Solving elastoplasticity problems by the Asymptotic Numerical Method: Influence of the parameterizations

Hamdaoui, Abdellah; Braikat, Bouazza; Damil, Noureddine

doi:10.1016/j.finel.2016.03.001

Cited by 13 publications

(6 citation statements)

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“…The first application of ANM in elastoplasticity [120] was disappointing because of an unsuitable regularization. The key point is the regularization based on the consistency equation introduced in [126] and assessed for boundary value problems in [121][122][123]. FE computations for large strain modellings were discussed in [75,121,124].…”

Section: (D) a Numerical Example In Large Strain Elastoplasticitymentioning

confidence: 99%

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Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

Potier-Ferry

2024

Proc. R. Soc. A.

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The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding algorithms for finite strain elasticity and elastoplasticity being summarized here. Taylor series is not only a computation tool, but it contains also useful information about the structure of the considered solution curve. The paper ends with a short historical account about the development of this numerical method.

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Section: (D) a Numerical Example In Large Strain Elastoplasticitymentioning

confidence: 99%

“…Extensions to plasticity with strain hardening and to small strain three-dimensional elastoplasticity are straightforward, which is described in [121][122][123]. In the next section, the treatment of a large strain elastoplastic model is presented for completeness.…”

Section: (B) How To Regularize Elastoplastic Lawsmentioning

confidence: 99%

Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

Potier-Ferry

2024

Proc. R. Soc. A.

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“…The use of Pade' approximants (Cochelin et al, 1994b;Elhage-Hussein et al, 2000 andNajah et al, 1998) with ANM showed greater numerical efficiency. The solution methodology for elasto-plasticity problems using ANM (Assidi, 2007;Assidi et al, 2005Assidi et al, , 2007Assidi et al, , 2009Hamdaoui et al, 2016;Potier-Ferry and Cadou, 2004;Zahrouni et al, 1998Zahrouni et al, , 2005 with a single regularized expression for Kuhn-Tucker conditions (Assidi et al, 2007(Assidi et al, , 2009 is proposed. The regularization procedures required to handle the non-differentiable relations at the elasto-plastic transition (Zahrouni et al, 1998) and elastic unloading (Zahrouni et al, 2005) have been suggested.…”

Section: Introductionmentioning

confidence: 99%

“…Computation of material damage to assess crack initiation at rotor inlet notches through the damage parameter using the formalism of Continuum Damage Mechanics is carried out for the first time using ANM. The objective of development of the ANM technique for solving cyclic viscoplasticity problems is to realize the computational advantage ANM inherently possesses (Assidi et al, 2009;Cochelin, 1994;Damil and Potier-Ferry, 1990;Hamdaoui et al, 2016;Zahrouni et al, 1998). The ANM solution is compared with a conventional Newton Raphson method where the accumulated errors and computation times are analyzed to assess the performance of the proposed ANM.…”

Section: Introductionmentioning

confidence: 99%

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

Sen,

Patel

2023

International Journal of Damage Mechanics

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Conscious efforts on reduction of greenhouse gas emissions have led to an energy transition to renewable energy, however uncertainties of renewable energy production have resulted in higher thermal cycling demands from conventional power plants. Thermal load cycling at high temperature regions of steam turbine components leads to enhanced creep-fatigue damage accumulation. It is well established that such damage mechanism is numerically best predicted by unified constitutive modeling including damage as a variable as per the formalism of continuum damage mechanics at an expense of considerable computational efforts using finite element analysis. In this paper, the non-iterative Asymptotic Numerical Method (ANM), currently limited to partial cycle analysis with linear hardening plasticity model, is proposed for the first time to address cyclic viscoplasticity problems including damage capable of handling multiple cycles and most generalized loading conditions. Regularization techniques additionally necessary to implement loading-unloading-reloading criteria and advanced constitutive models etc. are presented. The constitutive model chosen for the formulation includes the non-linear multiple back stress variable modified Chaboche model to include damage combined with modified Chaboche-Rousselier isotropic hardening model to include damage, power law for viscoplasticity, Lemaitre’s damage potential and Kachanov-Rabotnov’s creep damage law. The method is verified with defined error measures and then applied to two high pressure steam turbine rotors, one with and another without thermal stress relief groove (TSRG) at the inlet under service type loading conditions to study the beneficial effect of the TSRG on creep-fatigue damage evolution. The accumulated errors of the proposed ANM and computational time are compared to a conventional Newton-Raphson solution.

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“…The idea in the Riks' method is to add a constraint equation to the nonlinear system, which would limit both the variations in load level and displacements (figure 1). Several variants were proposed to the original algorithm: to name just a few, we mention the line-search (Crisfield, 1983), local arc-length (Alfano and Crisfield, 2003), local arc-length for strain softening (De Borst, 1987;May and Duan, 1997), orthogonal methods (Forde and Stiemer, 1987), asymptoticnumerical methods based on Pade approximants (Cochelin et al, 1994;Elhage-Hussein et al, 2000;Hamdaoui et al, 2016), dissipation-based arc-length (Gutierrez, 2004;Verhoosel et al, 2009;Singh et al, 2016;May et al, 2016) and kinetic damping (Lee et al, 2011).…”

Section: Introductionmentioning

confidence: 99%