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

Eterovic, Adrian Luis; Bathe, Klaus‐Jürgen

doi:10.1016/0045-7949(91)90347-o

Cited by 76 publications

(27 citation statements)

References 22 publications

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“…Since any equation containing the ramp function x h i is non-smooth, the Newton-Raphson method will typically have convergence difficulties or fail to converge, a replacement can be used with convergence advantages. Eterovic and Bathe recognized this in 1991 [36] and used a semi-smooth function. We use the ChenMangasarian replacement function ( [31,30]) SðxÞ ffi hxi, which is smooth in the complete domain, to replace the ramp function.…”

Section: The Rousselier Model and Its Integrationmentioning

confidence: 99%

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

Godinho

Dias-da-Costa

Valença

et al. 2013

Strain

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a b s t r a c tIn the context of plane fracture problems, we introduce an algorithm based on our previously proposed rotation of edges but now including the injection of continuum softening elements directly in the process region. This is an extension of the classical smeared (or regularized) approach to fracture and can be seen as an intermediate proposition between purely cohesive formulations and the smeared modeling. Characteristic lengths in softening are explicitly included as width of injected elements. For materials with process regions with macroscopic width, the proposed method is less cumbersome than the cohesive zone model. This approach is combined with smoothing of the complementarity condition of the constitutive law and the consistent updated Lagrangian method recently proposed, which simplifies the internal variable transfer. Propagation-wise, we use edge rotation around crack front nodes in surface discretizations and each rotated edge is duplicated. Modified edge positions correspond to the crack path (predicted with the Ma-Sutton method). Regularized continuum softening elements are then introduced in the purposively widened gap. The proposed solution has algorithmic and generality benefits with respect to enrichment techniques such as XFEM. The propagation algorithm is simpler and the approach is independent of the underlying element used for discretization. To illustrate the advantages of our approach, yield functions providing particular cohesive behavior are used in testing. Traditional fracture benchmarks and newly proposed verification tests are solved. Results are found to be good in terms of load/deflection behavior.

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Section: The Rousselier Model and Its Integrationmentioning

confidence: 99%

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

Godinho

Dias-da-Costa

Valença

et al. 2013

Strain

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“…[5]. The mechanical model is based on previous work, see Eterovic and Bathe [6,7] and Anand and Tong [8,9]. However, the aforementioned models do not include the thermal aspects of the problem and are therefore only applicable in isothermal processes.…”

Section: Computers and Structures 75 (2000) 551±573mentioning

confidence: 99%

“…(13) holds, we say that the bodies are sticking, otherwise they are slipping. We use the constraint function method [1,7] to impose the contact conditions (6) and (12)± (14). On the other hand, the contact heat transfer will be speci®ed by means of a constitutive equation.…”

Section: Variational Equationsmentioning

confidence: 99%

A finite element procedure for the analysis of thermo-mechanical solids in contact

Pantuso

Bathe

Bouzinov³

2000

Computers & Structures

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We present a ®nite element procedure for the analysis of fully coupled thermo-elasto-plastic response of solids including contact conditions. The continuum mechanics formulation for the solid and contact conditions is summarized and eective ®nite element techniques for solution are given. The constraint function method is employed to impose the contact conditions at the Gauss points of the contact surface. Other procedures widely used in ®nite element analysis can be considered as particular cases of the constraint function method discussed herein. 7

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“…(8) and (9). Developed, in ADINA, is the constraint function algorithm [1,12,13], which can be used to solve very complex contact conditions, including two-sided contact, contact of a surface onto itself, and contact with thickness oset as employed in thin shell analyses. The solution algorithm has been developed for static analysis and dynamic solutions.…”

Section: Contact Algorithmmentioning

confidence: 99%

Advances in crush analysis

Bathe

Walczak²,

Guillermin³

et al. 1999

Computers & Structures

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Advances in capabilities for the crush analysis of structures are presented. Such analyses are dicult to perform and require state-of-the-art analysis procedures: ecient and reliable shell elements, an eective and general contact algorithm, ecient procedures to calculate the element stresses in elasto-plasticity, the use of consistent tangent matrices, eective nonlinear incremental solution strategies and the ecient solution of the algebraic ®nite element equations. Moreover, the eectiveness of the complete analysis process can only be achieved by ensuring that each of the above solution procedures is in an eective manner integrated into a complete solution scheme. This paper focuses on the advances developed in ADINA and presents various analysis cases solved with the program. #

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

Cited by 76 publications

References 22 publications

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

An Efficient Technique for Surface Strain Recovery from Photogrammetric Data using Meshless Interpolation

A finite element procedure for the analysis of thermo-mechanical solids in contact

Advances in crush analysis

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