This diploma thesis deals with the creation of computational model of arterial aneurysm, which respects its real geometry and constitutive behaviour. Subsequently there is explored the risk of rupture, comparing the values of the highest main stress in aneurysm´s and intact aorta´s wall. This thesis also offers the comprehensive summary and mutual comparision of current constitutive (hyperelastic) models, which are for simplicity isochoric considered. The main task of this thesis is to formulate the method for finding of „unloaded“ = „outstressed“ = „primary“ = reduced geometry, which is generally unavailable. Models of aneurysm´s geometry, used so far, present already deformed configurations from blood pressure, axial prestrech and rezidual strain.

The master's thesis deals with the determination of macroscopic behavior of a particulate composite with cross-linked polymer matrix under tensile load. The main focus of thesis is estimation of mechanical properties of a composite loaded by tensile loading using numerical methods (especially finite elements method). Investigated composite is composed of matrix in a rubbery state filled by alumina-based particles (Al2O3). Hyperelastic properties of the matrix have been modeled by the Mooney-Rivlin material model. Different compositions of particles, their different shape, orientation and different volume fractions have been considered. For all these characteristics of composite numerical models have been developed. The damage mechanisms of the matrix have also been taken into account. Results of numerical analyses have been compared with experimental data and good agreement between numerical models with damage mechanisms of matrix and experimental data has been found.

This master thesis is focused on usage of monitoring pulse wave propagation in aortic system in a field of diagnostic abdominal aortic aneurysm (AAA). There is a description of cardio-vascular system and its pathology in a form of AAA. A summarization of temporary diagnostic method was created and some new methods were proposed. This new methods presume monitoring of pulse wave propagation. Fluid structure interaction (FSI) analyses of pulse wave propagation were performed on simplified models of geometry which representing specific sections of aorta. The goal of these analyses was to prove usage of FSI method in a future development of proposed diagnostic methods.

This doctoral thesis deals with the study of electro-hydrodynamics in the area of numerical modelling of biomechanical systems, concretely in the method of bioimpedance plethysmography. Solving tasks of pulsatile blood flow in the elastic vessel wall is currently one of the most complicated problem in mechanics and biomechanics due to the interaction of two continua on the common boundary. The whole system is additionally loaded by diagnostic electric current. This doctoral thesis was created in cooperation with the Institute of Scientific Instruments of the CAS, v. v. i. Brno with the team engaged in medical signals (the leader Ing. Pavel Jurák, CSc.). Experimental measurements were made independently in the St. Anne's University Hospital Brno in the International Clinical Research Center ICRC and in the Mayo Clinic USA.

This diploma thesis focuses on realization of a computational model of fibre composite with elastomer matrix and on homogenization of properties of this composite. The work deals with computational modelling of strain-stress states which arise in mechanical tests of composites. The composites investigated by mechanical tests comprise of hyperelastic rubber matrix and steel reinforcing fibres. Computational modelling is carried out at two levels of the model. First, with three-dimensional modelling of fibres and matrix as two different materials and, second, using a homogenized model of composite; this constitutive model describes the composite as a homogeneous anisotropic material. It means that properties of fibres are encompassed into strain energy density by the mathematical formulation of the constitutive model. Further, the work deals with computational modelling of mechanical tests of hyperelastic isotropic materials used for identification of their material parameters and for verification of the selected constitutive model of material. For particular hyperelastic material, simulations of tests were carried out, namely of uniaxial tension, biaxial tension, uniaxial compression, biaxial compression, pure shear and uniaxial tension with constrained transversal strain (planar tension). Parameters of the constitutive model were determined of experimental input data. Verification of the constitutive model was carried out by comparison of the data acquired by experiments with the results of simulations of mechanical tests in FE program system Ansys. Then the authentic constitutive model of material was used for description of matrix behaviour in models of mechanical tests of composite material and results were compared with experimental data. Principal objectives which I want to attain are following: • to acquaint with the constitutive models of hyperelastic isotropic and anisotropic materials and identification of their perameters on base of mechanical tests. • to create computational models of testing specimens of composite “ rubber – steel fibre“ for different fibre arrangements and to use the created computational models in simulations of chosen tests. • to test the possibilities of computational modelling of composites with application of homogenized properties and to compare the results of both approaches. Results which were attained: • the computational models were created with the fibres modelled; the strain – stress characteristics are qualitatively corresponding to experiments, and quantitative difference is 20% - 40% (see (4.3)). • the computational models based on homogenization of properties were tested and gave results corresponding to the models with modelled fibres (see (4.4)) with a good accuracy.

This master thesis analyses stress and strain of iliac artery with atheroma. Model of artery is created as 2D and symmetric about the y-axis. The first part of the thesis deals with a research, which includes obtaining information from medicine, which is necessary fort the right solution of the task. Next part dedicates to nonlinear mechanics, constitutive modeling from the view of biomechanice and computational modeling of arteries. In the next part is made analysis for load on artery by physiological and also by high blood pressure. In the end were specified uncertainties of the used model and evaluated chance of atherosclerotic plaque rupture.

This thesis deals with computational modelling of rubber damper using Finite element method (FEM). This thesis includes experimental measurement of material properties of rubber subjected to static and dynamic loading and their implementation into viscoelastic and hyperelastic material models with respect to given task. Dependance of dynamic stiffness on loading frequency obtained from the simulation is validated with experimental measurement. In the end the difference between results is investigated and possible causes of that are introduced.

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.

The diploma thesis is focused on the creation of the aneurysm finite element model and the making of the aneurysm wall stess-strain analysis using ANSYS software. The model of abdominal aortic aneurysm geometry starts from the CT scan of the particular patient. In the thesis there are compared two chosen constitutive models, each of them appears from different mechanical tests done on human arterial fibre samples. Furthermore, a limiting condition for aneurysm wall structure damage is expressed. On the basis of the results of stress calculation in the aneurysm wall and the limiting condition, the safety coefficient and rupture factors risk are worked out.

This master thesis is focused on stress-strain analysis abdominal aortic aneurysm using ANSYS software. The model of abdominal aortic aneurysm are based on CT scans of five specific patients. The branching arteries are included to the model and one goal of this thesis is decision about their influence of the wall stress. In this thesis was used a hyperelastic materiál model, which is based on mechanical tests done on human arterial samples.