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.

Thin sheets and membrane structures are widely used in space applications such as solar sails, sunshields and membrane optics. Surface flatness over a large area is one of the key requirements for many applications using the flexible thin structures. However, wrinkles are commonly observed in thin sheets. It is thus important to understand the mechanics of thin sheets for practical applications that require reliable control of surface wrinkles. In this study, a model problem of stretch-induced wrinkling of thin sheets is considered. First, a two-dimensional (2-D) finite element model was developed to determine stretch-induced stress distribution patterns in hyperelastic thin sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction was found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain. Next, an eigenvalue analysis was performed to predict the critical conditions for buckling of the elastic sheet under the prescribed boundary conditions, followed by a nonlinear post-buckling analysis to simulate evolution of stretch-induced wrinkles. Experiments were conducted to measure stretch-induced wrinkling of polyethylene thin sheets, using the three-dimensional digital image correlation (3D-DIC) technique. It was observed that the wrinkle amplitude first increased and then decreased with increasing nominal strain, in agreement with finite element simulations for a hyperelastic thin sheet. However, unlike the hyperelastic model, the stretch-induced wrinkles in the polyethylene sheet were not fully flattened at high strains (> 30%), with the residual wrinkle amplitude depending on the loading rate. The hyper-viscoelastic and the parallel network nonlinear viscoelastic material models were adopted for finite element simulations to improve the agreement with the experiments, including the wrinkle amplitude, residual wrinkles and rate dependence. Finally it is noted that wrinkling is sensitive to defects and material inhomogeneity in thin sheets. By varying the elastic stiffness in a narrow region, numerical simulations show drastically different wrinkling behavior, including the critical strain and evolution of wrinkle amplitude and wavelength. In conclusion, a comprehensive understanding of stretch-induced wrinkling is established, where geometry, material, and boundary conditions all play important roles. / text

A finite element based method for solution of large-deformation hyperelastic constitutive models is developed, which solves the Cauchy-stress balance equation using a single rotation of stress from principal directions to a fixed co-ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration-order incompressibility enforcement, and an iterative solution method that employs notional `small strain¿ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer `necking¿; the method is shown to give good agreement with published results from a well-established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved.

No description available.

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

This work aims at dimensional reduction of nonlinear material models in an asymptotically accurate manner. The three-dimensional(3-D) nonlinear material models considered include isotropic, orthotropic and dielectric compressible hyperelastic material models. Hyperelastic materials have potential applications in space-based inflatable structures, pneumatic membranes, replacements for soft biological tissues, prosthetic devices, compliant robots, high-altitude airships and artificial blood pumps, to name a few. Such structures have special engineering properties like high strength-to-mass ratio, low deflated volume and low inflated density. The majority of these applications imply a thin shell form-factor, rendering the problem geometrically nonlinear as well. Despite their superior engineering properties and potential uses, there are no proper analysis tools available to analyze these structures accurately yet efficiently. The development of a unified analytical model for both material and geometric nonlinearities encounters mathematical difficulties in the theory but its results have considerable scope. Therefore, a novel tool is needed to dimensionally reduce these nonlinear material models. In this thesis, Prof. Berdichevsky’s Variational Asymptotic Method(VAM) has been applied rigorously to alleviate the difficulties faced in modeling thin shell structures(made of such nonlinear materials for the first time in the history of VAM) which inherently exhibit geometric small parameters(such as the ratio of thickness to shortest wavelength of the deformation along the shell reference surface) and physical small parameters(such as moderate strains in certain applications). Saint Venant-Kirchhoff and neo-Hookean 3-D strain energy functions are considered for isotropic hyperelastic material modeling. Further, these two material models are augmented with electromechanical coupling term through Maxwell stress tensor for dielectric hyperelastic material modeling. A polyconvex 3-D strain energy function is used for the orthotropic hyperelastic model. Upon the application of VAM, in each of the above cases, the original 3-D nonlinear electroelastic problem splits into a nonlinear one-dimensional (1-D) through-the-thickness analysis and a nonlinear two-dimensional(2-D) shell analysis. This greatly reduces the computational cost compared to a full 3-D analysis. Through-the-thickness analysis provides a 2-D nonlinear constitutive law for the shell equations and a set of recovery relations that expresses the 3-D field variables (displacements, strains and stresses) through thethicknessintermsof2-D shell variables calculated in the shell analysis (2-D). Analytical expressions (asymptotically accurate) are derived for stiffness, strains, stresses and 3-D warping field for all three material types. Consistent with the three types of 2-D nonlinear constitutive laws,2-D shell theories and corresponding finite element programs have been developed. Validation of present theory is carried out with a few standard test cases for isotropic hyperelastic material model. For two additional test cases, 3-Dfinite element analysis results for isotropic hyperelastic material model are provided as further proofs of the simultaneous accuracy and computational efficiency of the current asymptotically-correct dimensionally-reduced approach. Application of the dimensionally-reduced dielectric hyperelastic material model is demonstrated through the actuation of a clamped membrane subjected to an electric field. Finally, the through-the-thickness and shell analysis procedures are outlined for the orthotropic nonlinear material model.

