Advertisement

Anisotropic Adaptive Meshes for Brittle Fractures: Parameter Sensitivity

  • Marco Artina
  • Massimo Fornasier
  • Stefano Micheletti
  • Simona Perotto
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)

Abstract

We deal with the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional to model quasi-static crack propagation in brittle materials. We employ anisotropic mesh adaptation to efficiently capture the crack path. Aim of this work is to investigate the numerical sensitivity of the crack behavior to the parameters involved in both the physical model and in the adaptive procedure.

Keywords

Brittle Fracture Parameter Sensitivity Crack Path Adaptive Procedure Posteriori Error Estimator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Ambrosio, V.M. Tortorelli, Approximation of functional depending on jumps by elliptic functional via Γ-convergence. Commun. Pure Appl. Math. 43(8), 999–1036 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    M. Artina, M. Fornasier, S. Micheletti, S. Perotto, Anisotropic Mesh Adaptation for Crack Detection in Brittle Materials, Mox-Report 21/2014Google Scholar
  3. 3.
    B. Bourdin, G. Francfort, J.-J. Marigo, Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48(4), 797–826 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    S. Burke, C. Ortner, E. Süli, An adaptive finite element approximation of a variational model of brittle fracture. Soc. Ind. Appl. Math. 48(3), 980–1012 (2010)zbMATHGoogle Scholar
  5. 5.
    G. Dal Maso, R. Toader, A model for the quasi-static growth of brittle fractures based on local minimization. Math. Models Methods Appl. Sci. 12(12), 1773–1799 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    G. Francfort, J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    S. Micheletti, S. Perotto, Output functional control for nonlinear equations driven by anisotropic mesh adaption: the Navier-Stokes equations. SIAM J. Sci. Comput. 30(6), 2817–2854 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    D. Mumford, J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marco Artina
    • 1
  • Massimo Fornasier
    • 1
  • Stefano Micheletti
    • 2
  • Simona Perotto
    • 2
  1. 1.Faculty of MathematicsTechnische Universität MünchenGarchingGermany
  2. 2.MOX – Dipartimento di Matematica “F.Brioschi”Politecnico di MilanoMilanoItaly

Personalised recommendations