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Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

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Abstract

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.

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References

  1. Mühlhaus H B, Aifantis E C. A variational principle for gradient plasticity[J]. International Journal of Solids and Structures, 1991, 28(7):845–857.

    Article  MATH  MathSciNet  Google Scholar 

  2. Assempour A, Safikhani A R, Hashemi R. An improved strain gradient approach for determination of deformation localization and forming limit diagrams[J]. Journal of Materials Processing Technology, 2008. DOI 10.1016/j.jmatprotec.2008.04.030

  3. Zhu H X, Karihaloo B L. Size-dependent bending of thin metallic films[J]. International Journal of Plasticity, 2008, 246:991–1007.

    Article  MATH  Google Scholar 

  4. Tsagrakis I, Aifantis E C. Strain gradient and wavelet interpretation of size effects in yield and strength[J]. Mechanics of Materials, 2003, 35(8):733–745.

    Article  Google Scholar 

  5. Aifantis E C. Update on a class of gradient theories[J]. Mechanics of Materials, 2003, 35(3):259–280.

    Article  Google Scholar 

  6. Jiang G L. Nonlinear finite element formulation of kinematic limit analysis[J]. International Journal for Numerical Methods in Engineering, 1995, 38(16):2775–2807.

    Article  MATH  Google Scholar 

  7. Haghi M, Anand L. Analysis of strain-hardening viscoplastic thick-walled sphere and cylinder under external pressure[J]. International Journal of Plasticity, 1991, 7(3):123–140.

    Article  MATH  Google Scholar 

  8. Leu S Y. Analytical and numerical investigation of strain-hardening viscoplastic thick-walled cylinders under internal pressure by using sequential limit analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(25):2713–2722.

    Article  Google Scholar 

  9. Gao X L. An expanding cavity model incorporating strain-hardening and indentation size effects[J]. International Journal of Solids and Structures, 2006, 43(21):6615–6629.

    Article  MATH  Google Scholar 

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Correspondence to Ming-fu Fu  (扶名福).

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(Contributed by FU Ming-fu)

Project supported by the Ph. D. Programs Foundation of Ministry of Education of China (No. 20050403002)

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Li, Ml., Fu, Mf. Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory. Appl. Math. Mech.-Engl. Ed. 29, 1553–1559 (2008). https://doi.org/10.1007/s10483-008-1203-x

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  • DOI: https://doi.org/10.1007/s10483-008-1203-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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