Thesis (Ph.D.)--University of Central Florida, 2008. / Advisers: Xin Li, Mubarak Shah. Includes bibliographical references (p. 127-130).

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by Dp-operators with p = 5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p = 5.

Polymeric adhesives play an increasingly critical role in today's engineering designs. When used, adhesively bonded components reduce or eliminate the need for bolted or welded connections. In many cases, this can reduce stress concentrations and weight. With energy dissipating adhesives, noise and vibration reduction are possible, as is the use of unique or complicated designs that could not otherwise be constructed. Adhesive properties however, can vary greatly with time, temperature, and environmental exposure conditions such as moisture. It is therefore critical, to understand the behavior of adhesives over the range of conditions that a bonded component might experience. In this work, the behavior of a urethane-based adhesive was characterized and long-term durability predictions were developed as a result of the data collected. The popular T-peel sample geometry has been used extensively in this study to explore the mechanics of a bonded system and the resulting impact on adhesive durability. The T-peel specimens used, consist of two aluminum sheets or adherends bonded together, with tabs bent back in the shape of a "T" for gripping in a universal load frame. Unlike some other test geometries, T-peel samples are often made with relatively thin adherends that may experience significant plastic deformation during testing. This extraneous energy dissipation greatly complicates the analysis to extract meaningful fracture properties of the adhesive. During testing, the load required to propagate a crack in the adhesive layer is measured at fixed displacement rates. The total system energy can then be partitioned into the energy dissipated within the adhesive (fracture energy), and the energy dissipated through plastic work in bending of the adherends. By performing these tests at different temperatures and rates, the calculated fracture energies span a wide range of possible material behavior. Using the principles of Time Temperature Superposition (TTS), the collected data can be shifted to different times or temperatures. This behavior is well understood in polymer physics, and is made possible with material specific "shift factors". By using the principles of TTS, data collected in in a relatively short experimental window, can be used to accurately predict the behavior of the adhesive in years or even decades. In this work, nearly 200 T-peel samples were tested in four different studies. A preliminary set of unaged specimens was used to develop testing and data analysis methodologies. A second set of unaged samples was tested over a wide range of temperatures and rates, in addition to a third group, subjected to constant moisture and cyclically varying temperature. The final set of specimens, was exposed to 20 separate isothermal aging conditions. The experimental data showed that the 400+ cycles, were insufficient to statistically distinguish these samples from their unaged counterparts. Additionally, samples aged for up to 2000 hours in a dry environment, or 500 hours in a wet environment, showed no reduction in fracture energies in comparison with unaged samples. Specimens aged for more than 500 hours however, were observed to have a significant decrease in fracture energy values. Strong correlations between the thickness of the adhesive layer and estimated fracture energy values were found in this study. As adhesive thickness varied substantially due to manufacturing differences in the specimens tested, new analysis techniques were developed to deal with the variations in adhesive thickness. A MATLAB code based on the ICPeel program, was written to provide a spatial variation of parameters such as adhesive thickness, peel load, and fracture energy. This provided additional insights into the behavior of these T-peel coupons, and prompted the investigation of the Universal Peel Diagram concept. While this diagram was not found to be applicable to the adhesive tested in this study, the analysis indicated that T-peel coupons could be multivalued. That is, a single measured load value does not always describe an adhesive's fracture energy (as is widely believed). Depending on the sample's geometry and material properties, several measured loads could cause debonding. This has potentially far reaching implications on the selection of appropriate T-peel test geometries, as a single measured load is often assumed to correlate to an adhesive's true fracture energy. In this work, both aged and unaged T-peel specimens were tested and the basis of the Universal Peel Diagram investigated. Given sufficient exposure times to moisture, elevated temperatures were found to significantly reduce the amount of energy dissipated in the urethane-based adhesive. Additionally, the Universal Peel Diagram indicated that for some systems, the load required for debond is in fact, multivalued. Therefore, care should be taken when designing a T-peel test configuration to avoid the multivalued regions. / Master of Science / Polymeric adhesives play an increasingly critical role in today's engineering designs. When used, adhesively bonded components reduce or eliminate the need for bolted or welded connections, reducing their weight in the process. With adhesives, noise and vibration reduction are possible, as is the use of unique or complicated designs that could not otherwise be constructed. Adhesive properties, however, can vary greatly with time, temperature, and other environmental exposure conditions such as moisture. It is therefore critical to understand the behavior of adhesives over the range of conditions that a bonded component might experience. In this work, the behavior of a urethane-based adhesive was characterized in order to develop long-term durability predictions. Numerous test methods have been developed to characterize the behavior of adhesively bonded joints. In this work, T-peel specimens were used consisting of two aluminum sheets (the adherends), bonded together with tabs bent back in the shape of a "T" for gripping in a universal load frame. During testing, the load required to propagate a crack in the adhesive layer is measured. An outcome of this measurement and subsequent data analysis is the fracture energy—a measure of the effectiveness of the adhesive in transferring loads. If we perform these tests at different temperatures and loading rates, we can determine fracture energy values which span a wide range of possible material behavior. Using principles from basic polymer physics, the collected data can be shifted to different times or temperatures enabling us to accurately predict the behavior of the adhesive over years or even decades. In this work, nearly 200 T-peel samples were tested in four different studies. A preliminary set of unaged specimens was used to develop testing and data analysis methodologies. Unaged and cyclically (temperature) aged samples were tested over a wide range of temperatures and rates. The fourth set of specimens was subjected to 20 separate isothermal aging conditions and also tested at different temperatures and rates. The experimental data showed that the 400+ temperature cycles were insufficient to damage these samples significantly. Additionally, samples aged for up to 2000 hours in a dry environment, or 500 hours in a wet environment showed no reduction in performance in comparison with unaged samples. Specimens aged for more than 500 hours in a wet environment however, demonstrated a significant decreases in fracture energy values. Strong correlations between the thickness of the adhesive layer and estimated fracture energy values were found in this study, and new analysis techniques were developed to analyze the effect of these thickness variations on the joint performance.