The understanding of the deformation mechanics within porous structures is an important field of study as these materials exist in nature as well as can be manufactured industrially influencing our lives daily. The motivation of the research contained within this manuscript was inspired by the desire to understand the mechanics of an elastomeric closed–cell porous material. This type of porous material is often used in load–bearing applications such as sport helmet liners and packing material which can be subjected to large deformations at high rates. Additionally, short term transient effects were explored. In order to investigate the deformation mechanics of a closed cell elastomeric foam, a polychloroprene (neoprene) material was chosen as it was available in both rubber form and a foam with relatively consistent cell size. Compression tests were conducted on the polychloroprene rubber at strain rates ranging from 0.001/s to 2700/s which identified that it had a hyper–viscoelastic behaviour with a significant strain rate dependence. A newly developed constitutive model was created to capture the response of the polychloroprene rubber. A coupled finite element model of the polychloroprene foam was created and compared to experimental tests for validation. The model slightly over predicted the stress level response of the experimental tests. The model was used to identify momentum dissipation mechanisms that contributed to the low wave speed measurement of approximately 70 m/s determined from the model. The investigation of wave transit times through use of the model was key to interpreting experimental data. Of the morphological factors investigated, it was determined that wall thickness had the most significant impact on the stress response of the foam. The pore–scale model was useful for visualizing wavepropagation effects and deformation mechanics which was not feasible experimentally.

The understanding of the deformation mechanics within porous structures is an important field of study as these materials exist in nature as well as can be manufactured industrially influencing our lives daily. The motivation of the research contained within this manuscript was inspired by the desire to understand the mechanics of an elastomeric closed–cell porous material. This type of porous material is often used in load–bearing applications such as sport helmet liners and packing material which can be subjected to large deformations at high rates. Additionally, short term transient effects were explored. In order to investigate the deformation mechanics of a closed cell elastomeric foam, a polychloroprene (neoprene) material was chosen as it was available in both rubber form and a foam with relatively consistent cell size. Compression tests were conducted on the polychloroprene rubber at strain rates ranging from 0.001/s to 2700/s which identified that it had a hyper–viscoelastic behaviour with a significant strain rate dependence. A newly developed constitutive model was created to capture the response of the polychloroprene rubber. A coupled finite element model of the polychloroprene foam was created and compared to experimental tests for validation. The model slightly over predicted the stress level response of the experimental tests. The model was used to identify momentum dissipation mechanisms that contributed to the low wave speed measurement of approximately 70 m/s determined from the model. The investigation of wave transit times through use of the model was key to interpreting experimental data. Of the morphological factors investigated, it was determined that wall thickness had the most significant impact on the stress response of the foam. The pore–scale model was useful for visualizing wavepropagation effects and deformation mechanics which was not feasible experimentally.

The propagation of waves through nonlinear media is of interest here, namely as it pertains to two specific examples, a nonlinear dielectric and a hyperelastic solid. In both cases, we examine the propagation of two-dimensional, weakly nonlinear, quasi-planar waves. It is found that such systems will have a nonlinearity that is intrinsically cubic, and therefore, a classical Zabolotskaya-Khokhlov equation cannot give an accurate description of the wave evolution. To determine the general evolution equation in such systems, a multi-timing technique developed by Kluwick and Cox (1998) and Cramer and Webb (1998) will be employed. The resultant evolution equations are seen to involve only one new nonlinearity coefficient rather than the three coefficients found in other studies of cubically nonlinear systems. After determining the general evolution equation, inclusion of relaxation, dispersion and dissipation effects can be easily incorporated. / Master of Science

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