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Constitutive Modelling of Composites with Elastomer Matrix and Fibres with Significant Bending Stiffness
Fedorova, Svitlana ; Kotoul, Michal (referee) ; Menzel, Andreas (referee) ; Burša, Jiří (advisor)
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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Stress-strain analysis of winepress frame
Vaculka, Miroslav ; Fedorova, Svitlana (referee) ; Novák, Kamil (advisor)
This bachelor’s thesis deals with stress-strain analysis of winepress frame. The press is made of self help. No analysis has been performed for it yet. The thesis contains its detailed research, then basic research about other winepresses and research in the Mechanics of Materials. A computational model was set and stress-strain analysis was done in an analytical approach and numerical approach using the program ANSYS. Everything was evaluated in the discussion of the results, including the achievement of the safety factor to limit the state of elasticity. A system approach was used in the entire bachelor’s thesis.
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Determination of principal material directions in tissues of aortic wall
Bogdan, Miloš ; Fedorova, Svitlana (referee) ; Burša, Jiří (advisor)
Main goal of this thesis is to find a way how to determine principal material directions in the tissues of aortic wall at large strains. A method is designed for this purpose on the basis of same principles as the method of detemination of principal strains and their directions using rosette gauges. These principles are consequences of tensor properties. In this work the method is applied for a stiffness tensor instead of strain tensor. An algorithm that calculates with this new method is also made and the required experiments are realised on three samples of porcine aorta. Principal material directions and deviations of the values are calculated for both small and large strains.
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Constitutive Modelling of Composites with Elastomer Matrix and Fibres with Significant Bending Stiffness
Fedorova, Svitlana ; Kotoul, Michal (referee) ; Menzel, Andreas (referee) ; Burša, Jiří (advisor)
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.
|
|
|
Stress-strain analysis of winepress frame
Vaculka, Miroslav ; Fedorova, Svitlana (referee) ; Novák, Kamil (advisor)
This bachelor’s thesis deals with stress-strain analysis of winepress frame. The press is made of self help. No analysis has been performed for it yet. The thesis contains its detailed research, then basic research about other winepresses and research in the Mechanics of Materials. A computational model was set and stress-strain analysis was done in an analytical approach and numerical approach using the program ANSYS. Everything was evaluated in the discussion of the results, including the achievement of the safety factor to limit the state of elasticity. A system approach was used in the entire bachelor’s thesis.
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|
Determination of principal material directions in tissues of aortic wall
Bogdan, Miloš ; Fedorova, Svitlana (referee) ; Burša, Jiří (advisor)
Main goal of this thesis is to find a way how to determine principal material directions in the tissues of aortic wall at large strains. A method is designed for this purpose on the basis of same principles as the method of detemination of principal strains and their directions using rosette gauges. These principles are consequences of tensor properties. In this work the method is applied for a stiffness tensor instead of strain tensor. An algorithm that calculates with this new method is also made and the required experiments are realised on three samples of porcine aorta. Principal material directions and deviations of the values are calculated for both small and large strains.
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