Previous decades of cartilage research have predominantly focused on decoupling the solid and fluid interactions of the mechanical response. The resulting biphasic and triphasic models are widely used in the biomechanics community. However, a simple viscoelastic model is able to account for the stress-relaxation behavior of cartilage, without the added complexity of solid and fluid interactions. Using a viscoelastic model, cartilage is considered a single material with elastic and dissipative properties. A mechanical characterization is made with fewer material parameters than are required by the conventional biphasic and triphasic models. This approach has tremendous utility when comparing cartilage of different species and varying healths. Additionally, the viscoelastic models can be easily extended in dynamic analysis and FEA programs. Cartilage primarily experiences compressive motion during exercise. Therefore, to mimic biological function, a mechanical test should also compress the cartilage. One such test is a viscoelastic stress-relaxation experiment. The Prony and fractional calculus viscoelastic models have shown promise in modeling stress-relaxation of equine articular cartilage. The elastic-viscoelastic correspondence principle is used to extend linear viscoelasticity to the frequency domain. This provides a comparison of articular cartilage based on stored and dissipated moduli. The storage and loss moduli metrics are hypothesized to serve as benchmarks for evaluating osteoarthritic cartilage, and provide guidelines for newly engineered bio-materials. The main goal of the current study is to test the applicability of modeling articular cartilage with viscoelastic models. A secondary goal is to establish a rigorous set of harvesting techniques that allows access to fresh explants with minimal environmental exposure. With a complex substance like cartilage, it is crucial to avoid unnecessary emph{in vitro} environmental exposure. Additional areas of study include: determining the strain-dependency of the mechanical response, exploring the response of cartilage in different fluid mediums such as saline, synovial fluid, and synthetic substitutes, and studying the time-dependent properties of cartilage during stress-relaxation experiments. Equine stifle joints, which are mechanically analogous to human knees, are harvested and used for analysis in this study. It is believed that the proposed viscoelastic models can model other articulating joints as well. If viscoelastic theory can be used to characterize cartilage, then comparisons can be drawn between real and artificial cartilage, leading to better joint replacement technology.

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer (Derakane 441-400, Ashland Co.,) with variations in its material properties. Short-term tensile creep/creep recovery experiments were conducted at two stress levels and at four temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. Experimental strains in both the longitudinal and transverse directions were measured using a digital image correlation technique. The measured creep strain versus time responses were subsequently used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of Derakane 441-400 was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using the two-parameter Weibull and log-normal distributions. The maximum likelihood estimation technique was used to obtain the Weibull shape and its scale parameters and the log-normal location and its scale parameters. The goodness-ofit of the distributions was determined by performing Kolmogorov-Smirnov (K-S) hypothesis tests. Based on the K-S test results, the Weibull distribution is a better representation of the creep compliances of Derakane 441-400 when compared to the log-normal distribution. Additionally, the Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Therefore, two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and subsequently the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for CDF values of 0.05, 0.50 and 0.95 and compared with the experimentally obtained lowest, mean and highest creep compliances, respectively. The predicted creep compliances of Derakane 441-400 in the design space are in good agreement with the experimental data.

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Traditional large space structure construction incorporates the use of lightweight tubular metal alloys that have good strength to weight and stiffness to weight ratio. Recently, however, space structure construction has shifted focus on materials that are ultra lightweight, have high strength, have low package volume and possess excellent damping characteristics. Substantial damping is required in space since there is no surrounding medium to provide damping. Such a construction uses composites in a fabric form that displays viscoelastic behavior. The viscoelastic behavior is attributed to energy dissipation because of the shear stresses between the various fibrous strands that are kept in place by constraining viscoelastic layers. This type of vibration control falls under the rubric of passive damping of structures and has been found to have certain advantages over active damping such as less complexity as it does not require sensors, actuators and power supply that are needed for active damping. One such material consists of woven carbon strands constrained by layers of viscoelastic damping material. Dynamics and buckling behavior of a structure in the form of a tube made from this material with metallic end caps is modeled and analyzed using commercially available Finite Element Analysis code ABAQUS®. The current analysis deals with the non-pressurized tube since the structure can maintain the tubular configuration as well as support end caps on account of the stiffness provided by the composites. Since no simple analytical approaches are available to predict damping of these materials, experimental data was used to estimate the damping characteristics of the material. The mass of the end cap was also estimated from the experimental impulse response as exact mass of the end cap (that was rigidly fixed to the tube) was unknown. / Master of Science

