Breast cancer is one of the most frequently diagnosed cancers affecting women in the United States. An ongoing objective of many research groups is to develop a biomechanical breast model for different applications, ranging from surgical outcome predictions for patients undergoing breast reconstruction surgery, to image registration for planning plastic surgery. Achieving the goal of developing a physics based biomechanical model of the human breast requires the determination of material properties of the various tissues constituting the breast. The objective of this thesis is to develop an appropriate hybrid experimental-numerical technique to enable the calibration of material parameters of skin for different constitutive models (commonly used for skin). The quantification of the material parameters thus obtained validates the bulge test method to be used in testing soft tissue specimens like skin. A bulge test device was custom-built for this work; it consists of a pressure chamber, two digital cameras, and a syringe pump as its main components. The syringe pump provides a constant flow rate of water into the pressure chamber and results in the bulging of specimens with a diameter between 45 mm and 80 mm. Three-dimensional Digital Image Correlation technique is used to obtain full field displacement measurements of the three dimensional shape of the bulge. Tests were performed on commercial rubber sheets of different thickness and on porcine skin specimens; in these tests, the bulge shape was measured at monotonically increasing and decreasing pressure levels, as well as during cyclic loading allowing determination of the deformation and strain fields over the specimen surface. In order to extract the material properties, a hybrid experimental-numerical method was used: the experiment was modeled numerically using the finite element analysis software Abaqus, imposing the commonly used Mooney-Rivlin model for isotropic materials and the Gasser-Ogden-Holzapfel model for anisotropic materials. A comparison between the experimentally measured and numerically simulated bulge shapes was used to determine the optimized material parameters under biaxial loading conditions over a large range of stretch levels. / text

This thesis will be focusing on studies about the hyperelastic material method and how to best implement it in a FEA model. It will look more specific at the Mooney-Rivlin method, but also have a shorter explanation about the different methods. This is due to problems Roxtec has today about simulating rubber takes long time, are instable and unfortunately not completely trustworthy, therefore a deep study about the hyperelastic material method were chosen to try and address these issuers. The Mooney-Rivlin method (which is a part of the hyperelastic material method) is reliant on a few constant to represent the material, how to obtain these constants numerical and later implement these is suggested in this thesis as well. The results is the methodology needed to obtain constants for Mooney-Rivlin and later how to implement these in FEA software. In this thesis the material Roxylon has been studied and given suggestion on these constants as well as an implementation of the given material. / För en bra simulering utav hyperelastiska material, exempelvis för gummi, har detta examensarbete fokuserat på att undersöka hyperelastiska material metoder och hur man kan implementera det i FEA program.

Cascade Drives develops electromechanical actuators using a rack and pinion configuration to achieve a combination of high load and high-speed operation. A patented load distribution mechanism enables the use of multiple pinions on a single rack, resulting in a compact unit with high positional accuracy capable of absorbing shock loads. The key to the invention lies in the load distribution mechanism. This can be realized in several ways, using an elastically deformable element. These deformable elements could be subjected to large deformation without there being any internal energy dissipation and such materials are classified under hyperelastic material models. Experimentation of these rubber elements was conducted along with developing a mathematical and analytical model to investigate different geometry and material hardness. A MATLAB code using the Mooney-Rivlin equation was generated and ANSYS was utilized to produce the analytical model, these models were then verified with the experimental results. It is concluded from the results that, the material with medium hardness has the perfect match between the three models. Along with this, a method was investigated to analyze the behavior of rubber after it had been aged. The outcome of this method didn’t derive any conclusion. / Cascade Drives utvecklar elektromekaniska ställdon som använder en rack-och-pinjong-princip för att uppnå en kombination av hög kraft och hög hastighet. En patenterad lastfördelningsmekanism möjliggör användning av flera kugghjul på en kuggstång, vilket ger en kompakt lösning med hög positionsnoggrannhet som kan absorbera stötbelastningar. Nyckeln till uppfinningen ligger i lastfördelningsmekanismen. Detta kan realiseras på flera sätt med hjälp av elastiskt deformerbara element. Dessa deformerbara element ska kunna utsättas för stor deformation utan intern energiförlust och sådana material klassificeras under hyperelastiska materialmodeller. Experimentering av sådana gummielement genomfördes tillsammans med framtagande av en matematisk och analytisk modell föratt undersöka olika geometrier och materialhårdheter. En MATLAB-kod med MooneyRivlin-ekvationen genererades och ANSYS användes för att producera den analytiska modellen. Dessa modeller verifierades sedan med experimentresultaten. Av resultaten dras slutsatsen att materialet med medelhårdhet har den bästa matchningen mellan de tre modellerna. Tillsammans med detta undersöktes en metod för att analysera beteendet hos gummi efter att det åldrats. Resultatet av denna metod drog inte någon slutsats

