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International Journal of Fracture

, Volume 178, Issue 1–2, pp 281–298 | Cite as

A non-iterative approach for the modelling of quasi-brittle materials

  • R. Graça-e-Costa
  • J. Alfaiate
  • D. Dias-da-Costa
  • L. J. Sluys
Original Paper

Abstract

Due to the softening behaviour of quasi-brittle materials, in particular the localisation of initially diffused cracking, convergence problems are often found using an iterative procedure, such as the Newton–Raphson method. This is why a new non-iterative procedure is adopted in this paper, which is inspired by the sequentially linear approach(SLA) (Rots et al. in Eng Fract Mech 75(3–4):590–614, 2008). However, several important differences between the present approach and the SLA are presented. In the present model, multi-linear material laws are adopted such that non-linearities occur only due to changes in loading/unloading states. An incremental solution is obtained until non-convergence occurs, upon which a secant approach is used in a corresponding step. The update of the stiffness in the secant approach is based on information obtained from the previous incremental solution. This method is applied to: (i) softening materials, within the scope of the discrete crack approach, and to (ii) hardening materials. As a consequence, conversely to the smeared crack approach adopted in the SLA, no mesh size sensitivity problems are obtained and there is no need to adjust material parameters. Several numerical examples are shown in order to illustrate the proposed formulation.

Keywords

NIEM Fracture Non-iterative procedure Sequentially linear analysis 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • R. Graça-e-Costa
    • 1
    • 3
  • J. Alfaiate
    • 1
    • 4
  • D. Dias-da-Costa
    • 2
    • 5
  • L. J. Sluys
    • 6
  1. 1.ICISTLisbonPortugal
  2. 2.INESC CoimbraCoimbraPortugal
  3. 3.Department of Civil Engineering, Instituto Superior de EngenhariaUniversidade do AlgarveFaroPortugal
  4. 4.Department of Civil Engineering and Architecture, Instituto Superior TécnicoTechnical University of LisbonLisbonPortugal
  5. 5.Department of Civil EngineeringUniversity of CoimbraCoimbraPortugal
  6. 6.Department of Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands

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