Analýza viskoelastických modelů rychlostního typu používaných při modelování lidských tkání
| Thesis title in Czech: | Analýza viskoelastických modelů rychlostního typu používaných při modelování lidských tkání |
|---|---|
| Thesis title in English: | Analysis of rate-type viscoelastic models used in modelling of human tissues |
| Key words: | viskoelastické modely rychlostního typu|slabé řešení|lidské tkáně |
| English key words: | viscoelastic rate-type models|weak solution|human tissues |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. RNDr. Miroslav Bulíček, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 25.09.2024 |
| Date of assignment: | 25.09.2024 |
| Confirmed by Study dept. on: | 04.10.2024 |
| Advisors: | prof. RNDr. Josef Málek, CSc., DSc. |
| doc. Mgr. Vít Průša, Ph.D. | |
| Guidelines |
| 1) The student should study available models that describe the deformation of human tissues in particular brain tissues. Potentially relevant and interesting models should be designed so that they meet the fundamental principles. The student should focus on rate-type models and also mixture-like models.
2) The student should learn the available mathematical theory for the fluid and/or solid rate-type models and mixture-like models. 3) The indicated models should be compared in simple geometries. 4) Finally, the student should focus on establishing an adequate mathematical theory for the underlying problems. |
| References |
| Mohammad Hosseini-Farid, Mohammadreza Ramzanpour, Jayse McLean, Mariusz Ziejewski, Ghodrat Karami: A poro-hyper-viscoelastic rate-dependent constitutive modeling for the analysis of brain tissues, Journal of the Mechanical Behavior of Biomedical Materials, Volume 102, 2020, https://doi.org/10.1016/j.jmbbm.2019.103475.
Durga Prasad, P. Sreejith, K. Kannan: A new viscoelastic model for human brain tissue using Lode invariants based rate-type thermodynamic framework, Applications in Engineering Science, Volume 15, 2023, https://doi.org/10.1016/j.apples.2023.100130. K. R. Rajagopal, A. R. Srinivasa: A thermodynamic frame work for rate type fluid models. J. Non-Newton. Fluid Mech. 88 (3), 207–227, 2000, http://dx.doi.org/10.1016/S0377-0257(99)00023-3. M. Bulíček, T. Los, Y. Lu and J. Málek: On planar flows of viscoelastic fluids of Giesekus type, Nonlinearity, 35, No. 12, 6557--6604, 2022, https://doi.org/10.1088/1361-6544/ac9a2c. M. Bathory, M. Bulíček and J. Málek: Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion, Advances in Nonlinear Analysis, 10, No. 1, 501--521, 2021, https://doi.org/10.1515/anona-2020-0144. Y. Sengul, Y. 2021. Nonlinear viscoelasticity of strain rate type: an overview. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477(2245), article number: 20200715. https://doi.org/10.1098/rspa.2020.0715. |