Compression of elastomer elements are nonlinear due to the cross-linked molecular structure owing to a property known as hyperelasticity. Hyperelasticity is defined as the nonlinear stress-strain behavior shown by rubber like materials which can be strained up to a range of 700% in tension and up to 40% in compression. The stress-strain behavior is modeled by using different material models which predict the behavior very precisely.  Linear actuators from Cascade Drives AB uses a patented load sharing mechanism using elastically deformable elements to distribute the torque evenly between all the gears interacting with a common gear rack. An accurate model predicting the response of elastomer under compression has been developed in this thesis project. The elastomers were loaded in compression to provide flexibility for the system. First a static model was developed, where both a rectangular and a cylindrical roller model were analyzed.  The two models were derived using a continuum mechanics approach and the stiffness of the elastomers along with the torque output of the gearbox was calculated. A MATLAB model and an FEA model using ANSYS was created, and the results were compared. An error estimate between the MATLAB and FEA results for the rectangular and roller model was plotted for a certain β° of rotation of the gear. The models were also checked for different materials and the output torque for the different materials was plotted and analyzed. Finally, the experimental results were compared with the MATLAB results for the rectangular and roller models. The rectangle and roller model can be both used to predict the behaviour of using elastomers as the load sharing elements in applications. / Kompression av elastomerelement är olinjär till följd av den tvärbundna molekylära strukturen, en egenskap som kallas hyperelasticitet. Hyperelasticitet definieras som det icke-linjära spännings-töjningsbeteendet som uppvisas av gummiliknande material vilka kan töjas upp till av 700% och upp till komprimeras upp till 40%. Spänningsbelastningsbeteendet modelleras med hjälp av olika materialmodeller som förutsäger beteendet.  Cascade Drives linjäraktuatorer använder elastiskt komprimerbara element i sin lastfördelningsmekanism för att använda multipla plinjonger på ett kuggrack utan att få ett överbestämt system. Lastfördelningsmekanismen ger även en viss flexibilitet för systemet.  En modell som förutsäger responsen hos elastomerer under kompression har utvecklats i denna avhandling. Två geometriska former undersöktes modeller togs fram för både en rektangulär och cylindrisk rulle. De två modellerna härleddes med en kontinuummekanisk metod och elastomerernas styvhet beräknades. En MATLAB-modell och en FEM-modell i ANSYS skapades och resultaten jämfördes och en feluppskattning modellerna gjordes. Modellerna undersöktes också för olika material och utmattningsegenskaperna för de olika materialen analyserades.  Rektangel- eller rullmodellen kan båda användas för att förutsäga hur en elastomer skulle bete sig i en växellådsapplikation.

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

Despite being one of the most important organs of vertebrates, the material properties of skin are also one of the most poorly understood. In the field of designing medical devices and surgical tools there are significant advantages to having a model that describes the interaction of forces between a blade tip and skin during surgical cutting. In general, skin can best be described as a composite layer consisting of a viscoelastic dermis with interwoven collagen and elastin fibers beneath a superficial epidermis. The purpose of this research is to study the fracture toughness of porcine skin during practical cutting applications, the behavior of skin under quasistatic loads, and viscoelastic behavior of skin during stress relaxation. To fully describe the mechanics of skin in this model tensile test are conducted to determine the material properties of skin. The fracture toughness of the material is calculated by measuring the energy release rate of the material during required during cutting with Number 11 scalpel blade with a tip radius of 12 [micro]m . These results are then compared to a finite element analysis with a debonding interface and a Mooney-Rivlin hyperelastic material model with viscoelastic relaxation in an effort to predict the loads required by tools during surgical applications. The main outcome of this research is the development of a testing protocol and material model of skin that can be used in finite element simulations of uniaxial loads and surgical cutting.

