Initially rigid cohesive laws and fracture based on edge rotations

P. Areias, Timon Rabczuk, P. P. Camanho

Research output: Contribution to journalArticle

66 Citations (Scopus)

Abstract

We propose alternative methods for performing FE-based computational fracture: a mixed mode extrinsic cohesive law and crack evolution by edge rotations and nodal reposition. Extrinsic plastic cohesive laws combined with the discrete version of equilibrium form a nonlinear complementarity problem. The complementarity conditions are smoothed with the Chen-Mangasarian replacement functions which naturally turn the cohesive forces into Lagrange multipliers. Results can be made as close as desired to the pristine strict complementarity case, at the cost of convergence radius. The smoothed problem is equivalent to a mixed formulation (with displacements and cohesive forces as unknowns). In terms of geometry, our recently proposed edge-based crack algorithm is adopted. Linear control is adopted to determine the displacement/load parameter. Classical benchmarks in computational fracture as well as newly proposed tests are used in assessment with accurate results. In this sense, the proposed solution has algorithmic and accuracy advantages, at a slight penalty in the computational cost. The Sutton crack path criterion is employed in a preliminary path determination stage.

Original languageEnglish
Pages (from-to)931-947
Number of pages17
JournalComputational Mechanics
Volume52
Issue number4
DOIs
Publication statusPublished - 2013 Apr 11
Externally publishedYes

Fingerprint

Crack
Cracks
Strict Complementarity
Radius of convergence
Nonlinear Complementarity Problem
Path
Mixed Formulation
Mixed Mode
Lagrange multipliers
Linear Control
Complementarity
Replacement
Penalty
Computational Cost
Plastics
Benchmark
Unknown
Geometry
Alternatives
Costs

Keywords

  • Complementarity
  • Computational fracture
  • Edge rotation
  • Extrinsic law
  • Mixed-mode fracture

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mathematics

Cite this

Initially rigid cohesive laws and fracture based on edge rotations. / Areias, P.; Rabczuk, Timon; Camanho, P. P.

In: Computational Mechanics, Vol. 52, No. 4, 11.04.2013, p. 931-947.

Research output: Contribution to journalArticle

Areias, P. ; Rabczuk, Timon ; Camanho, P. P. / Initially rigid cohesive laws and fracture based on edge rotations. In: Computational Mechanics. 2013 ; Vol. 52, No. 4. pp. 931-947.
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