Polydimethylsiloxane (PDMS) mechanical properties were measured using custom-built compression test device. PDMS elastic modulus can be varied with the elastomer base to the curing agent ratio, i.e. by changing the cross-linking density. PDMS samples with different crosslink density in terms of their elastic modulus were measured. In this project the PDMS samples with the base/curing agent ratio ranging from 5:1 to 20:1 were tested. The elastic modulus varied with the amount of the crosslinker, and ranged from 0.8 MPa to 4.44 MPa. The compression device was modified by adding digital displacement gauges to measure the lateral strain of the sample, which allowed obtaining the true stress-strain data. Since the unloading behavior was different than the loading behavior of the viscoelastic PDMS, it was utilized to asses viscoelastic properties of the polymer. The thesis describes a simple method for measuring mechanical properties of soft polymeric materials.

This dissertation revolves around various mathematical aspects of nonlinear wave motion in viscoelasticity and free surface flows. The introduction is devoted to the physical derivation of the stress-strain constitutive relations from the first principles of Newtonian mechanics and is accessible to a broad audience. This derivation is not necessary for the analysis carried out in the rest of the thesis, however, is very useful to connect the different-looking partial differential equations (PDEs) investigated in each subsequent chapter. In the second chapter we investigate a multi-dimensional scalar wave equation with memory for the motion of a viscoelastic material described by the most general linear constitutive law between the stress, strain and their rates of change. The model equation is rewritten as a system of first-order linear PDEs with relaxation and the well-posedness of the Cauchy problem is established. In the third chapter we consider the Euler equations describing the evolution of a perfect, incompressible, irrotational fluid with a free surface. We focus on the Hamiltonian description of surface waves and obtain a recursion relation which allows to expand the Hamiltonian in powers of wave steepness valid to arbitrary order and in any dimension. In the case of pure gravity waves in a two-dimensional flow there exists a symplectic coordinate transformation that eliminates all cubic terms and puts the Hamiltonian in a Birkhoff normal form up to order four due to the unexpected cancellation of the coefficients of all fourth order non-generic resonant terms. We explain how to obtain higher-order vanishing coefficients. Finally, using the properties of the expansion kernels we derive a set of nonlinear evolution equations for unidirectional gravity waves propagating on the surface of an ideal fluid of infinite depth and show that they admit an exact traveling wave solution expressed in terms of Lambert’s W-function. The only other known deep fluid surface waves are the Gerstner and Stokes waves, with the former being exact but rotational whereas the latter being approximate and irrotational. Our results yield a wave that is both exact and irrotational, however, unlike Gerstner and Stokes waves, it is complex-valued.

Orientador: Paulo José Paupitz Gonçalves / Resumo: O modelo de Zener, também conhecido como o modelo SLS, do inglês (Standard Linear Solid), é um modelo simples que descreve o comportamento de um material viscoelástico como isolador de vibração, utilizando uma combinação linear de molas e amortecedores para representar componentes elásticos e viscosos, respectivamente. Sabe-se que, o modelo mais semelhante de Maxwell, que é uma mola em série com um amortecedor, e o modelo de Kelvin-Voigt, que é uma mola em paralelo com um amortecedor, são utilizados. No entanto, estes modelos são muitas vezes insuficientes para representar tal comportamento desejado, o modelo de Maxwell não descreve a fluência ou recuperação, e o modelo de Kelvin-Voigt não descreve o stress e o relaxamento. O SLS é o modelo mais simples, que prevê dois fenômenos, com isso em mente, esta tese propõe a investigação do modelo de amortecimento de Zener substituindo as molas simples por molas não lineares (mola Duffing), no que diz respeito ao comportamento de isolamento de vibração, mostrando as curvas de transmissibilidade para vários valores de parâmetros. São utilizados métodos analíticos aplicáveis a sistemas não lineares, bem como método numérico para realizar análises de transmissibilidade do modelo de Zener e também o desenvolvimento de um aparato experimental que representa o modelo de isolador de vibração de Zener, essencial para um entendimento substancial dos fenômenos envolvidos. O objetivo principal da tese é investigar oportunidades de melhoria de i... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Zener model, also known as the solid linear standard model (SLS), is a simple model that describes the behavior of a viscoelastic material as a vibration isolator, using a linear combination of springs and dampers to represent elastic and viscous components , respectively. Often the most similar Maxwell model, which is a spring in series with a damper, and the Kelvin-Voigt model, which is a spring in parallel with a damper, are used. However, these models are often insufficient to represent such behavior, the Maxwell model does not describe fluency or recovery, and the Kelvin-Voigt model does not describe stress and relaxation. The SLS is the simplest model, which predicts two phenomena, with this in mind, this thesis proposes the investigation of the Zener damping model replacing the simple springs with non-linear springs (Duffing spring), with respect to the vibration isolation behavior, showing the transmissibility curves for various parameter values . Analytical methods will be used for non-linear systems, as well as a numerical method to carry out Zener model transmissibility analyzes, as well as the development of an experimental apparatus that represents Zener’s vibration isolator model, which is essential for a substantial understanding of the phenomena involved. The main objective of the thesis is to investigate opportunities for improvement of mechanical isolators when designed to act in dynamic bands with non-linear responses. / Doutor

Cancer progression is accompanied with alterations in the cell biomechanical phenotype, including changes in cell structure, morphology, and responses to microenvironmental stress. These alterations result in an increased deformability of transformed cells and reduced resistance to mechanical stimuli, enabling motility and invasion. Therefore, single cell biomechanical properties could be served as a powerful label-free biomarker for effective characterization and early detection of single cancer cells. Advances and innovations in microsystems and nanotechnology have facilitated interrogation of the biomechanical properties of single cells to predict their tumorigenicity, metastatic potential, and health state. This dissertation utilized Atomic Force Microscopy (AFM) for the cell biomechanical phenotyping for cancer diagnosis and early detection, efficacy screening of potential chemotherapeutic agents, and also cancer stem-like/tumor initiating cells (CSC/TICs) characterization as the critical topics received intensive attention in the search for effective cancer treatment. Our findings demonstrated the capability of exogenous sphingosine to revert the aberrant biomechanics of aggressive cells and showed a unique, mechanically homogeneous, and extremely soft characteristic of CSC/TICs, suitable for their targeted isolation. To make full use of cell biomechanical cues, this dissertation also considered the application of nonlinear viscoelastic models such as Fractional Zener and Generalized Maxwell models for the naturally complex, heterogeneous, and nonlinear structure of living cells. The emerging need for a high-throughput clinically relevant alternative for evaluating biomechanics of individual cells led us to the development of a microfluidic system. Therefore, a high-throughput, label-free, automated microfluidic chip was developed to investigate the biophysical (biomechanical-bioelectrical) markers of normal and malignant cells. Most importantly, this dissertation also explored the biomechanical response of cells upon a dynamic loading instead of a typical transient stress. Notably, metastatic and non-metastatic cells subjected to a pulsed stress regimen exerted by AFM exhibited distinct biomechanical responses. While non-metastatic cells showed an increase in their resistance against deformation and resulted in strain-stiffening behavior, metastatic cells responded by losing their resistance and yielded slight strain-softening. Ultimately, a second generation microfluidic chip called an iterative mechanical characteristics (iMECH) analyzer consisting of a series of constriction channels for simulating the dynamic stress paradigm was developed which could reproduce the same stiffening/softening trends of non-metastatic and metastatic cells, respectively. Therefore, for the first time, the use of dynamic loading paradigm to evaluate cell biomechanical responses was used as a new signature to predict malignancy or normalcy at a single-cell level with a high (~95%) confidence level. / Ph. D.