Elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states

Ohno, Nobutada; Tsuda, Makoto; Kamei, Takafumi

doi:10.1016/j.finel.2012.11.001

Cited by 24 publications

(41 citation statements)

References 31 publications

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“…and can be semi‐implicitly implemented in finite element methods as follows. The constitutive variables at

n + 1

, except for

Δ ε_{n + 1}^{normalp}

ρ_{n + 1}

, and

c_{n + 1}

, are fully implicitly computed using the elastic trial stress scheme and the backward Euler method, as demonstrated in , under the assumption that

Δ ε^{normalp}

, ρ, and c do not vary in [ n , n +1]. The consistent tangent modulus

\partial {bold-italicσ}_{n + 1} / \partial^{Δ} {bold-italic ε}_{n + 1}

is also computed. For

{bold-italic ε}_{n + 1}^{p}

determined in step 1,

^{normalΔ} ρ_{n + 1}

and

^{normalΔ} {boldc}_{n + 1}

are computed using Eqs.…”

Section: Implementation In Finite Element Methodsmentioning

confidence: 99%

“…The semi‐implicit integration scheme described in Sect. was implemented in Abaqus by extending the UMAT subroutine developed in . A quarter of the longitudinal cross section of the notched bar was divided into 132 finite elements using eight‐noded quadrilateral axisymmetric solid elements (CAX8R).…”

Section: Finite Element Analysis Of Cyclically Loaded Notched Barmentioning

confidence: 99%

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Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

et al. 2017

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Key wordsCyclic plasticity, constitutive model, cyclic hardening, strain range dependence, plastic strain surface.A resetting scheme is proposed for correctly evaluating the plastic strain range to analyze structural components subjected to regular cyclic loading following pre-loading. In this scheme, a plastic strain surface, referred to as the plastic-strainrange surface in the present paper, is reset to a point and re-evolves every cycle, with its size at the end of the last cycle considered to be the plastic strain range of the current cycle. This resetting scheme provides a definite value for the evolution parameter of the plastic-strain-range surface irrespective of the amounts of cyclic hardening, pre-straining, and ratcheting. The resetting scheme is implemented in a cyclic viscoplastic model in finite element methods, and is applied to analyze a notched bar subjected to cyclic loading at its ends. Furthermore, the validity of the resetting scheme for non-proportional cyclic loading is examined by analyzing the cyclic behavior along elliptic and rhombic strain paths. It is shown that the resetting scheme allows the use of a definite value for the evolution parameter of the plastic-strain-range surface in the presence of any cyclic hardening and/or ratcheting. Moreover, it is shown that the resetting scheme can be valid for cyclic loading with a certain degree of non-proportionality.

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“…and can be semi‐implicitly implemented in finite element methods as follows. The constitutive variables at

n + 1

, except for

Δ ε_{n + 1}^{normalp}

ρ_{n + 1}

, and

c_{n + 1}

, are fully implicitly computed using the elastic trial stress scheme and the backward Euler method, as demonstrated in , under the assumption that

Δ ε^{normalp}

, ρ, and c do not vary in [ n , n +1]. The consistent tangent modulus

\partial {bold-italicσ}_{n + 1} / \partial^{Δ} {bold-italic ε}_{n + 1}

is also computed. For

{bold-italic ε}_{n + 1}^{p}

determined in step 1,

^{normalΔ} ρ_{n + 1}

and

^{normalΔ} {boldc}_{n + 1}

are computed using Eqs.…”

Section: Implementation In Finite Element Methodsmentioning

confidence: 99%

Section: Finite Element Analysis Of Cyclically Loaded Notched Barmentioning

confidence: 99%

Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

et al. 2017

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“…The stress-strain hysteresis loop in the beginning of the tests was used. Only cyclic hardening was considered to obtain the material parameters as mentioned in the report [11].…”

Section: ℃mentioning

confidence: 99%

“…The use of the yield surface in macroscopic cyclic plasticity theories ensures the accurate description of the Bauschinger effect. The Armstrong and Frederick (A-F) [7] model, improved by Chaboche [8], Cailletaud [9], Macdowell [10], Ohno [11], Kang [12] and Khan [13] is suitable for the description of cyclic kinematic hardening. The splitting of the back stress into several parts was found to be successful for kinematic hardening in the LCF.…”

Section: Introductionmentioning

confidence: 99%

A low cycle fatigue model for low carbon manganese steel including the effect of dynamic strain aging

Zhi

Wagner

Wang

et al. 2016

Materials Science and Engineering: A

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Carbon-manganese steel A48 (French standards) is used in steam generator pipes of the nuclear power plant where it is subjected to the cyclic thermal load. The Dynamic Strain Aging (DSA) influences the mechanical behavior of the steel in low cycle fatigue (LCF) at favorable temperature and strain rate. The peak stress of A48 steel experiences hardening-softening-hardening (HSH) evolution at 200°C and 0.4%s -1 strain rate in fatigue loading. In this study, isotropic and kinematic hardening rules with DSA effect have been modified. The HSH evolution of cyclic stress associated with cumulative plastic deformation has also been estimated.

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“…One is explicit (see, e.g., [3][4][5][6][7][8]). The other is implicit (see, e.g., [9][10][11][12]). A method is explicit if the equation of motion of the current time step is not applied to determine the current displacement, while it is implicit if that is involved.…”

Section: Introductionmentioning

confidence: 99%

An explicit time integration method for structural dynamics using septuple B-spline functions

Wang

Jian

Luo

2013

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper, an explicit time integration method with three parameters is proposed for structural dynamics using periodic septuple B‐spline interpolation polynomial functions. In this way, by use of septuple B‐splines, the authors have proceeded to solve the DE of motion governing a single DOF system, and later, the presented method has been generalized for a multiple DOF system. In the proposed method, a direct recursive formula for response of the system was formulated on the basis of septuple B‐spline interpolation approximation. In terms of the specific requirements of this proposed method, two initialization approaches are given for initial calculation. One is called direct initialization, and the other is indirect initialization. The stability analysis of the proposed method illustrates that, by use of adjustable parameters, a high‐frequency response can be damped out without inducing excessive algorithmic damping in important low frequency modes. The computational accuracy and efficiency of the proposed method is demonstrated with three numerical examples, and the results from the proposed method are compared with those from some of the existent numerical methods, such as the Newmark and Wilson‐ θ methods. The compared results show that the proposed method has high accuracy with low time consumption. Copyright © 2013 John Wiley & Sons, Ltd.

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Elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states

Cited by 24 publications

References 31 publications

Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

A low cycle fatigue model for low carbon manganese steel including the effect of dynamic strain aging

An explicit time integration method for structural dynamics using septuple B-spline functions

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