Complete elastic–plastic stress asymptotic solutions near general plane V-notch tips
| Autor: | Zongjun Hu, Changzheng Cheng, Cong Li, Zhongrong Niu, Bin Hu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Plane (geometry) Applied Mathematics Mathematical analysis 02 engineering and technology 01 natural sciences Displacement (vector) Stress (mechanics) Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering Modeling and Simulation Ordinary differential equation 0103 physical sciences Hardening (metallurgy) 010301 acoustics Matrix method Plane stress |
| Zdroj: | Applied Mathematical Modelling. 87:91-110 |
| ISSN: | 0307-904X |
| DOI: | 10.1016/j.apm.2020.04.023 |
| Popis: | An efficient method is developed to determine the multiple term eigen-solutions of the elastic–plastic stress fields at the plane V-notch tip in power-law hardening materials. By introducing the asymptotic expansions of stress and displacement fields around the V-notch tip into the fundamental equations of elastic–plastic theory, the governing ordinary differential equations (ODEs) with the stress and displacement eigen-functions are established. Then the interpolating matrix method is employed to solve the resulting nonlinear and linear ODEs. Consequently, the first four and even more terms of the stress exponents and the associated eigen-solutions are obtained. The present method has the advantages of greater versatility and high accuracy, which is capable of dealing with the V-notches with arbitrary opening angle under plane strain and plane stress. In the present analysis, both the elastic and the plastic deformations are considered, thus the complete elastic and plastic stress asymptotic solutions are evaluated. Numerical examples are shown to demonstrate the accuracy and effectiveness of the present method. |
| Databáze: | OpenAIRE |
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