Peridynamics, presented by Silling in 2000 [1], is a reformulation of the elastic theory from differential equations to integral equations, which are more equipped to handle discontinuities, such as crack initiation and propagation. Because of this, peridynamics is an effective tool to address many of the problems relevant to the aerospace and defense industries. For example, airborne sand particles and raindrops cause local damage to aircraft in flight. This damage manifests itself as radial and subsurface lateral cracking, as well as increased surface roughness. All of these damage morphologies may result in undesired degradation of mechanical and optical properties. This dissertation aims to address the question of how peridynamics (PD) can be used as a tool to help understand impact problems and resultant damage. Three main types of problems will be discussed: (1) modeling of quasi-static nano- and micro-indentation in PD; (2) solid impact experiments and simulations involving glass micro-spheres impacting coated and uncoated advanced ceramics, and sand particles impacting optical glasses; and (3) the implementation of a new, fully three-dimensional hyperelastic material model in state-based PD to simulate nylon bead impact and capture the damage patterns relevant to raindrop impact. In the first portion, a new method for modeling indentation in PD is presented using the principle of viscous damping and automatic convergence checking. In these simulations, depth-controlled indentation is performed by splitting up the total indentation depth into multiple stages, and applying damping at each stage to ensure the system reaches equilibrium before allowing for failure. PD results show good agreement to experimental data, in terms of crack lengths and force-displacement curves. In a chapter about solid particle impact, two studies are presented. In the first, glass spheres with diameters ranging from 200 to 700 um impact multi-spectral zinc sulfide (MS-ZnS) with various coating systems. It was found that samples containing the REP coating had better resistance to damage than those without. This resistance was evident in all three damage metrics used: impact pit diameter, radial crack length, and lateral crack size. Simulations were carried out in bond-based PD, with good agreement to experiments regarding damage metrics and rebound velocity. The second solid particle impact study involved sand particles impacting four different types of optical glasses: BK7, alumino-boro-silicate, fused silica, and Pyrex. First, data from experiments was analyzed, and a multi-variable power law regression was performed to show that sand particle shape plays a significant role in resultant damage. This was confirmed via bond-based PD simulations, with damage quantities agreeing well with experimental values. Finally, the problem of how to model raindrop impact using nylon beads was examined. Due to the large amounts of elastic strain experienced by the nylon beads during impact experiments, it was determined that a hyperelastic material model could be a good fit. Based on elastic theory and classical continuum mechanics, a new, fully three-dimensional Neo-Hookean material model was implemented in nonordinary state-based peridynamics. This model was verified against results and finite element analysis, with very good agreement. Preliminary simulations including damage show good results, consistent with experiments.

No description available.

Structural engineering has progressed from design for life safety limit states to performance based engineering, in which energy dissipation systems in structural frameworks assume prime importance. A visco-hyperelastic device is a completely new type of passive energy dissipation system that not only combines the energy dissipation properties of velocity and displacement dependent devices but also provides additional stability to the structure precluding overall collapse. The device consists of a viscoelastic material placed between two steel rings. The energy dissipation in the device is due to a combination of viscoelastic dissipation from rubber and plastic dissipation due to inelastic behavior of the steel elements. The device performs well under various levels of excitation, providing an excellent means of energy dissipation. The device properties are fully controlled through modifiable parameters. An initial study was conducted on motorcycle tires to evaluate the hyperelastic behavior and energy dissipation potential of circular rubber elements, which was preceded by preliminary finite element modeling. The rubber tires provided considerable energy dissipation while displaying a nonlinear stiffening behavior. The proposed device was then developed to provide additional stiffness that was found lacking in rubber tires. Detailed finite element analyses were conducted on the proposed device using the finite element software package ABAQUS, including parametric studies to determine the effect of the various parameters of device performance. This was followed by a nonlinear dynamic response history analysis of a single-story steel frame with and without the device to study the effects of the device in controlling structural response to ground excitations. Static analyses were also done to verify the stabilizing effects of the proposed device. Results from these analyses revealed considerable energy dissipation from the device due to both viscoelastic as well as plastic energy dissipation. Detailed experimental analyses on the proposed device, finite element analyses of the device on multistory structures have been put forth as the areas of future research. It may also be worthwhile to conduct further research, as suggested, in order to evaluate the use of scrap tires which is potentially a very valuable structural engineering material. / Master of Science

