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Brezinski, Claude; Redivo–Zaglia, Michela

doi:10.1007/978-3-030-58418-4_7

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2024

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“…Other interesting procedures are the ‘extrapolation methods’ [77], especially the ‘Modified Minimal Polynomial Extrapolation’ (MMPE) [78] that was applied several times for convergence acceleration of sequences of vectors obtained by ANM. Let us consider a sequence of vectors boldSk for 1≤k≤K and let us introduce the incremental vectors boldVk=boldSk+1−boldSk.…”

Section: Solution Proceduresmentioning

confidence: 99%

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: Solution Proceduresmentioning

confidence: 99%

Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

Potier-Ferry

2024

Proc. R. Soc. A.

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show abstract

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Cited by 1 publication

References 4 publications

Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

Asymptotic numerical method for hyperelasticity and elastoplasticity: a review

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