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Special Section Papers

Stochastic Finite Element Method Elasto-Plastic Analysis of the Necking Bar With Material Microdefects

[+] Author and Article Information
Michał Straąkowski

Department of Structural Mechanics,
Faculty of Civil Engineering, Architecture and
Environmental Engineering,
Łódź University of Technology,
Al. Politechniki 6,
Łódź 90-924, Poland
e-mail: michal.strakowski@p.lodz.pl

Marcin Kamiński

Professor
Department of Structural Mechanics,
Faculty of Civil Engineering, Architecture and
Environmental Engineering,
Łódź University of Technology,
Al. Politechniki 6,
Łódź 90-924, Poland
e-mail: marcin.kaminski@p.lodz.pl

1Corresponding author.

Manuscript received August 28, 2018; final manuscript received January 30, 2019; published online June 5, 2019. Assoc. Editor: George Stefanou.

ASME J. Risk Uncertainty Part B 5(3), 030908 (Jun 05, 2019) (12 pages) Paper No: RISK-18-1057; doi: 10.1115/1.4043401 History: Received August 28, 2018; Revised January 30, 2019

The main aim of this work is to study a significance of structural microdefects and their uncertainty in structural steel on its elastoplastic large deformations subjected to tensile test with the use of the generalized stochastic perturbation method. Elastoplastic behavior of the macroscopically homogeneous material is defined by the Gurson–Tvergaard–Needleman (GTN) constitutive model, where Young's modulus and this model constants q1 and q2 are consecutively randomized according to the Gauss probability distribution. The stochastic finite element method (SFEM) analysis has been carried out in the system abaqus for the problem of necking under tension to compute the first four probabilistic moments and coefficients of displacements, deformations, and stresses. The tenth-order perturbation scheme has been implemented via statistically optimized least-squares method (LSM) determination of the structural nodal polynomial response functions. A comparison with Monte Carlo simulation (MCS) as well as the semi-analytical integral technique based on the same polynomial bases confirms applicability of the method proposed for the input uncertainty not larger than 0.10. Further numerical experiments with this constitutive law including stochastic nucleation and/or coalescence would be necessary to better understand deformations and stresses of stochastic porous plastic materials. This model may find its applications in various stress states of the plastic materials with voids as well as in numerical simulations of the composite materials with imperfect interphases, for instance, where some parameters exhibit initial Gaussian statistical scattering.

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References

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Figures

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Fig. 1

Stochastic finite element method flow chart

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Fig. 2

Geometry and initial notch of the specimen

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Fig. 3

Mechanical (left) boundary conditions and mesh

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Fig. 4

Displacements without (left) and with pores (right)

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Fig. 5

Plastic strains without (left) and with pores (right)

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Fig. 6

Reduced stress without (left) and with pores (right)

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Fig. 7

Horizontal displacements at the beginning (10% of the nonlinear analysis progress) and in the end of the analysis

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Fig. 8

Response functions of the extreme horizontal displacement as a function of E without (left) and with pores (right)

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Fig. 9

Response functions of the extreme horizontal displacement as a function of q1

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Fig. 10

Response functions of the extreme horizontal displacement as a function of q2

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Fig. 11

Expectations of the extreme horizontal displacement E[ux(E)] without (left) and with pores (right)

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Fig. 12

Expectations of the extreme horizontal displacement E[ux(q1)]

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Fig. 13

Expectations of the extreme horizontal displacement E[ux(q2)]

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Fig. 14

Coefficient of variation of the extreme horizontal displacement α[ux(E)] without (left) and with pores (right)

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Fig. 15

Coefficient of variation of the extreme horizontal displacement α[ux(q1)]

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Fig. 16

Coefficient of variation of the extreme horizontal displacement α[ux(q2)]

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Fig. 17

Skewness of the extreme horizontal displacement S[ux(E)] without (left) and with pores (right)

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Fig. 18

Skewness of the extreme horizontal displacement S[ux(q1)]

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Fig. 19

Skewness of the extreme horizontal displacement S[ux(q2)]

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Fig. 20

Kurtosis of the extreme horizontal displacement κ[ux(E)] without (left) and with pores (right)

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Fig. 21

Kurtosis of the extreme horizontal displacement κ[ux(q1)]

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Fig. 22

Kurtosis of the extreme horizontal displacement κ[ux(q2)]

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