This thesis presents the results of testing and modeling conducted to characterize the performance of 3M™ VHB™ structural glazing tape in both shear and tension. Creep rupture testing results provided the failure time at a given static load and temperature, and ramp-to-fail testing results provided the ultimate load resistance at a given rate of strain and temperature. Parallel testing was conducted on three structural silicone sealants to compare performance. Using the time temperature superposition principle, master curves of VHB tape storage and loss moduli in shear and tension were developed with data from a dynamic mechanical analyzer (DMA). The thermal shift factors obtained from these constitutive tests were successfully applied to the creep rupture and ramp-to-fail data collected at 23°C, 40°C, and 60°C (73°F, 104°F, and 140°F), resulting in master curves of ramp-to-fail strength and creep rupture durability in shear and tension. A simple linear damage accumulation model was then proposed to examine the accumulation of wind damage if VHB tape is used to attach curtain wall glazing panels to building facades. The purpose of the model was to investigate the magnitude of damage resulting from the accumulation of sustained wind speeds that are less than the peak design wind speed. The model used the equation derived from tensile creep rupture testing, extrapolated into the range of stresses that would typically be generated by wind loading. This equation was applied to each individual entry in the data files of several real wind speed histories, and the fractions of life used at each entry were combined into a total percentage of life used. Although the model did not provide evidence that the established design procedure is unsafe, it suggested that the accumulation of damage from wind speeds below the peak wind speed could cause a VHB tape mode of failure that merits examination along with the more traditional peak wind speed design procedure currently recommended by the vendor. / Master of Science

