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Research Papers: Design and Analysis

Constitutive Law of Finite Deformation Elastoplasticity With Proportional Loadings

[+] Author and Article Information
H. Darijani

Mechanical Engineering Department,
Shahid Bahonar University of Kerman,
Jomhouri Boulevard,
P.O. Box 76175-133, Kerman, Iran
e-mail: darijani@uk.ac.ir and hdarijani@gmail.com

R. Naghdabadi

Mechanical Engineering Department,
Institute for Nano Science and Technology,
Sharif University of Technology,
Azadi Ave,
Tehran 145888-9694, Iran

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 21, 2012; final manuscript received May 12, 2013; published online September 18, 2013. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 135(6), 061201 (Sep 18, 2013) (7 pages) Paper No: PVT-12-1152; doi: 10.1115/1.4024581 History: Received September 21, 2012; Revised May 12, 2013

In this paper, decomposition of the total strain into elastic and plastic parts is investigated for extension of elastic-type constitutive models to finite deformation elastoplasticity. In order to model the elastic behavior, a Hookean-type constitutive equation based on the logarithmic strain is considered. Based on this constitutive equation and assuming the deformation theory of Hencky as well as the yield criteria of von Mises, the elastic-plastic behavior of materials at finite deformation is modeled in the case of the proportional loading. Moreover, this elastoplastic model is applied in order to determine the stress distribution in thick-walled cylindrical pressure vessels at finite deformation elastoplasticity.

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References

Figures

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Fig. 1

Multiplicative decomposition of the deformation gradient

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Fig. 2

The isolated strip from a pressurized thick-walled cylinder

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Fig. 3

Comparison of the hoop stresses obtained based on the present method and analytical method [8] for a cylinder with B/A = 3,n = 1,E/σy0 = 500,E1 = 0 and P1/σy0 = 1.115

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Fig.4

Comparison of the hoop stresses obtained based on the present technique and analytical method for a cylinder with B/A = 3,n = 1,E/σy0 = 500,E1/σy0 = 100 under internal pressure P1/σy0 = 1.574

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Fig. 5

Comparison of the hoop stresses obtained based on the small and finite deformations in a cylinder made of linear strain-hardening with B/A = 3,n = 1,E/σy0 = 50,E1/E = 0.2 under internal pressure P1/σy0 = 2.25

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Fig. 6

Comparison of the equivalent strains obtained based on the small and finite deformations in a cylinder with B/A = 3,n = 1,E/σy0 = 50,E1/E = 0.2 under internal pressure P1/σy0 = 2.25

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Fig. 7

Comparison of the hoop stresses obtained based on the small and finite deformations in a cylinder made of nonlinear strain-hardening with B/A = 3,n = 0.6,E/σy0 = 50,α/σy0 = 12 under internal pressure P1/σy0 = 3.5

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Fig. 8

Comparison of the equivalent strains obtained based on the small and finite deformations in a cylinder with B/A = 3,n = 0.6,E/σy0 = 50,α/σy0 = 12 under internal pressure P1/σy0 = 3.5

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Fig. 9

Deviation percentage between the equivalent strains at the inner radius for a cylinder with B/A = 5,E/σy0 = 100

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Fig. 10

Deviation percentage between the hoop stresses at the inner radius for a cylinder with B/A = 5,E/σy0 = 100

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