An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat

0482286 - ÚT 2018 RIV US eng J - Journal Article
Roubíček, Tomáš
An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat.
Discrete and Continuous Dynamical systems - Series S. Roč. 10, č. 4 (2017), s. 867-893. ISSN 1937-1632. E-ISSN 1937-1179
R&D Projects: GA ČR GA14-15264S; GA ČR(CZ) GA16-03823S
Institutional support: RVO:61388998
Keywords : viscoelasticity at small strains * inertia * damage
OECD category: Pure mathematics
Impact factor: 0.561, year: 2017
http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=13967

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 resulting 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.
Permanent Link: http://hdl.handle.net/11104/0278088