An augmented lagrangian treatment of contact problems involving friction

Simo, J. C.; Laursen, Tod A.

doi:10.1016/0045-7949(92)90540-g

Cited by 762 publications

(500 citation statements)

References 12 publications

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“…This extra variable is incorporated via the Enhanced Assumed Strain (EAS) concept introduced in [47]. The elastic constitutive law (4), (5), (6) is modified. It is an explicit function (θ = ∇u,γ) → (T, S) that is written as:…”

Section: Unilateral Contact With An Elastic Shellmentioning

confidence: 99%

“…Unilateral contact involves a non smooth relation between the contact forces and the distance between the two bodies. The numerical techniques to solve unilateral contact are often based on Lagrange multipliers [3], augmented Lagrangian [4] [5] and regularization of the non smooth function like in penalty method [6] [7] [8]. The tool shape may have significant impact on the deformation and the stability of the sheet [1].…”

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: Unilateral Contact With An Elastic Shellmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…Therefore besides the penalty method introduced above the so called Augmented Lagrangian approach as proposed in [25] and [21] is also tested for the contact description. This method can be considered as a combination of the penalty method and the method of Lagrangian multipliers.…”

Section: Augmented Lagrangian Contact Formulationmentioning

confidence: 99%

Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements

Harnau

Konyukhov

Schweizerhof

2005

Computers & Structures

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A special application for the so-called 'Solid-Shell' elements are sheet metal forming problems with high stretching and large local contact pressure where standard 2D-shells fail to converge resp. do not give reasonable results. To describe such kind of problems besides a full 3D continuum discretization appropriate contact formulations are necessary to introduce the contact condition of the metal sheets against the rigid tools. In this contribution a velocity description is taken for formulation of contact conditions. A penalty as well as an Augmented Lagrangian approach for frictionless contact is used as a first step in our developments. Special attention is paid to different numerical integration schemes of the contact integral and tangent matrices. As a result a series of different contact elements including various cases as "node-to-surface", "segment-to-segment" and "analytical rigid surface-to-segment" is considered under the unified description. For selected numerical examples the influence of the order of the quadrature formulae in a subdomain integration approach as well as the order of finite element interpolation used in the computations is discussed. The algorithms appear also to work well for friction type problems, which will be tested in a following paper.

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“…Moreover, most of the earlier studies devoted to systems with multiple contacts were related mainly to dynamics of granular materials or rigid and flexible blocks or metal forming (e.g., [20][21][22][23]) and not to classical structural dynamics applications.…”

Section: Introductionmentioning

confidence: 99%

“…In the first one, the emphasis is put on considering dynamical systems with relatively simple sets of unilateral constraints and the main objective is to develop a better understanding on fundamental issues related to the dynamic response, stability and bifurcation of non-smooth systems (e.g., [5][6][7][8][9][10][11][12][13][14][15]). On the other hand, a parallel and equally intensive effort is also underway, where the attention is focused on developing accurate and efficient numerical methodologies for capturing the response of models involving more complex sets of multiple unilateral constraints, by employing set-valued force law theory (e.g., [16][17][18][19][20][21][22][23]). …”

Section: Introductionmentioning

confidence: 99%

Dynamics of finite element structural models with multiple unilateral constraints

Theodosiou¹,

Natsiavas²

2009

International Journal of Non-Linear Mechanics

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Fast and accurate simulation of mechanical structures with complex geometry requires application of the finite element method. Τhis leads frequently to models with a relatively large number of degrees of freedom, which may also possess nonlinear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements. The characteristics of these elements must be selected in a delicate way, but even so the success of these methods can not be guaranteed. This study presents a numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems with multiple unilateral constraints. The method developed is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models possessing smooth nonlinearities. The second class of methods includes specialized methodologies that simulate response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.

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An augmented lagrangian treatment of contact problems involving friction

Cited by 762 publications

References 12 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

Algorithmic aspects in large deformation contact analysis using ‘Solid-Shell’ elements

Dynamics of finite element structural models with multiple unilateral constraints

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