Dependence of stress order in notched non-linear elastic solids under anti-plane deformation
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...
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| Format: | Final Year Project |
| Language: | English |
| Published: |
2019
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/77794 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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