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Deformation response of polydimethylsiloxane substrates subjected to uniaxial quasi-static loading
Vinařský, V. ; Martino, F. ; Forte, G. ; Šleichrt, Jan ; Rada, Václav ; Kytýř, Daniel
To investigate cellular response of cardiomyocytes to substrate mechanics, biocompatible material with stiffness in physiological range is needed. PDMS based material is used for construction of microfluidic organ on chip devices for cell culture due to ease of device preparation, bonding, and possibility of surface functionalization. However it has stiffness orders of magnitude out of physiological range. Therefore, we adapted recently available protocol aiming to prepare substrates which offer stiffness in physiological range 5−100 kPa using various mixtures of Sylgard. An in-house developer loading device with single micron position tracking accuracy and sub-micron position sensitivity was adapted for this experimental campaign. All batches of the samples were subjected to uniaxial loading. During quasi-static experiment the samples were compressed to minimally 40% deformation. The results are represented in the form of stress-strain curves calculated from the acquired force and displacement data and elastic moduli are estimated.
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Constitutive Modelling of Composites with Elastomer Matrix and Fibres with Significant Bending Stiffness
Fedorova, Svitlana ; Kotoul, Michal (oponent) ; Menzel, Andreas (oponent) ; Burša, Jiří (vedoucí práce)
Constitutive modelling of fibre reinforced solids is the focus of this work. To account for the resulting anisotropy of material, the corresponding strain energy function contains additional terms. Thus, tensile stiffness in the fibre direction is characterised by additional strain invariant and respective material constant. In this way deformation in the fibre direction is penalised. Following this logic, the model investigated in this work includes the term that penalises change in curvature in the fibre direction. The model is based on the large strain anisotropic formulation involving couple stresses, also referred to as “polar elasticity for fibre reinforced solids”. The need of such formulation arises when the size effect becomes significant. Mechanical tests are carried out to confirm the limits of applicability of the classical elasticity for constitutive description of composites with thick fibres. Classical unimaterial models fail to take into account the size affect of fibres and their bending stiffness contribution. The specific simplified model is chosen, which involves new kinematic quantities related to fibre curvature and the corresponding material stiffness parameters. In particular, additional constant k3 (associated with the fibre bending stiffness) is considered. Within the small strains framework, k3 is analytically linked to the geometric and material properties of the composite and can serve as a parameter augmenting the integral stiffness of the whole plate. The numerical tests using the updated finite element code for couple stress theory confirm the relevance of this approach. An analytical study is also carried out, extending the existing solution by Farhat and Soldatos for the fibre-reinforced plate, by including additional extra moduli into constitutive description. Solution for a pure bending problem is extended analytically for couple stress theory. Size effect of fibres is observed analytically. Verification of the new constitutive model and the updated code is carried out using new exact solution for the anisotropic couple stress continuum with the incompressibility constraint. Perfect agreement is achieved for small strain case. Large strain problem is considered by finite element method only qualitatively. Three cases of kinematic constraints on transversely isotropic material are considered in the last section: incompressibility, inextensibility and the double constraint case. They are compared with a general material formulation in which the independent elastic constants are manipulated in order to converge the solution to the “constraint” formulation solution. The problem of a thick plate under sinusoidal load is used as a test problem. The inclusion of couple stresses and additional bending stiffness constant is considered as well. The scheme of determination of the additional constant d31 is suggested by using mechanical tests combined with the analytical procedure.
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Výpočtová simulace vibrací gumového silentbloku
Krupa, Lukáš ; Návrat, Tomáš (oponent) ; Burša, Jiří (vedoucí práce)
Tato práce se zabývá výpočtovým modelováním vibrací gumového silentbloku metodou konečných prvků (MKP). Práce zahrnuje popis experimentálních měření materiálových charakteristik gumy při statickém a dynamickém zatížení a jejich použití pro určení vhodného viskoelastického a hyperelastického modelu materiálu pro danou aplikaci. Závislost dynamické tuhosti silentbloku na frekvenci zatížení získaná výpočtovým modelováním je validována s experimentálním měřením. Na závěr jsou vyšetřovány odchylky mezi simulací a experimentem a jejich příčiny.
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Proposal of hyperelastic proportional damping as dissipated energy model of hard rubbers
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Košina, Jan ; Cibulka, Jan
The paper deals with a stress analysis of hard rubber under large torsion deformations. This study was motivated by effort to find the dependency the dissipated energy on the deformation energy. Based on the results of an experiment, a function of dissipation energy of hard rubbers for finite strains using the theory hyperelasticity was proposed herein analogically as a proportional damping for elastic theory. Samples of hard rubber of different hardness (EPDM, Silicone) were dynamically tested on the developed torsional test-rig at different frequencies, amplitudes. First the Mooney Rivlin model (MRM) for a shear case of loading was analytically developed and then MRM constants were attained by fitting of the MRM to the experimental torsion-deformation curve. These constants were used to obtain the deformation energy of the MRM models. The coefficients of hyperelastic proportional damping relating a dissipated energy to a strain energy were evaluated for tested rubbers on the basis of experimental results.
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Experimental analysis of torsion vibration of hard rubbers under large deformation
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Cibulka, Jan ; Košina, Jan
The paper deals with a stress analysis of hard rubber under large torsion deformations. This study was motivated by effort to enhance the theoretical background for experimental evaluation of material behaviour of hard rubbers on our test rig. First the Mooney Rivlin model (MRM) for shear case of loading was developed and then MRM constants were attained by fitting of the MRM to the experimental torsiondeformation curve. Then the tuned MRM cylindrical model was tested under torsion loading for evaluation of stress state. Besides the radial distribution of shear stress and strain the attention was paid to evaluation of axial stresses. It could help to assess the influence of the tension stresses on the tangential deformations of the test sample during large torsion.