L’objectif de cette thèse est de proposer une stratégie simplifiée et précise pour caractériser et modéliser le comportement mécanique des polymères amorphes de l'état quasi-fluide à l'état solide.L'étude a été réalisée sur des PMMA de masses molaires et de degré de réticulations différentes.D’abord, le comportement mécanique dans le domaine viscoélastique linéaire est étudié à l'aide de tests DMTA et rhéologiques. Il ressort de l’étude que l'augmentation de la masse molaire et du degré de réticulation augmentait les modules de stockage et de perte en tant que la transition α. En parallèle, l'utilisation du principe de superposition temps-température a permis de déterminer «des vitesses de déformation équivalentes à la température de référence».Ensuite, le comportement mécanique à grande déformation est étudié par essais cycliques en traction uni-axial et de cisaillement à haute température et couplés à la DIC. De plus, les effets de la vitesse de déformation et de la température ont été couplés grâce à "vitesse de déformation équivalent à la température de référence" extrait des observations dans le domaine linéaire. Les résultats ont montré que cibler la même vitesse de déformation équivalente conduira aux mêmes courbes contrainte-déformation, c'est-à-dire la même réponse mécanique. Ceci permet de réduire le nombre de tests expérimentaux nécessaires pour caractériser le comportement mécanique des polymères amorphes.Enfin, un modèle basée dans un cadre thermodynamique a été utilisée pour reproduire la réponse mécanique des PMMAs à grande déformation. Le modèle présentait un bon accord avec les données expérimentales, étant capable de reproduire des comportements visco-élasto-plastiques, viscoélastiques, hyperélastiques et visco-hyperelastiques pour la traction cyclique. / The present PhD thesis proposes a simplified and accurate strategy for characterising and modelling the mechanical behaviour of amorphous polymers from the quasi-fluid state up to the solid state.The study was carried out on PMMAs with different molar masses and crosslinking degree.First, we addressed the mechanical behaviour in the linear viscoelastic domain using DMTA and rheological tests. Results showed that increasing the molar mas and crosslinking degree increased the elastic and loss moduli as the α-transition. In parallel, using the time-temperature superposition principle allowed determining “equivalent strain rates at reference temperature”.Then, we performed uniaxial tensile and shear uploading-unloading tests at high temperature and coupled with DIC, to characterise the mechanical behaviour at large strain. Additionally, strain rate and temperature effects were coupled by means of the “equivalent strain rate at reference temperature” extracted from observations in the linear domain. Results showed that targeting the same equivalent strain rate lead to the same stress-strain curves, i.e. same mechanical response. This allows reducing the number of experimental tests needed to characterise the mechanical behaviour of amorphous polymers.Finally, a constitutive modelling based in a thermodynamics framework, was used to reproduce the mechanical response of the PMMAs at large deformation. The model presented a good agreement with the experimental data, being able to reproduce viscoelastoplastic, viscoelastic, hyperelastic and viscohyperelastic behaviours for cyclic loading tensile.

Made available in DSpace on 2016-12-12T20:25:13Z (GMT). No. of bitstreams: 1 Thais Clara da Costa Haveroth.pdf: 3726370 bytes, checksum: 204349100247f52ea6bf4916ec49a0ab (MD5) Previous issue date: 2015-10-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Dentre a vasta gama de polímeros estruturais atualmente disponíveis no mercado, este trabalho está particularmente voltado ao estudo do polietileno de alta densidade. Embora este material já tenha sido investigado por diversos autores, seu típico comportamento viscoelástico não-linear apresenta dificuldades na modelagem. Visando uma nova contribuição, este trabalho propõe a descrição de tal comportamento utilizando uma abordagem baseada em derivadas fracionários. Esta formulação produz equações constitutivas fracionais que resultam em boas propriedades de ajuste de curvas com menos parâmetros a serem identificados que nos métodos tradicionais. Neste sentido, os resultados experimentais de fluência para o polietileno de alta densidade, avaliados em diferentes níveis de tensão, são ajustados por este esquema. Para estimar a deformação à níveis de tensão que não tenham sido medidos experimentalmente, o princípio da equivalência tensão-tempo é utilizado e os resultados são comparados com aqueles apresentados por uma interpolação linear dos parâmetros. Além disso, o princípio da superposição modificado é aplicado para predizer a comportamento de materiais sujeitos a níveis de tensão que mudam abruptamente ao longo do tempo. Embora a abordagem fracionária simplifique o problema de otimização inversa subjacente, é observado um grande aumento no esforço computacional. Assim, alguns algoritmos que objetivam economia computacional, são estudados. Conclui-se que, quando acurária é necessária ou quando um modelo de séries Prony requer um número muito grande de parâmetros, a abordagem fracionária pode ser uma opção interessante. / Among the wide range of structural polymers currently available in the market, this work is concerned particularly with high density polyethylene. The typical nonlinear viscoelastic behavior presented by this material is not trivial to model, and has already been investigated by many authors in the past. Aiming at a further contribution, this work proposes modeling this material behavior using an approach based on fractional derivatives. This formulation produces fractional constitutive equations that result in good curve-fitting properties with less parameters to be identified when compared to traditional methods. In this regard, experimental creep results of high density polyethylene evaluated at different stress levels are fitted by this scheme. To estimate creep at stress levels that have not been measured experimentally, the time-stress equivalence principle is used and the results are compared with those presented by a linear interpolation of the parameters. Furthermore, the modified superposition principle is applied to predict the strain for materials subject to stress levels which change abruptly from time to time. Some comparative results are presented showing that the fractional approach proposed in this work leads to better results in relation to traditional formulations described in the literature. Although the fractional approach simplifies the underlying inverse optimization problem, a major increase in computational effort is observed. Hence, some algorithms that show computational cost reduction, are studied. It is concluded that when high accuracy is mandatory or when a Prony series model requires a very large number of parameters, the fractional approach may be an interesting option.

