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An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat
Type of publication: Misc
Citation:
Journal: AIMS’ journal “Discrete and Cont. Dynam. Syst.”
Year: 2016
Abstract: The model of brittle cracks in elastic solids at small strains is approximated by the Ambrosio-Tortorelli functional and then extended into evolution situation to an evolutionary system, involving viscoelasticity, inertia, heat transfer, and coupling with Cahn-Hilliard-type diffusion of a fluid due to Fick’s or Darcy’s laws. Damage resulted from the approximated crack model is considered rate independent. The fractional-step Crank-Nicolson-type time discretisation is devised to decouple the system in a way so that the energy is conserved even in the discrete scheme. The numerical stability of such a scheme is shown, and also convergence towards suitably defined weak solutions. Various generalizations involving plasticity, healing in damage, or phase transformation are mentioned, too.
Preprint project: NCMM
Preprint year: 2016
Preprint number: 11
Preprint ID: NCMM/2016/11
Keywords:
Authors Roubíček, Tomáš
Added by: [JP]
Total mark: 0
Attachments
  • tr-PDE2015-preprint.pdf
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