Robust integration schemes for generalized viscoplasticity with internal-state variables

Saleeb, A. F.; Wilt, T. E.; Li, W.

doi:10.1016/s0045-7949(99)00020-6

Cited by 19 publications

(11 citation statements)

References 25 publications

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“…superior stability and convergence properties for isotropic and anisotropic coupled viscoelastoplastic-damage models [6,7]. The closed-form expressions for the tangent stiffness arrays are derived such that their dimensions are independent of the number of the state variables employed (stress tensor and tensorial viscoplastic state variables), i.e.…”

Section: Analysis Modulementioning

confidence: 99%

“…It is well known that the classical Newton-Raphson scheme is fast and stable only when the trial solution is close to the converged value. Thus, the purpose of the line search algorithm is to guide the solution towards convergence by searching for a scalar multiplier that adjusts the amount of the increment vector to be updated during an iteration [7]. On the constitutive level, the line search is used to adjust the suitable increment of stress and internal variables to guarantee the convergence of the local iterations.…”

Section: Analysis Modulementioning

confidence: 99%

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Interactive software for material parameter characterization of advanced engineering constitutive models

Saleeb

Marks

Wilt

et al. 2004

Advances in Engineering Software

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Section: Analysis Modulementioning

confidence: 99%

Section: Analysis Modulementioning

confidence: 99%

Interactive software for material parameter characterization of advanced engineering constitutive models

Saleeb

Marks

Wilt

et al. 2004

Advances in Engineering Software

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“…The related evolution problem has received much attention mostly between the late seventies and the eighties, resulting in significant advances in the integration schemes [13][14][15][16][17][18]. For practical industrial applications and in the case of viscoplasticity, return mapping algorithms represent a very common scheme to integrate the rate constitutive equations [13,[19][20][21][22][23]. In this process, associated with a Newton iterative procedure, an elastic predictor is first estimated before being corrected onto a suitably updated yield surface.…”

Section: Introductionmentioning

confidence: 99%

A time increment control for return mapping algorithm applied to cyclic viscoplastic constitutive models

Szmytka

Forre

Augustins

2015

Finite Elements in Analysis and Design

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a b s t r a c tThis paper proposes two algorithms for better controlling the size of time increment in case of returnmapping integration scheme for elasto-viscoplastic constitutive models. Computation errors in terms of local stress-strain loops in Finite Element Analyses could indeed have a very strong impact on fatigue lifetime estimation protocol if time increment size are freely chosen by the FE solver. Proposed algorithm enables both to precisely describe the transition between elasticity and viscoplasticity and to avoid too important increase of time step during large viscoplasticity evolutions. The precision of the computed mechanical answer has been successfully tested for different kinds of multi-axial and anisothermal loading conditions on simple finite element and more complex meshed structures. Fatigue lifetime estimation errors have also been investigated for stabilized stress-strain cycle and common criteria and the proposed algorithm show very precise results with a limited computation time increase and without drastic limitation of the time increment size.

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“…in terms of the effective stress, the plastic multiplier or the 'magnitude' of the inelastic strain vector. In order to achieve an efficient algorithmic treatment for any complex viscoplasticity constitutive model used in conjunction with large-scale deformation, the following three tasks are required [11]. (1) A detailed study of the mathematical structure of the viscoplasticity equations, and the corresponding integrated field of stress and internal state variables, (2) the development and implementation of the implicit backward-Euler stress-updating algorithm, and the associated nonlinear iteration equation solver (e.g.…”

Section: Introductionmentioning

confidence: 99%

Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals

Voyiadjis

Abed

2006

Int. J. Numer. Meth. Engng

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SUMMARYAn implicit objective stress update algorithm is proposed for a hypoelastic-viscoplastic model. A thermal/dynamic yield function, which is derived based on the thermal activation analysis and dislocation interaction mechanisms, is used, along with the Consistency approach and the framework of additive viscoplasticity, in deriving the proposed model for fcc metals. The corotational formulation approach is utilized in developing the proposed model in the finite deformation field. For the case of the Newton-Raphson iteration method, a new expression for the consistent (algorithmic) tangent stiffness matrix of rate-dependent metals is derived by direct linearization of the stress update algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS. Numerical implementation for a simple tensile problem is used for validating the material parameters of the OFHC Copper under low and high strain rates and temperatures. The numerical results of the adiabatic true stress-true strain curves compare very well with the experimental data. The effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem. Results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh-independent results.

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Robust integration schemes for generalized viscoplasticity with internal-state variables

Cited by 19 publications

References 25 publications

Interactive software for material parameter characterization of advanced engineering constitutive models

Interactive software for material parameter characterization of advanced engineering constitutive models

A time increment control for return mapping algorithm applied to cyclic viscoplastic constitutive models

Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals

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