A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

Parisch, Horst

doi:10.1002/nme.1620280807

Cited by 116 publications

(46 citation statements)

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“…It has been observed that the local convergence properties of the Newton iteration are hard to achieve, and emphasis has been given to the use of consistent tangent stiffness matrices for nonlinear contact analysis [20,23,24].…”

Section: ~Odu~onmentioning

confidence: 99%

On the treatment of inequality constraints arising from contact conditions in finite element analysis

Eterovic

Bathe

1991

Computers & Structures

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Abstract--Existing methods for the analysis of contact problems deal with the inequality constraints arising from contact conditions by means of an implicit iteration on all constraints. This paper presents a formulation for contact problems with friction for large deformations where all inequality constraints are enforced explicitly. A robust solution technique for the resulting system of nonlinear equations can then be used. This approach admits the use of line search procedures to enlarge the region of convergence.

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Section: ~Odu~onmentioning

confidence: 99%

On the treatment of inequality constraints arising from contact conditions in finite element analysis

Eterovic

Bathe

1991

Computers & Structures

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“…Therefore, in contrast to earlier works (see for example Wriggers and Simo [8] and Parisch [9]), continuum mechanical arguments are used to derive the underlying variational formulation.…”

Section: Introductionmentioning

confidence: 99%

An augmentation technique for large deformation frictional contact problems

Franke

Hesch

Betsch

2013

Numerical Meth Engineering

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SUMMARYThe present work deals with a new approach to frictional large deformation contact problems. In particular, a new formulation of the frictional kinematics is introduced that is based on a specific augmentation technique used for the introduction of additional variables. This augmentation technique substantially simplifies the formulation of the whole system. A size reduction of the resulting system of algebraic equations is proposed. Consequently, the augmentation technique does not lead to an increase in size of the algebraic system of equations to be ultimately solved. The size reduction retains the simplicity of the formulation and preserves important conservation laws such as conservation of angular momentum.

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“…See also the monographs by Kikuchi and Oden [4], Zhong [5] and Wriggers [6]. The popular penalty approximation and 'mixed' or 'trial-and-error' methods [7,8] appear, at first glance, suitable for many applications. But in this kind of method, the contact boundary conditions and friction laws are not satisfied accurately and it is tricky for the users to choose appropriate penalty factors.…”

Section: Introductionmentioning

confidence: 99%

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

Feng

Magnain

Cros

et al. 2007

Int. J. Simul. Multidisci. Des. Optim.

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-The bi-potential method has been successfully applied for the modelling of frictional contact problems in static cases. This paper presents the extension of this method for dynamic analysis of impact problems with multiple deformable bodies. Instead of second order algorithms, a first order algorithm is applied for the numerical integration of the time-discretized equation of motion. The solution algorithm, named Bi-First, is simple and efficient. The principle of energy conservation for the given exemples is well preserved using the algorithm without any regularization. The numerical results also show clearly the physical energy dissipation introduced by frictional effects between the solids in contact.

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A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis

Cited by 116 publications

References 10 publications

On the treatment of inequality constraints arising from contact conditions in finite element analysis

On the treatment of inequality constraints arising from contact conditions in finite element analysis

An augmentation technique for large deformation frictional contact problems

Bi-First: A simple and efficient algorithm to identify dissipated energy in impact problems

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