Uma mistura asfÃltica apresenta um comportamento mecÃnico complexo que pode ser idealizado por um modelo viscoelastoplÃstico, que considera a existÃncia de deformaÃÃes recuperÃveis (elÃstico e viscoelÃstico) e nÃo recuperÃveis (plÃstico e viscoplÃstico). No entanto, o estado da arte da pesquisa brasileira tem considerado um modelo mais restrito, o modelo viscoelÃstico linear. Este modelo trata o comportamento mecÃnico do material como dependente do carregamento e da correspondente taxa (temporal) de aplicaÃÃo, que representa um avanÃo considerÃvel na modelagem mecÃnico-computacional de misturas asfÃlticas frente ao modelo elÃstico linear (clÃssico) comumente empregado em projetos nacionais de dimensionamento de pavimentos. Ainda assim, o modelo viscoelÃstico apresenta alguns inconvenientes que dificultam seu uso. Um primeiro inconveniente à que para uma representaÃÃo compatÃvel com os dados experimentais, a caracterizaÃÃo constitutiva viscoelÃstica exige a manipulaÃÃo de uma grande quantidade de coeficientes da sÃrie de Prony, dificultando o processo de ajuste de curva e posterior manipulaÃÃo da sÃrie. AlÃm disso, o processo formal de interconversÃo entre as propriedades viscoelÃsticas fundamentais, comumente necessÃrio por questÃes operacionais, trata-se de um mÃtodo nÃo trivial. Para facilitar o emprego da teoria da viscoelasticidade (linear) na caracterizaÃÃo de misturas asfÃlticas, o presente trabalho se propÃs ao desenvolvimento de um programa computacional especÃfico que facilita o uso do modelo viscoelÃstico linear. Este programa realiza o ajuste de curva de sÃries de Prony e a interconversÃo entre propriedades viscoelÃsticas fundamentais no domÃnio do tempo, quais sejam, a FunÃÃo FluÃncia D(t) e o MÃdulo de RelaxaÃÃo E(t). Como principal resultado, foi possÃvel aplicar este programa computacional na caracterizaÃÃo de duas misturas nacionais tÃpicas, Areia Asfalto (AA) e Concreto AsfÃltico (CA), mostrando de forma detalhada os passos necessÃrios para uma representaÃÃo constitutiva viscoelÃstica adequada. Ainda como parte dos resultados obtidos, foi avaliada a eficÃcia da tÃcnica de ajuste de curva por MÃnimos Quadrados NÃo Linear (MQNL) para sÃries de Prony, sob a expectativa de incorporaÃÃo desta tÃcnica em versÃes futuras do programa computacional desenvolvido. Para explicitar o avanÃo da simulaÃÃo mecÃnica de pavimentos que o modelo viscoelÃstico possibilita frente ao modelo elÃstico (clÃssico), ao final do trabalho foram realizadas anÃlises computacionais utilizando o MÃtodo dos Elementos Finitos (MEF) para estimar os parÃmetros mecÃnicos de projeto de pavimentos (tensÃes de deformaÃÃes) considerando o modelo viscoelÃstico das misturas asfÃlticas investigadas, AA e CA. / An asphalt mixture has a complex mechanical behavior can be idealized by a viscoelastoplastic model that considers the existence of recoverable (elastic and viscoelastic) and non-recoverable deformations (plastic and viscoplastic). However, the state of the art of Brazilian research has considered a more restricted model, the linear viscoelastic model. This model treats the mechanical behavior of the material as dependent on the load and the corresponding (temporal) rate, which represents a considerable advance in mechanical-computational modeling of asphalt mixtures compared to the linear elastic (classic) model commonly employed on projects of national pavement design. But the viscoelastic model has some drawbacks that hinder its use. A first drawback is that for a representation compatible with the experimental data, the constitutive viscoelastic characterization requires handling a large number of Prony series coefficients, which makes difficult the curve fitting process and subsequent handling of the series. Futhermore, the formal process of interconversion between the fundamental viscoelastic properties, commonly required for operational reasons, is a non-trivial task. In order to enable the employment of the theory of (linear) viscoelasticity in the characterization of asphalt mixtures, this study proposed the development of a specific computer program that facilitates the use of the linear viscoelastic model. This program carries out curve fitting of Prony series and interconversion of fundamental viscoelastic properties in time domain, namely, Creep Compliance D(t) and Relaxation Modulus E(t). As a main result, it was possible to use this program in characterization of two national typical mixtures, Sand Asphalt (SA) and Asphalt Concrete (AC), showing in details the steps necessary for a proper viscoelastic constitutive representation. Also as part of the results, it was tested the efficacy of the technique of curve fitting by Nonlinear Least Squares (NLS) for the Prony series, under the expectation of incorporating this technique in future versions of this ongoing software. In order to explain the advances that viscoelastic model can enable in mechanical simulation of pavement, instead of using the elastic (classic) model, at the end of this study it was performed computational analysis using the Finite Element Method (FEM) to estimate the mechanical design parameters of pavements (stress and strains), considering the viscoelastic model of the investigated asphalt mixtures, SA and AC.

