WIAS Preprint No. 2799, (2020)

Approximation schemes for materials with discontinuities


  • Bartels, Sören
  • Milicevic, Marijo
  • Thomas, Marita
    ORCID: 0000-0001-6771-0742
  • Tornquist, Sven
  • Weber, Nico

2010 Mathematics Subject Classification

  • 35K86 74R05 49J45 49S05 65M12 65M60 74H10 74H20 74H30 35M86 35Q74


  • Visco-elastodynamic damage, Ambrosio-Tortorelli model for phase-field fracture, viscous evolution, rate-independent limit, partial damage, damage evolution with gradient regularization, semistable energetic solutions, numerical approximation, iterative solution, damage evolution with spatial regularization, functions of bounded variation




Damage and fracture phenomena are related to the evolution of discontinuities both in space and in time. This contribution deals with methods from mathematical and numerical analysis to handle these: Suitable mathematical formulations and time-discrete schemes for problems with discontinuities in time are presented. For the treatment of problems with discontinuities in space, the focus lies on FE-methods for minimization problems in the space of functions of bounded variation. The developed methods are used to introduce fully discrete schemes for a rate-independent damage model and for the viscous approximation of a model for dynamic phase-field fracture. Convergence of the schemes is discussed.

Appeared in

  • Non-standard Discretisation Methods in Solid Mechanics, J. Schröder, P. Wriggers, eds., vol. 98 of Lecture Notes in Applied and Computational Mechanics, Springer, Cham, 2022, pp. 505--565, DOI 10.1007/978-3-030-92672-4_17 .

Download Documents