Model tankega filma na elastičnem substratu za simulacijo ovirane rasti bioloških tkiv

magistrsko delo magistrskega študijskega programa II. stopnje Strojništvo

Nina Kumer (Author), Miha Brojan (Mentor)

Abstract

V magistrski nalogi je obravnavana mehanska stabilnost površine. Teoretični del je razdeljen na dva dela: v prvem je analiziran površinski uklon zaradi ovirane volumetrične rasti tkiva, v drugem pa je obravnavan tlačno obremenjen dvoslojni sistem, sestavljen iz tankega filma, ki leži na debelejšem substratu. Sistem obremenimo na tri različne načine: obremenitev celotne domene, obremenitev filma zaradi rasti filma in obremenitev filma zaradi pred-raztegnjenega substrata. Obravnavani so sistemi z različnimi razmerji togosti med filmom in substratom, beta. Izpeljan je splošen nabor 8 vodilnih enačb za nestabilnost dvoslojnih sistemov, ki ga nadalje skrčimo glede na obravnavan primer. Kot rezultat dobimo kritične deformacije v odvisnosti od razmerja togosti in od normirane valovne dolžine. Za vse primere izvedemo še numerične simulacije v Abaqusu, pri čemer ugotovimo, da se numerični rezultati precej dobro ujemajo z analitičnimi za beta=100 in 10, pri nižjih razmerjih togosti pa so odstopanja zelo velika. Za ravninske primere izvedemo tudi statično strukturno analizo in na podlagi dobljenih podatkov izrišemo grafe, iz katerih je razvidno, kdaj sistem ukloni. Z numerično simulacijo dobimo tudi uklone v več smereh, ki jih analitično ne predvidimo. Na koncu analiziramo še več lastnih oblik, po tem ko površina že ukloni, in ugotovimo, da so si v nekaterih primerih le-te zelo blizu, kar se tiče kritične obremenitve.

Keywords

magistrske naloge;uklon površine;gubanje;rast;film;substrat;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.09 - Master's Thesis
Organization:	UL FS - Faculty of Mechanical Engineering
Publisher:	[N. Kumer]
UDC:	620.179.11:576.7:004.942(043.2)
COBISS:	44263683
Views:	684
Downloads:	165
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Thin film on elastic substrate as a model for simulation of constrained growth of biological tissues
Secondary abstract:	The mechanical stability of the surface is discussed in this master thesis. The theoretical part is divided into two sections: in the first, surface buckling due to volumetric tissue growth is analyzed, and the second deals with stresses and strains in the twolayer system, which consists of a thin film lying on a thicker substrate. The system is loaded in three different ways: over the entire domain, through a film due to its growth, and by pre-stretching the substrate. Systems with different stiffness ratios between the film and the substrate, [beta] = Ef /Es are considered. A general set of 8 governing equations for the instability of two-layer systems is derived and further reduced depending on the case under consideration. As a result, a relationship for the critical deformation as a function of the stiffness ratio and the normalized wavelength is obtained. We also perform numerical simulations in Abaqus and find that the results are quite consistent with the analytical results for [beta] = 100 and 10, while the deviations become very large at lower ratios. For planar cases we also perform a static structural analysis. Based on the data obtained, we show where the system buckles. The numerical simulations also predict wrinkling in several directions, which are not predicted analytically. Finally, we also analyze some of the eigenmodes and find that in some cases they are very close to each other in terms of critical load.
Secondary keywords:	master thesis;surface buckling;wrinkling;growth;film;substrate;Abaqus;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. Ljubljana, Fak. za strojništvo
Pages:	XXII, 54 str.
ID:	12192364