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 | |
| Added by: | [JP] |
| Total mark: | 0 |
|
Attachments
|
|
|
|
|
Notes
|
|
|
|
|
|
Topics
|
|
