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Modeling the Isotropic Growth of an Incompressible Neo-Hookean Material

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Abstract

The article analyzes the mathematical model of the volumetric growth of an incompressible neo-Hookean material. Models of this kind are used to describe the evolution of the human brain under the action of an external load. We show that the space of deformation fields in the homeostatic state coincides with the Möbius group of conformal transformations in \({\mathbb R}^3 \). We prove the well-posedness of the linear boundary value problem obtained by linearization of the governing equations on the homeostatic state. We study the behavior of solutions when the time variable tends to infinity. The main conclusion is that the changes of the material caused by temporary increase of pressure (hydrocephalus) are irreversible.

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Funding

The author was supported by the Russian Science Foundation (project no. 19–11–00069).

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia

    P. I. Plotnikov

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  1. P. I. Plotnikov
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Correspondence to P. I. Plotnikov.

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Plotnikov, P.I. Modeling the Isotropic Growth of an Incompressible Neo-Hookean Material. J. Appl. Ind. Math. 15, 647–657 (2021). https://doi.org/10.1134/S1990478921040086

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  • DOI: https://doi.org/10.1134/S1990478921040086

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