominates the stress field. Some discrepancy with the linear theory have emerged.