Mathematical Modeling of Neo-Hookean Material Growth Full article
| Journal |
Doklady Mathematics
ISSN: 1064-5624 |
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| Output data | Year: 2021, Volume: 104, Number: 3, Pages: 380-384 Pages count : 5 DOI: 10.1134/s1064562421060144 | ||
| Tags | Möbius group; neo-Hookean material; Stokes equations; volumetric growth | ||
| Authors |
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Abstract:
A mathematical model of the volumetric growth of an incompressible neo-Hookean material is derived. Models of this type are used to describe the evolution of the human brain under the action of an external load. In the paper, we show that the space of deformation fields in a homeostatic state coincides with the Möbius group of conformal transforms in R3s. We prove the well-posedness of the linear boundary value problem obtained by linearizing the governing equations around a homeostatic state. The behavior of solutions when the time variable tends to infinity is studied. The main conclusion is that changes in the material, caused by a temporary increase in pressure (hydrocephalus) are irreversible.
Cite:
Plotnikov P.I.
Mathematical Modeling of Neo-Hookean Material Growth
Doklady Mathematics. 2021. V.104. N3. P.380-384. DOI: 10.1134/s1064562421060144 WOS Scopus РИНЦ OpenAlex
Mathematical Modeling of Neo-Hookean Material Growth
Doklady Mathematics. 2021. V.104. N3. P.380-384. DOI: 10.1134/s1064562421060144 WOS Scopus РИНЦ OpenAlex
Original:
Плотников П.И.
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РОСТА МАТЕРИАЛА НЕО-ГУКА
ДОКЛАДЫ РОССИЙСКОЙ АКАДЕМИИ НАУК. МАТЕМАТИКА, ИНФОРМАТИКА, ПРОЦЕССЫ УПРАВЛЕНИЯ. 2021. Т.501. №1. С.74-78. DOI: 10.31857/S268695432106014X РИНЦ OpenAlex
МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ РОСТА МАТЕРИАЛА НЕО-ГУКА
ДОКЛАДЫ РОССИЙСКОЙ АКАДЕМИИ НАУК. МАТЕМАТИКА, ИНФОРМАТИКА, ПРОЦЕССЫ УПРАВЛЕНИЯ. 2021. Т.501. №1. С.74-78. DOI: 10.31857/S268695432106014X РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000776892300014 |
| Scopus: | 2-s2.0-85127831486 |
| Elibrary: | 48961885 |
| OpenAlex: | W4285336711 |