Initially rigid cohesive laws and fracture based on edge rotations

P. Areias, T. Rabczuk, P. P. Camanho

Research output: Contribution to journalArticlepeer-review

76 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2013


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

ASJC Scopus subject areas

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


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