This thesis presents the results of an investigation of a multiple degree of freedom (MDOF) structure with hyperelastic bracing using nonlinear and incremental dynamic analysis. New analytical software is implemented in the investigation of the structure, and the study seeks to investigate the effectiveness of hyperelastic bracing as a seismic protection device. Hyperelastic braces incorporate a new idea of a nonlinear elastic material that gains stiffness as the brace deforms. Structural behaviors of particular concern for an MDOF frame are stability, residual displacement, base shear, and dispersion. The structure is analyzed under two ground motion records of varying content, and for two separate P-Delta cases of varying severity. Two sets of hyperelastic braces are investigated for their influence under the two ground motions and two P-Delta cases. Each scenario is analyzed using nonlinear dynamic analyses to investigate the response histories, and Incremental Dynamic Analysis (IDA) to investigate dispersion and the behavior of specific response measures as ground motion intensity increases. IDA curves are created for interstory drift and base shear for comparison between the two response measures. The research shows that the inclusion of hyperelastic braces in the MDOF frame improves the overall stability of the structure and reduces the amount of dispersion and residual displacement. The hyperelastic braces are shown to give positive performance characteristics while not detrimentally increasing system forces under regular service loads. The results highlight the benefit of the unique stiffening properties of hyperelastic braces as a seismic protection device. / Master of Science

<p dir="ltr">Magnetorheological elastomers (MREs) are a type of smart material composed of ferrous particles suspended in a solid elastic matrix [5, 6]. When an external magnetic field is applied to an MRE, the ferrous particles tend to align with the field, causing either deformation and/or a change in the mechanical properties of the system. MREs are utilized in applications such as soft robotics, actuators, sensors, vibration control systems, and mechanical metamaterials[20, 19, 27, 5, 6, 13]. Recent demand for theses technologies has motivated an increasing focus on the material properties of MRE’s over the last 20 years [6]. Multiple authors have proposed a variety of hyperelastic mechanical and magnetomechanical models to describe these materials [16, 12, 15, 25, 14, 38, 2, 6, 8, 24]. The research presented in this dissertation focuses on the modeling and characterization of MRE’s using a systematic development of the conservation and balance laws, Maxwell’s equations, and constitutive equations needed to describe the MRE as a multi-constituent system. The material parameters resulting from the derived constitutive equations are estimated using data collected from a series of compression experiments coupled with an externally applied magnetic field. The multi-constituent constitutive equations predicted the stress of the MRE in these compression experiments for a variety of ferrous particle concentrations.</p>

No description available.

No description available.

No description available.

The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena. The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoff plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic. The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations. In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.

