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Aplikace gradientní pružnosti v problémech lomové mechaniky
Klepáč, Jaromír ; Profant, Tomáš (oponent) ; Kotoul, Michal (vedoucí práce)
Předkládaná diplomová práce se zabývá aplikací gradientní pružnosti na problémy lomové mechaniky. Konkrétně jde o analytické vyjádření pole posuvů a následně pole napětí v okolí kořene trhliny. Uvažuje se přitom vliv mikrostruktury materiálu. Úvodní kapitoly jsou věnovány stručnému historickému přehledu gradientních modelů a definici základních rovnic gradientní dipolární pružnosti odvozené z II. varianty Mindlinovy gradientní teorie. Pro srovnání jsou uvedeny také vztahy z klasické pružnosti. Následuje odvození asymptotického pole posuvů užitím Williamsovy asymptotické techniky. Pro případ gradientní pružnosti je uveden také výpočet J-integrálu. Vzhledem k singulárnímu charakteru problému jsou zmíněny metody řešení singulárních integrálních rovnic, ke kterým vede matematická formulace problému ve smyslu Cauchyho hlavní hodnoty a Hadamardovy konečné části. Pro výpočet složitého regulárního jádra, je zde uvedena rovněž Gauss-Čebyševova kvadratura. V práci jsou uvedeny také metody přibližného řešení systémů integrálních rovnic. Jedná se o metody vážených reziduí, zejména o pak metodu nejmenších čtverců v kolokačních bodech. V hlavní části práce je odvozen s využitím Fourierovy transformace systém integrálních rovnic pro nekonečnou desku s přímou vnitřní trhlinou zatíženou v nekonečnu tahovým napětím. Tento systém je následně numericky řešen v softwaru Mathematica a výsledky jsou porovnány s konečně prvkovým modelem keramické pěny.
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Solution of General Stress Concentrators in Anisotropic Media by Combination of FEM and the Complex Potential Theory
Ševeček, Oldřich ; Kotoul, Michal (vedoucí práce)
The thesis focuses to the solution of the problems of general stress concentrators in anisotropic media. Particularly, it is a problem of cracks terminating on the interface of two dissimilar materials or problems of general multi-material wedge. The main aim of the work is to work up a complex toolbox for the assessment of general stress concentrators, i.e. a tool for the description of the stress field in its vicinity, the inclusion of the crack bridging effect into the resulting stress field, and the definition of the fracture criteria for the crack impinging at the interface in dissimilar anisotropic media. For the description of the stress field the so-called Lechnitskii-Stroh formalism and continuously distributed dislocation technique, exploiting the complex potential theory is used. The work also widely employs the two-state "psi"-integral (for the calculation of various factors of the asymptotic stress expansions) based on the Betti´s reciprocal theorem in combination with FEM. For the fracture criterion definition the theory of Finite Fracture Mechanics and matched asymptotic expansions is used. Especially the competition between the crack deflection along the interface and the crack penetration into the base material is studied. All the needed calculations are performed in the mathematical softwares MAPLE 10.0, MATLAB 7.1 and in the finite element system ANSYS 10.0.