Thermoplastic materials have significant nonlinear behaviour. The nonlinear behaviour is described by creep curves. The curves of creep modules are dependent on stress, temperature and time. The dissertation thesis deals with the approximation of the creep modules by Prony series. Subsequently three procedures are proposed to take account of creep modules. The proposed procedures are used in two applications. The first application deals with the ring stiffness value of a corrugated sewage pipe. The ring stiffness value is influenced by the creep modulus. The other one deals with a thermoplastic flange connection. The clamping force is dependent on the creep modulus of thermoplastics. The problems were solved by ANSYS program system.

Every moment of every day, at least hundreds of thousands of tires roll across a surface throughout the world. Tires are indisputably important in our daily life. The tire's primary component is rubber, which consumes energy when it rotates on a substrate due to the viscoelastic material's internal friction: a phenomenon referred to as rolling resistance. The interaction between the tire and the road surface is one of the most intricate and crucial phenomena in an automobile, because it is responsible for creating forces, moments, and deformation in the tire. Additionally, the road's roughness interacts with the tire and contributes significantly to its performance. This dissertation aims to develop a comprehensive physics-based model for predicting the rolling resistance of a viscoelastic material due to dynamic deformations caused by tire rotation using an analytical approach. The model was developed by proposing a Gaussian wave function propagating across a tire circumference's viscoelastic medium. The wave function was selected to describe the displacement field produced by tire-road interaction. Additionally, by adopting a multi-scale modeling technique, the model was upgraded to estimate rolling resistance while taking into account surface roughness at all length scales, from macroscopic to microscopic. Additionally, another mathematical model was developed using the Fourier series approach to evaluate the steady-state stress response and energy dissipation for any harmonic and non-harmonic periodic strain signals. Additionally, the dissertation strove to build a continuum damage mathematical model using a combined testing/modeling methodology to predict the aging of Styrene-Butadiene Rubber (SBR) after continuous exposure to the atmosphere. The obtained model was developed through the implementation of optimization techniques while formulating a mathematical model, which was then combined with a physics-based model to predict rolling resistance while taking into account rubber aging. Calibration of hyperelastic and viscoelastic material models with testing data was performed using an optimization technique that yielded sufficient results. The results of all mathematical models obtained in this dissertation are reported subsequently. The stress response of a viscoelastic material under harmonic and non-harmonic strain input yielded good agreement with the FEA model obtained using ABAQUS. The rolling resistance behavior under various operating conditions, including texture and aging effects, was reported, and the results aligned with the experimental results found in the literature. / Doctor of Philosophy / Every moment of every day, hundreds of thousands of automobile tires roll across a surface somewhere in the world. A tire is an undeniably important part of everyday life. Rubber is the tire's main component, and when it rotates on a surface, it loses energy, resulting in a force that resists motion, known as rolling resistance force. The contact between the tire and the road is one of the most complicated and important phenomena that happens in an automobile because it is responsible for the vehicle's dynamic performance in areas such as acceleration, stopping distance, and stability. Another factor that affects tire and car performance and should be taken into account is the road's roughness. This dissertation used an analytical method to come up with an accurate physics-based model for predicting the rolling resistance force of a viscoelastic material caused by tire rotation. The model was developed by assuming a Gaussian wave function would move across the tire circumference. Additionally, using a multi-scale modeling technique, the model was improved so that it could calculate the value of rolling resistance force considering surface roughness in all lengths of scale. This project also developed an additional mathematical model using the Fourier series method to determine how the stress response and energy dissipation would behave for any harmonic and nonharmonic periodic strain signals. Additionally, the dissertation presents the developing of a continuum damage mathematical model that could predict the material property of styrene-butadiene rubber (SBR) after being exposed to the air for a long time (i.e., aged). The model was developed based on experimental data and optimization techniques. This model was then combined with a physics-based model to predict rolling resistance force while taking aging into account. The material models were defined using an optimization method that yielded good results. The stress response of a viscoelastic material when it was subjected to harmonic and non-harmonic strain was in good agreement with the Finite Element Analysis (FEA) model made with ABAQUS. Rolling resistance behavior was observed, and the results were consistent with those found in the literature.