Hyperelasticity is a significant property of rubber, taken advantage of in engineering applications. A common application is the use of seals to prevent fluid transfer (liquid or gas) between solid regions. Volvo CE is often depending on external supplier when developing seals. However, it could be beneficial to be able to do design and analysis in-house. Thus, they want with this master thesis to increase their knowledge about rubber and FEM simulations of seals in ANSYS. The aim with this work is to develop a method and guidelines for analysis and simulation of seals of hyperelastic materials. Components analyzed in this thesis work are two static seals, an O-ring andan in-house modified X-ring design. Selected materials, HNBR and FKM, are commonly used elastomers at Volvo CE. Material tests performed at RISE are for three different load cases:uniaxial tension test, planar tension test and biaxial tension test. Quasi-static analyses are performed in ANSYS. Hyperelastic materials need different constitutive models, hyperelastic material models, to describe their material behavior and these are defined in terms of a strain energy density function.However, the challenge is to determine the material constants in the equation, to characterize the material properties, by processing test data. Research questions answered are ‘’What material tests are needed for hyperelastic materials?’’, ‘’How is the test data converted to work as input to ANSYS and obtain material constants?’’ and ‘’How is an appropriate material model selected for simulation in ANSYS?’’. The study shows the importance of that material test represents the condition the application will experience. It should capture material behavior at the specific frequency, strain amplitude and temperature range for the application. The expected strain range and deformation modes that will play a functional role in the application should be considered in the material testing. Material constants can be determined from test data separately or simultaneously. Test data from at least one deformation mode is required, but one can't accurately predict full deviatoric behavior of hyperelastic material models by using one mode. If data only is used for one deformation mode, simulations in other deformation modes can yield erroneous results. It is therefore recommended to use several deformation modes. For applications with more complex load cases more deformation modes are needed. Generally, recommended tests are uniaxial tension test, planar tension test and biaxial tension test due to homogenous deformation is achieved. It is important to verify the material model before analysis. Using test data from one deformation mode can still provide a good fit. In the cases investigated verifications of the material model Yeoh 3rd order show that the fit obtained by only using uniaxial tension test data and using test data from three tests doesn’t seem to differ. Both uniaxial tension test data and test data from three tests give agood fit when simulating the tests with this material model. The benefit of using test data from three tests is questionable due to costs. It seems that only uniaxial tension test data could have been used as it provided a good fit. Moreover, test data must be processed to work as input to ANSYS. ANSYS requires engineering stress-strain test data for hyperelastic materials besides from the volumetric test, where true stress strain is required. The biaxial tension state which is realized with so called Bulge test thus needs to be converted to engineering stress. Then, test data needs to be adjusted to account for effects such as hysteresis and Mullin’s effect, where choice of curve and a process zero-shift must be done. Hyperelastic material models have different validity for different strain ranges. The selected material model was Yeoh 3rd order, which showed be a good fit for both the materials, HNBR and FKM, in strain range 30 %. The curve fit is based on three tests. The selection was based on the material model with lowest relative error with stability. Material constants were obtained for that material model, and these were used in simulations. Material models tends to be unstable for strains outside the test data. Simulations of seals with fluid pressure were performed for different pressure and stretch of the seal. If the contact pressure is larger than fluid pressure in the seals no leakage will occur. / Hyperelasticitet är en betydande egenskap hos gummi, som används i tekniska tillämpningar. En vanlig tillämpning är tätningar för att förhindra vätskeöverföring (vätska eller gas) mellan fasta områden. Volvo CE är ofta beroende av externa leverantörer vid utveckling av tätningar. De vill därför med detta examensarbete öka sina kunskaper om gummi och FEM-simuleringar av tätningar i ANSYS. Målet med arbetet är att utveckla en metod och riktlinjer för analys och simulering av tätningar av hyperelastiska material. Komponenter som analyseras i detta examensarbete är två statiska tätningar, en O-ring och en intern modifierad X-ringdesign. Utvalda material, HNBR och FKM, är vanliga elastomerer hos Volvo CE. Materialtester som genomförts på RISE är för tre olika belastningsfall: enaxligt dragprov, plant dragprov och biaxialt dragprov. Quasi-statiska analyser genomfördes i ANSYS. Hyperelastiskt material behöver olika konstitutiva modeller, hyperelastsiska materialmodeller, för att beskriva dess materialbeteende och dessa definieras i termer av töjningsenergidensitetsfunktion. Utmaningen är att bestämma materialkonstanterna i ekvationen, för att karakterisera materialegenskaper, genom att processa testdatat. Forskningsfrågor som besvaras är ’’Vilka materialtester är nödvändiga för hyperelastiska material?’’, ’’Hur konverteras testdata för att fungera som indata till ANSYS och erhålla materialkonstanter?’’ och ’’Hur väljs lämplig materialmodell för simulering i ANSYS?’’. Studien visar vikten av att materialtester representerar förhållanden som är representativa för applikationen. Det bör fånga materialbeteendet vid den specifika frekvensen, töjningsamplitud och temperatur för applikationen. Det förväntade töjningsomårdet och deformationslägen som kommer spela en funktionell roll i applikationen bör beaktas i materialtestningen. Materialkonstanter kan beräknas från testdata separat eller simultant. Testdata från minst ett deformationsläge krävs, men man kan inte exakt förutsäga fullständigt devatoriskt beteende hos hyperelastiska materialmodeller genom att använda ett deformationsläge. Om testdata endast används för ett deformationsläge kan simuleringar i andra deformationslägen ge felaktiga resultat. Det är därför rekommenderat att använda flera deformationslägen. Generellt rekommenderade tester är enaxligt dragprov, plant dragprov och biaxialt dragprov då homogen deformation uppnås. Det är viktigt at verifiera materialmodellen innan analys. Att använda testdata från ett deformationsläge kan fortfarande ge en bra passning. I de undersökta fallen visar verifikation av materialmodellen Yeoh 3:e ordningen att passningen som erhållits av enbart enaxligt dragprovtestdata och testdata från tre tester inte skiljer sig åt. Både enaxligt dragprov testdata och testdata från tre tester ger en bra passning när simulerar testerna med den materialmodellen. Fördelarna med att använda testdata från tre tester är ifrågasatt pga. kostnaderna. Det verkar som enbart enaxligt dragprov testdata kunde ha använts då det gav en bra passning. Vidare behövs testdata hanteras för att fungera som indata till ANSYS. ANSYS behöver nominellspänning-töjning testdata för hyperelastiska material förutom för det volymetriska testet, där sannspänning-töjning behövs. Det biaxiala dragprovet som realiserades med s.k. Bulge test måste därför konverteras till nominell spänning. Sedan behöver testdata justeras för att ta hänsyn till effekter som hysteres och Mullins effekt, där val av kurva samt en process ‘’zero-shift’’ måste göras. Hyperelastiska materialmodeller har olika giltighet för olika töjningsområden. Val av materialmodell blev Yeoh 3:e ordningen som visade sig vara en bra passning för båda materialen, HNBR och FKM, i töjningsområden 30%. Kurvanpassningen är baserad på tre tester. Valet baserades på den materialmodell som hade minst relativt fel och som var stabil. Materialkonstanterer hölls för den materialmodellen och dessa användes i simuleringar. Materialmodeller tenderar att vara ostabila för töjningar utanför testdata. Simuleringar av tätningar med flödestryck genomfördes för olika tryck och stretch av tätningen. Om kontakttrycket är större än flödestrycket i tätningen sker inget läckage.