The dynamic properties of the elastic coupling are not readily known; therefore testing has to be performed in order to determine these properties. This is the primary objective for this thesis. The dynamic properties in question are the stiffness and damping. An attempt to determine the dynamic properties was also be carried out through the use of finite element analysis. There are two different configurations of couplings. One configuration forms the coupling from several elastic elements, referred to as HRC elements, which are manufactured in three sizes: A, B, and C. The second configuration, referred to as the HEMD coupling, has a single elastic member in the form of a hollow rubber/fabric ring connecting the input to the output. The couplings have cords made of either polyester or nylon. These cords will affect the dynamic properties of the coupling.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-05-03T11:57:05Z No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-05-03T13:20:55Z (GMT) No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-05-03T13:20:55Z (GMT). No. of bitstreams: 2 Dissertação - Pedro Felipe Tavares do Amaral - 2018.pdf: 5863877 bytes, checksum: 084454dc18411f245114eb910cfa2474 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-02-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the present work, studies about the nonlinear static and dynamic behavior of a spherical membrane are presented. This membrane is composed by a hyperelastic, incompressible homogeneous and isotropic material, which is defined by either of the two distinct constitutive models: Mooney-Rivlin or the Neo-Hookean model. The equilibrium equations are obtained from the large-strain theory, by utilizing a variational formulation and by subjecting the membrane to an uniformly distributed internal radial pressure differential. From the nonlinear static analysis, internal membrane tensions and strains are obtained. From the dynamic analysis, the frequency-amplitude relation, the linear stability analysis, the time response, bifurcation diagrams, resonance curves and basins of attraction are obtained. As a first step, there is an analysis on a membrane composed by the same experimental material, which is described by the two different constitutive models presented in this work. It is observed that the dynamic responses are considerably distinct, due to the difference between the geometrical nonlinearities that each constitutive model insert on the equilibrium equation. The Neo-Hookean model has a lower pre-stretching limit, and its attraction basins are more eroded and irregular than the Mooney-Rivlin, that is still stable on regions of larger vibration amplitudes. Then, the influence of the Mooney-Rivlin parameter (α) is evaluated, and it is found that this parameter is the main source of the differences between the constitutive models, modifying the stability, nonlinear vibrations and also influencing on the loss or gain of the global rigidity of the membrane. / Neste trabalho são apresentados estudos dos comportamentos não lineares, estático e dinâmico, de uma membrana de geometria esférica composta por um material hiperelástico, incompressível, homogêneo e isotrópico definido por um entre esses dois modelos constitutivos: Mooney-Rivlin ou Neo-Hookeano. As equações de equilíbrio são obtidas a partir da teoria de grandes deformações, utilizando uma formulação variacional e considerando a membrana esférica submetida a uma pressão interna na direção radial uniformemente distribuída. A partir da análise não linear estática, encontram-se as tensões e as extensões radiais da membrana e da análise dinâmica obtêm-se as relações frequência-amplitude, a análise não linear da estabilidade, as respostas no tempo, os diagramas de bifurcação, as curvas de ressonância e as bacias de atração da membrana. Primeiramente, analisa-se a membrana composta por um mesmo material experimental e descrita pelos dois modelos hiperelásticos avaliados nesta dissertação. Observa-se que as respostas dinâmicas são consideravelmente distintas entre si devido à diferença entre as não linearidades geométricas que cada modelo constitutivo insere na equação de equilíbrio, sendo que o modelo Neo-Hookeano apresenta menor limite de pré-carregamento com bacias de atração mais erodidas e menos uniformes quando comparado ao modelo de Mooney-Rivlin, que ainda apresenta estabilidade em regiões de maior amplitude de vibração. Posteriormente, avalia-se a influência do parâmetro do material do tipo Mooney-Rivlin (α), que é a principal fonte das diferenças entre os modelos constitutivos, na estabilidade e nas vibrações não lineares da membrana esférica, observando-se que o parâmetro influência na perda ou no ganho de rigidez global do problema.

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

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.