Model velikih deformacij visko-hiperelastičnega gradiva za simulacijo rasti mehkih tkiv

Zavodnik, Jan (author), Brojan, Miha (mentor), Košmrlj, Andrej (comentor)

V delu je predstavljena splošna tri-dimenzionalna kontinuumska teorija, s katero je mogoče opisati rast in mehanske pojave pri raznovrstnih polimernih gradivih in rastlinskih ter živalskih tkivih. Teorija je uporabna za analizo in boljše razumevanje razvoja človeških organov, kot so pljuča, ledvice, črevo, možgani, itn. Poleg tega jo je možno uporabiti za modeliranje poškodb različnih človeških organov ob trkih v nezgodah, med operacijami ali v drugih nevarnih razmerah. Mehanski model, izpeljan v tem delu, temelji na teoriji velikih pomikov. Z njim je mogoče opisati visko-hiperelastične pojave pri deformacijah in obremenitvah tkiva, vključuje pa tudi rast tkiv in s tem povezano disipacijo energije. Model v tej nalogi je izpeljan tako, da izpolnjuje zakone kontinuumske mehanike in je termodinamsko pravilen. Rešitev modela smo iskali numerično, z metodo končnih elementov, ki je vgrajena v knjižnici FEniCS. Poleg tega smo po zgledu literature izpeljali tudi lastni analitični model gubanja rastočega filma na visko-elastični podlagi, s katerim smo primerjali in ovrednotili numerične simulacije našega modela.

• Language: Slovenian
• Keywords: mehanika kontinuov, visko-hiperelastičnost, mehanika rasti, gubanje, metoda končnih elementov
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FS - Faculty of Mechanical Engineering
• Place of publishing: Ljubljana
• Publisher: [J. Zavodnik]
• Year: 2019
• Number of pages: XXIII, 75 str.
• PID: 20.500.12556/RUL-109275
• UDC: 539.3:519.61(043.2)
• COBISS.SI-ID: 16865051
• Publication date in RUL: 29.08.2019

ZAVODNIK, Jan, 2019, Model velikih deformacij visko-hiperelastičnega gradiva za simulacijo rasti mehkih tkiv [online]. Master’s thesis. Ljubljana : J. Zavodnik. [Accessed 19 March 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109275

Secondary language

• Language: English
• Title: Finite strain visco-hyperelastic model for soft tissues growth modelling

Abstract

A general three dimensional continuum theory for growth and elastic deformation modelling of polymer materials, plant and animal tissues is presented. It can be used to better understand the development of human organs, such as lungs, kidneys, guts, brains, etc. It can also be used to model the damage to brain or other vital human body parts inflicted by impact, during surgery or in other hazardous situations. The mechanical model derived in this work is based on the theory of finite strains. It can be used to model visco-hyperelastic phenomena during tissue growth, deformation, relaxation and its intrinsic energy dissipation. The model follows the laws of continuum mechanics and is thermodynamically correct. The solution of partial differential equations of the model is obtained with the use of finite element method, incorporated in FEniCS library. To verify the developed continuum model, a simplified analytical model based on typical examples from the literature is derived.

• Keywords: continuum mechanics, visco-hyperelasticity, growth mechanics, wrinkling, finite element method