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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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Implementace, kalibrace a využití podmínek tvárného lomu v programech MKP
Kubík, Petr ; Plánička, František (oponent) ; Kotoul, Michal (oponent) ; Petruška, Jindřich (vedoucí práce)
Předkládaná práce se zabývá problematikou tvárného porušování při monotónním zatěžování, které je výsledkem postupné degradace materiálu za rozsáhlých plastických deformací. V současné době se pro jeho popis a predikci používá velká řada modelů, jejichž kalibrace není jednoduchá. V rešeršní části jsou popsány mechanismy tvárného porušování a oblast bez porušení. Dále je uveden přehled kritérií, které jsou založeny na různých přístupech k poškozování. V rámci této dizertační práce byla navržena a použita kritéria KHPS a KHPS2. V poslední části rešerše je popsán postup stanovení křivky napětí-přetvoření a kalibrace kritérií tvárného porušování. V experimentální části je uveden přehled zkoušek, které byly provedeny za účelem kalibrace vybraných kritérií. Pomocí těchto testů bylo dosaženo různých napěťových stavů v širokém rozsahu triaxiality napětí a Lodeho parametru. V rámci této práce byl navržen speciální typ vzorku, pomocí něhož je dosahováno velmi nízké hodnoty triaxiality napětí. Všechny vzorky byly vyrobeny z oceli 12 050. Jako polotovar byly použity tažené tyče kruhového průřezu o průměru 27 mm, vyrobené z jedné tavby. Pomocí výše uvedených zkoušek byla provedena kalibrace vybraných kritérií tvárného porušování. Tato kritéria byla autorem implementována do explicitního konečnoprvkového programu ABAQUS/Explicit pomocí uživatelského podprogramu VUMAT. Vybraná kritéria byla použita pro simulaci vícestupňového protlačování, u kterého dochází k tvorbě vnitřních centrálních trhlin. Tato kritéria byla také použita na simulaci stříhání tyčí kruhového průřezu. Výsledky ze simulací byly porovnány s experimenty, které provedl průmyslový partner J-VST.
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Effects of Defects on Composite Structures Load Carrying Capacity: Delaminations at a Bi-Material Interface
Matěják, Vladimír ; Kotoul, Michal (oponent) ; Růžička, Milan (oponent) ; Juračka, Jaroslav (vedoucí práce)
Composite materials exhibit a complex failure behaviour, which may be further affected by various defects that arise either during the manufacturing process or during the service life of the component. A detailed understanding of the failure behaviour, and the factors affecting it, is essential for designing composite structures that are safer, more durable and economical. First part of this thesis gives an overview of typical failure mechanisms in composite materials and describes mathematical theories, currently being used in analysing and predicting the failure. Different types of defects are reviewed and their effects on composite materials performance briefly discussed. Delaminations are described in more detail together with basic fracture mechanics principles and their application in the analysis and experimental testing of composite materials. The second part focuses on delamination at an interface of two different materials. An experimental measurement of fracture toughness was performed under three types of loading conditions in order to determine a delamination failure criterion based on a ratio of mode I and mode II. As a part of the experiment, a novel method of measuring the crack length based on digital image processing was developed and also a new type of delamination initiation point definition proposed. Analytical equations for calculating the energy release rate from experimentally measured data were reviewed and extended to account for different elastic moduli of the two materials at the interface. Analytical and finite element investigation revealed that the mode I and mode II contributions are dependent on the distance from the crack tip and therefore a failure criterion based on the mixed mode ratio cannot be used.
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Polymeric metamaterials with advanced mechanical properties
Štaffová, Martina ; Lehocký,, Marian (oponent) ; Kotoul, Michal (oponent) ; Jančář, Josef (vedoucí práce)
Thesis deals with 3D printed polymeric auxetic structures with an emphasis on their mechanical performance. Different designs of auxetic re-entrant cell architectures were used to enhance mechanical properties, especially the energy-absorption-to-weight ratio under compressive loading. The lattice structures were 3D printed by vat photopolymerization masked-stereolithography technique. A novel tool for the complex characterization of 3D printed bodies was developed and systematically demonstrated employing a commercial free-radical photopolymerization resin. The method relies on superimposed static and oscillatory mechanical test combining the heat deflection temperature (HDT) measurement with the dynamic mechanical analysis (DMA) in a single test for fast and reliable characterization of parameters determining the curing behavior of the photopolymer. The influence of printing conditions and post-curing time was investigated to elucidate their effects on residual stresses in 3D-printed cellular bodies. The auxetic architectures were printed using flexible and stiff resins, and the effect of porosity, cell size, and structural gradients was investigated. The results were evaluated from a structural and material point of view, comparing materials above and below Tg. The best energy-absorbing performance was found in a biaxially graded structure with a center-wise location of the highest local porosity. The presented data contribute to a fundamental understanding of the effects of lattice architecture on the deformation response of auxetic structures and identifies routes for structurally tuning the auxetic structures mechanical performance. In addition, the results demonstrate the versatility offered by additive manufacturing techniques in physically realizing complex nature inspired structural architectures.
