Stress growth in the vicinity of radiused V-notch subjected to in-plane loading for a strain limiting model based on Lode invariants of stress

Based on a Gibbs potential formulation for implicit elastic bodies, we propose a new strain limiting constitutive relation using Lode invariants of stress, and numerically study a non-dimensionalized problem of a plate with radiused V-notch subjected to tensile traction. The stress predicted by the new relation agrees with the linearized elastic model beyond a certain distance from the notch-tip. As we approach the tip, the stress associated with the new constitutive relation increases rapidly, and it is nonlinear in the vicinity of the radiused-tip, unlike bounded stress predicted by the linearized elastic model.