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Elektro-hydrodynamický model pro bioimpedanční pletysmografii
Vyroubal, Petr ; Uruba,, Václav (oponent) ; Horák,, Vladimír (oponent) ; Maxa, Jiří (vedoucí práce)
Předkládaná dizertační práce se zabývá studiem elektro-hydrodynamiky v oblasti numerického modelování biomechanických systémů, konkrétně v metodě bioimpedanční pletysmografie. Řešení úlohy pulsujícího proudění krve v pružné cévní stěně je v současnosti jeden z nejsložitějších problémů mechaniky a biomechaniky z důvodu interakce obou kontinuí na společné hranici. Celý systém je navíc zatížen procházejícím diagnostickým elektrickým proudem. Tato dizertační práce vznikla ve spolupráci s Ústavem přístrojové techniky AV ČR, v. v. i. v Brně, se skupinou zabývající se medicínskými signály (vedoucí Ing. Pavel Jurák, CSc.). Experimentální měření pak probíhala nezávisle ve Fakultní nemocnici U Svaté Anny v Brně v Mezinárodním centru klinického výzkumu ICRC a Mayo Clinic USA.
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Computational Modelling of Mechanical Behaviour of "Elastomer-Steel Fibre" Composite
Lasota, Tomáš ; Okrouhlík,, Miloslav (oponent) ; Nováček,, Vít (oponent) ; Burša, Jiří (vedoucí práce)
This thesis deals with composite materials made of elastomer matrix and steel reinforcement fibres with various declinations. It presents computational simulations of their mechanical tests in uniaxial tension and three-point bending realized using finite element (FE) method, and their experimental verification. The simulations were carried out using two different models - bimaterial and unimaterial computational models. The bimaterial model reflects structure of the composite in detail, i.e. it works with the matrix and individual fibres. When the bimaterial model is used, then it is necessary to create each fibre of the composite in the model and it makes numbers of disadvantages (creation of the model is laborious, higher number of elements are needed for discretization of an individual fibre in FE softwares and computational time is higher). On the other side, the unimaterial model does not distinguish the individual fibres, but it works with a model of the whole composite as a homogeneous material and the reinforcing effect of the fibres is included in the strain energy density function. Comparison between experiments and simulations shows that the bimaterial model is in good agreement with the experiments unlike the unimaterial one being able to provide adequate results in the case of tension load only. Hence, a new way was sought of how to extend the unimaterial model by the bending stiffness of fibres. In 2007 Spencer and Soldatos published a new extended unimaterial model that is able to work with both tension and bending stiffnesses of fibres. However, their model is based on Cosserat continuum theory, it is very complicated and is not suitable for practical application. Hence, a new simplified model was created in the thesis (partially according to the Spencer and Soldatos) with own strain energy density function proposed. In order to verify the new unimaterial model with bending stiffness, all the needed equations were derived and a new own finite element solver was written. This solver is based on Cosserat continuum theory and contains the mentioned anisotropic hyperelastic unimaterial model with bending stiffness. It was necessary to use the so called C1 elements, since the Cosserat theory works with second derivatives of displacements. The C1 elements ensure continuity of both displacements field and their first derivatives. Finally, new simulations were performed using the created FE solver and they show that the bending stiffness of fibres can be driven by the appropriate material parameter. In conclusion of this work it is discussed whether the new unimaterial model with bending stiffness is able to provide the same results as the bimaterial model, namely for both tension and bending loads of a composite specimen.
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Influence of Geometrical Parameters on Rupture Risk of Abdominal Aortic Aneurysm
Zemánek, Miroslav ; Janíček, Přemysl (oponent) ; Tonar,, Zbyněk (oponent) ; Holeček, Miroslav (oponent) ; Burša, Jiří (vedoucí práce)
The main objective of this thesis is finite element and experimental modeling of stress-strain states of the soft tissues specially focused on rupture risk of abdominal aortic aneurysm (AAA). The first chapter (chap. 1) summarizes the present state of the mentioned problematic and the major information published in the present-day literature. The key factors for AAA rupture risk decision are also summarized in this chapter. The next chapter (chap. 2) describe the artery wall histology, type of aneurysms and mechanical behavior of artery wall. The second part of the thesis (chap. 3) is focused on experimental modeling of stress-strain states of soft tissues which is necessary for reliable finite element modeling of this behavior. In this chapter a specially designed and produced experimental testing rig is described and the type of tests which is possible to realize with this testing rig. The key factors influencing the stress-strain behavior of the aortic tissue are also summarized and experimentaly tested on porcine thoracic aortas. The new knowledge resulting from experimental testing are summarized at the end of this chapter. The intention of third part (chap. 4) is the mathematical description of the stress-strain behavior of soft tissues, description of frequently used constitutive models and the parameter identification for these constitutive models based on the realized tension tests. The last chapter (chap. 5) is devoted to finite element modeling of the stress-strain states of AAA behavior. First the key factors and assumptions for finite element models creation and evaluation are summarized as well as the material parameters of the constitutive models which are implemented in ANSYS software. Several simulations were realized using hypothetical AAA geometry where the impact of some geometrical parameters change was tested. The backward incremental method using for evaluation of unloading state was designed and tested at real AAA geometry reconstructed from CT scans. Hypertension as one of the key factor for AAA rupture risk was tested using unloaded geometry. The new knowledge and possibilities of finite element modeling are summarized at the end of this thesis. The proposals to next research work is also summarized.
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