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Mechanical Reinforcement of Bioglass®-Based Scaffolds
Bertolla, Luca ; Prof. Dr.-Ing. habil. Aldo R. Boccaccini (oponent) ; Kotoul, Michal (oponent) ; Pabst, Willi (oponent) ; Dlouhý, Ivo (vedoucí práce)
Bioactive glasses exhibit unique characteristics as a material for bone tissue engineering. Unfortunately, their extensive application for the repair of load-bearing bone defects is still limited by low mechanical strength and fracture toughness. The main aim of this work was two-fold: the reinforcement of brittle Bioglass®-based porous scaffolds and the production of bulk Bioglass® samples exhibiting enhanced mechanical properties. For the first task, scaffolds were coated by composite coating constituted by polyvinyl alcohol (PVA) and microfibrillated cellulose (MFC). The addition of PVA/MFC coating led to a 10 fold increase of compressive strength and a 20 fold increase of tensile strength in comparison with non-coated scaffolds. SEM observations of broken struts surfaces proved the reinforcing and toughening mechanism of the composite coating which was ascribed to crack bridging and fracture of cellulose fibrils. The mechanical properties of the coating material were investigated by tensile testing of PVA/MFC stand–alone specimens. The stirring time of the PVA/MFC solution came out as a crucial parameter in order to achieve a more homogeneous dispersion of the fibres and consequently enhanced strength and stiffness. Numerical simulation of a PVA coated Bioglass® strut revealed the infiltration depth of the coating until the crack tip as the most effective criterion for the struts strengthening. Contact angle and linear viscosity measurements of PVA/MFC solutions showed that MFC causes a reduction in contact angle and a drastic increase in viscosity, indicating that a balance between these opposing effects must be achieved. Concerning the production of bulk samples, conventional furnace and spark plasma sintering technique was used. Spark plasma sintering performed without the assistance of mechanical pressure and at heating rates ranging from 100 to 300°C /min led to a material having density close to theoretical one and fracture toughness nearly 4 times higher in comparison with conventional sintering. Fractographic analysis revealed the crack deflection as the main toughening mechanisms acting in the bulk Bioglass®. Time–dependent crack healing process was also observed. The further investigation on the non-equilibrium phases crystallized is required. All obtained results are discussed in detail and general recommendations for scaffolds with enhanced mechanical resistance are served.
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Modeling of rigid body rotation movement in space
Komůrková, Lucia ; Kotoul, Michal (oponent) ; Franců, Jan (vedoucí práce)
This bachelor thesis is focused on rotation movement of rigid body in space. It is described rotation matrices and their characteristics. It is devoted to Euler angles representation of rotation in space and introduced Euler kinematic and dynamic equations. Moreover, it indicates the numerical and analytical method for solving these equations for special types of flywheels.
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Popis rozložení napětí v okolí bimateriálového vrubu pomocí zobecněného faktoru intenzity napětí
Hrstka, Miroslav ; Kotoul, Michal (oponent) ; Profant, Tomáš (vedoucí práce)
Předkládaná diplomová práce se zabývá problémem stanovení zobecněného faktoru intenzity napětí a následného popisu rozložení napětí v okolí bimateriálového vrubu kombinací analytických a numerických metod. Práci je možné rozdělit do tří částí. První část pojednává o základech lomové mechaniky a mechanice kompozitních materiálů. Druhá část se zabývá metodami řešení rovinné anizotropní pružnosti, za základě kterých jsou ve třetí části sestaveny výpočtové modely. První z nich slouží k určení vlastní hodnoty exponentu singularity pomocí Lechnicky-Eshelby-Strohova formalismu. Druhý výpočtový model slouží k stanovení zobecněného faktoru intenzity napětí metodou psi-integrálu založeného na Bettiho recipročním teorému. Všechny potřebné výpočty jsou prováděny v softwarech ANSYS 12, Maple 12 a Silverforst FTN95. Výsledky budou srovnány s hodnotami získanými metodou přímé extrapolace.
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