Dependence of stress order in notched non-linear elastic solids under anti-plane deformation

• Main Author: Wong, Wei Jiet
• Other Authors: Wu Mao See
• Format: Final Year Project
• Language: English
• Published: 2019
• Subjects: DRNTU::Engineering::Mechanical engineering
• Online Access: http://hdl.handle.net/10356/77794
• Institution: Nanyang Technological University

An investigation was done on the dependence of stress order in notched non-linear elastic solids under anti-plane deformation. The equilibrium equations are expressed in terms of the first Piola–Kirchhoff stresses, which are interchanged by displacements up till the third-order. The outcomes of the variable-coefficient partial differential equations are determined numerically, subjected to vanishing out-of-plane shear tractions on the faces of the notch. The key results are: (i) unlike in linear elastic solids, the stress exponent factoring the variation of stress with distance from the tip of a notch changes with the elastic constants (ii) In the case of notch angle being 180°, the stress exponent decreases with the decrease in the first Lamé constant λ, second Lamé constant μ(shear modulus), the third-order elastic constant n and with the increase in the magnitude of the negative third-order constant m.