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

Abstract

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.

Keywords:

• Gibbs Potential
• Lode invariants
• strain limiting model
• implicit elasticity
• V-notch
• stress concentration factor

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In general, even if the form $\mathbf{B}=\mathbf{f}(\mathbf{T})$ is invertible, if we linearize and then invert, it shall be different from the classical linear elastic model. On the other hand, if we invert $\mathbf{B}=\mathbf{f}(\mathbf{T})$ and then linearize, it will always lead to the classical linear model [15].