Elektroencefalografický záznamový systém slouží k vyšetření mozkové aktivity. Na základě tohoto vyšetření lze stanovit diagnózu některých nemocí, například epilepsie. Účelem této práce bylo zpracování signálu z toho systému a vytvoření modelového signálu, který bude s reálným signálem porovnán. Uměle vytvořený signál vychází z Jansenova matematického modelu, který byl dále implementován v prostředí MATLAB a rozšířen ze základního modelu na komplexnější zahrnující nelinearity a model rozhraní elektroda – elektrolyt. Dále bylo provedeno měření signálů na EEG fantomu a následná identifikace parametrů naměřených signálu. V první fázi byly testovány jednoduché signály. Identifikace parametrů těchto signálů sloužila k validaci daného EEG fantomu. V druhé fázi bylo přistoupeno k testování EEG signálů navržených podle matematického Jansenova modelu. Analýza veškerých signálů zahrnuje mimo jiné časově frekvenční analýzu či ověření platnosti principu superpozice.

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Resilin is a disordered elastomeric protein and can be found in specialized regions of insect cuticles. Its protein sequence, functions and dynamic mechanical properties vary substantially across the species. Resilin can operate across the frequency range from 5 Hz for locomotion to 13 kHz for sound production. To understand the functions of different exons of resilin, we synthesize recombinant resilin-like hydrogels from different exons, and investigate the water content and dynamic mechanical properties, along with estimating surface energies relevant for adhesion. The recombinant resilin-like hydrogel has 80wt% water and does not show any sign of tack even though it satisfies the Dahlquist criterion. Finally, doubly shifted dynamic moduli master curves are developed by applying the time-temperature concentration superposition principle (TTCSP), and compared to results obtained with natural resilin from locusts, dragonflies and cockroaches. The resulting master curves show that the synthetic resilin undergoes a prominent transition, though the responsible mechanism is unclear. Possible explanations for the significant increase in modulus include the formation of intramolecular hydrogen bonds, altered structural organization, or passing through a glass transition, all of which have been reported in the literature for polymeric materials. Results show that in nature, resilin operates at a much lower frequency than this glass transition frequency at room temperature. Moreover, recombinant resilins from different clones have comparable resilience with natural resilin, though the modulus is around 1.5 decades lower. Results from the clones with and without chitin binding domains (ChBD) indicate that the transition for the clone without ChBD occurs at lower frequencies than for those with the ChBD, perhaps due to the disordered nature of the clone without ChBD. Atomistic molecular modeling is applied on the repetitive motifs of resilin and different elastomeric proteins to better understand the relationship between elastomeric behavior and amino acid sequences. Results show that the motifs form a favorable bent conformation, likely enabled by glycine's lack of steric hindrance and held in place through intramolecular hydrogen bonds. During Steered Molecular Dynamic (SMD) pulling of these motifs, the hydrogen bonds break and they reform again when the peptides are released to move freely, returning to similar bent conformations. The transition seen in the master curves of recombinant resilins might be due to either these intramolecular hydrogen bonds or to glass transition behavior, though evidence indicates that the transition probably due to the glass transition. What we learned from the synthesized recombinant resilin and simulating the repetitive motifs of resilin may be applicable to the biology and mechanics of other elastomeric biomaterials, and may provide deeper understanding of their unique properties. / Ph. D.