Smooth Approximations to Nonlinear Complementarity Problems

Chen, Bintong; Harker, Patrick T.

doi:10.1137/s1052623495280615

Cited by 142 publications

(92 citation statements)

References 12 publications

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“…We direct the reader to the proofs by Chen and Harker [18] and Chen and Mangasarian [17]. In particular, as a relation is established with interior point methods, proofs concerning the iteration trajectory make use of similar conclusions.…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 97%

“…From a solution viewpoint, either line-search or trust region methods can be used in the inner stage of the method; a continuation method with adaptive smoothing P e e r R e v i e w O n l y parameters was proposed by Chen and Harker [18].…”

Section: Introductionmentioning

confidence: 99%

“…Further properties are provided in references [17,18]. The corresponding smoothed "plus" function is given by integration of s:…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 99%

“…However this should occur with the solution of the NCP problem, if exists. P e e r R e v i e w O n l y Chen and Mangasarian [17] and, more recently Chen and Harker [18] have shown that it is the case under the conditions given below. The statement of the NCP is:…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 99%

“…It is known that a strongly monotone NCP has a unique solution (see [18]). For a Lipschitz continuous G(x) (i.e.…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 99%

See 4 more Smart Citations

Quasi‐static crack propagation in plane and plate structures using set‐valued traction‐separation laws

Areias

Rabczuk

2007

Numerical Meth Engineering

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SUMMARYWe introduce a numerical technique to model set-valued traction-separation laws in plate bending and also plane crack propagation problems. By use of recent developments in thin (Kirchhoff-Love) shell models and the extended finite element method, a complete and accurate algorithm for the cohesive law is presented and is used to determine the crack path. The cohesive law includes softening and unloading to origin, adhesion and contact. Pure debonding and contact are obtained as particular (degenerate) cases. A smooth root finding algorithm (based on the trust region method) is adopted. A step-driven algorithm is described with a smoothed law which can be made arbitrarily close to the exact non smooth law. In the examples shown the results were found to be step-size insensitive and accurate. In addition, the method provides the crack advance law, extracted from the cohesive law and the absence of stress singularity at the tip.

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Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

“…Further properties are provided in references [17,18]. The corresponding smoothed "plus" function is given by integration of s:…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 99%

Section: Introduction To Cohesive Traction-separation Lawsmentioning

confidence: 99%

“…It is known that a strongly monotone NCP has a unique solution (see [18]). For a Lipschitz continuous G(x) (i.e.…”

Section: Introduction To Cohesive Traction-separation Lawsmentioning