Asymptotic numerical methods for unilateral contact

Aggoune, Woihida; Zahrouni, Hamid; Potier‐Ferry, Michel

doi:10.1002/nme.1714

Cited by 21 publications

(39 citation statements)

References 30 publications

(63 reference statements)

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“…It is well known within ANM [13] [14] that such a law leads to a constitutive law at order k: the higher-order derivative of the stress is a function of derivatives of the strain. The goal of this part is to show how this constitutive law at order k could be implemented automatically using Automatic Differentiation, even if the starting law is complex.…”

Section: Higher-order Differentiation Of Local Constitutive Lawsmentioning

confidence: 99%

“…As proposed in [13] the hard contact law (R N ≥ 0, h ≥ 0, R N h = 0) may be replaced by a smooth relation between the normal pressure R N and the gap h, following:…”

Section: Contact Modeling : the Mechanical Partmentioning

confidence: 99%

“…The Asymptotic Numerical Method is an efficient path following technique for the solution of strongly non-linear partial differential equations. For instance it has been applied to problems of unilateral contact [10] [11] [12] [13], plasticity [14] [15], viscoplasticity [16] and to problem coupling several non-linearities [16] [17].…”

Section: Introductionmentioning

confidence: 99%

“…The ANM algorithm does not differ significantly from the one presented in [13]. The contact law is regularized by a smooth function and the main unknowns are the displacement and the contact forces as in many contact algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…The contact law is regularized by a smooth function and the main unknowns are the displacement and the contact forces as in many contact algorithms. Up to now within ANM, the tool surfaces have been represented by simple surfaces as planes or cylinders [10] [12] [13]. The main goal of this paper is to establish an efficient and generic methodology to account for complex surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Lejeune

Boudaoud

Potier‐Ferry

et al. 2013

Numerical Meth Engineering

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In general, nonlinear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two nonlinear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, while the second one is a nonlinear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex nonlinear problems, a computation technique based on Automatic Differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher-order derivatives of these constitutive laws and thereafter to define Taylor series that are the basis of the continuation technique called Asymptotic Numerical Method. The algorithm is about the same with an explicit or an implicit constitutive relation. In the modeling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to get the higher-order derivatives.

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Section: Higher-order Differentiation Of Local Constitutive Lawsmentioning

confidence: 99%

“…As proposed in [13] the hard contact law (R N ≥ 0, h ≥ 0, R N h = 0) may be replaced by a smooth relation between the normal pressure R N and the gap h, following:…”

Section: Contact Modeling : the Mechanical Partmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Lejeune

Boudaoud

Potier‐Ferry

et al. 2013

Numerical Meth Engineering

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A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems

Guillot

Cochelin

Vergez

2019

Numerical Meth Engineering

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This paper is concerned with a Taylor series-based continuation algorithm, the so-called Asymptotic Numerical Method (ANM). It describes a generic continuation procedure to apply the ANM principle at best, in other words, that presents a high level of genericity without paying the price of this genericity by low computing performances. The way to quadratically recast a system of equation is now part of the method itself, and the way to handle elementary transcendental function is detailed with great attention. A sparse tensorial formalism is introduced for the internal representation of the system, which, when combined with a block condensation technique, provides a good computational efficiency of the ANM. Three examples are developed to show the performance and the versatility of the implementation of the continuation tool. Its robustness and its accuracy are explored. Finally, the potentiality of this method for complex nonlinear finite element analysis is enlightened by treating 2D elasticity problems with geometrical nonlinearities. KEYWORDS asymptotic numerical method, continuation, finite element method, nonlinear systems, quadratic recast, Taylor series *The term "numerical" stands in the name of the method because of this finite element discretization. Int J Numer Methods Eng. 2019;119:261-280.wileyonlinelibrary.com/journal/nme

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Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems

Tri

Zahrouni

Potier‐Ferry

2014

Numerical Methods Partial

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We propose in this work new algorithms associating asymptotic numerical method and meshless discretization (MFS‐MPS: Method of fundamental solutions‐Method of particular solutions) to compute branch solutions of nonlinear Poisson problems. To detect singular points on these branches, geometrical indicator, Padé approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 978–993, 2014

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Asymptotic numerical methods for unilateral contact

Cited by 21 publications

References 30 publications

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems

Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems

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