TY  - GEN 
T1  - An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat
A1  - Roubíček, Tomáš
JA  - AIMS’ journal “Discrete and Cont. Dynam. Syst.”
Y1  - 2016
N2  - 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.
M1  - Preprint project = NCMM
M1  - Preprint year = 2016
M1  - Preprint number = 11
M1  - Preprint ID = NCMM/2016/11
ER  -