Reinforced polymer composites consist of continuous fibers embedded in a polymer matrix. The matrix is usually a thermoplastic or thermosetting resin. When thermosetting matrices are cured during the manufacture of composite parts, residual stresses develop within the part during the manufacture due primarily the thermally and chemically induced volumetric strains imposed on them. This can lead to shape distortions and sometimes weakening of the structure itself. Curing is the manufacturing process in which the thermoset resin is transformed from a liquid to a solid material. The molecular mechanisms involved in this process are quite complex and not well understood. In the macro-level, in addition to volumetric strains, heat is also generated since most thermoset polymerization reactions are exothermic. The mechanical properties of the thermoset also undergo dramatic changes. The material changes from an initial liquid state to a rubbery gel and finally to a vitrified glassy state. In modern day composite manufacturing, to accommodate for the shape distortions caused due to residual stress formation, the mold geometry is compensated. To do this, accurate predictions of the distortion behavior is preferred via computer simulations. This in turn requires simple mathematical models that can replicate the complex processes that take place during manufacture. One such process that requires attention is the curing of the thermoset. While models exist that assume elastic behavior during cure, they are not accurate throughout the entire cure process. Models based on viscoelastic material during cure offer better prospects in this perspective. However, currently models that are based on full viscoelasticity are either not well defined or are computationally tasking. Viscoelastic materials can be classified further in to thermorheologically simple and complex materials depending on their molecular weights. In simpler terms, thermorheologically simple materials are those that obey the principles of time-temperature superposition (TTS). TTS requires that all response times (i.e., all relaxation or retardation time), depend equally on temperature. This is expressed using the temperature shift function. Master curves can be then generated extending the time scale beyond the range that could normally be covered in a single experiment. However to fully understand the development of viscoelasticity during cure it is also necessary that the effects of the degree of cure of the thermoset on these times be included in the model definition. This requires defining a cure shift function along with the temperature shift function. In the presented work, an attempt is made to develop a simplified methodology to characterize the viscoelastic material properties during curing. Two different methods are investigated in a DMTA instrument to determine the effects of curing on the glassy state of the resin system LY5052/HY5052. A cure shift function was identified in the process. Based on observations it was concluded that the total shift function could be possibly defined as a product of the temperature and cure shift functions. Unique super-master curves were generated as a result. However, these curves showed a dependency of the rubbery modulus on the degree of cure. Hence, in the second paper, the effect of the degree of cure on the rubbery modulus was investigated. Subsequently a model was reformulated from an existing one and this was used to further simplify the super-master curves. Following dynamic testing, it was necessary that macroscopic testing is performed to corroborate the results. The macroscopic experiments utilized for this purpose was stress relaxation tests to determine the viscoelastic Poisson’s ratio of neat resin. The Poisson’s ratio in particular is an important property to study, since it’s interaction with the fiber during curing is critical in the study of residual stresses. The focus of the study is to determine if there is a dependency of the Poisson’s ratio on degree of cure and whether master curves can be generated by horizontal shifting of data. Literature pertaining to the dependency of the Poisson’s ratio on degree of cure is scarce. If appropriate horizontal shifting can be performed, it can be easily compared to the results from dynamic testing to check if the shift factors are truly universal. Also presented is a brief study of the effect of degree of cure and time on the development of viscoplastic strains during curing. This is done by performing creep tests on composite specimens with varying degrees of cure. The experimental results were then used to validate the well-known Zapas-Crissman model for viscoplastic strain evolution with time and investigate how it is influenced by the cure state.

Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. Often swimming occurs in complex, nonlinear fluids, e.g. mucus. Futhermore even in simple Newtonian fluids, if swimming appendages are deformable then locomotion is subject to fluid-structure interactions. The fundamental question addressed in this thesis is how exactly locomotion is impacted, in particular if it is faster or slower, with or without these effects. First we study locomotion in shear-thinning and viscoelastic fluids with rigid swimming appendages. Following the introductory Chapter, in Chapter 2 we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in non-Newtonian fluids, based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the Carreau fluid model. We then use our models to address waving locomotion in shear-thinning fluids, and show that the resulting swimming speeds are systematically lowered a result which we are able to capture asymptotically and to interpret physically. In Chapter 3 we consider swimming using small-amplitude periodic waves in a viscoelastic fluid described by the Oldroyd-B constitutive relationship. Using Taylor’s swimming sheet model, we show that if all travelling waves move in the same direction, the locomotion speed of the organism is systematically decreased. However, if we allow waves to travel in two opposite directions, we show that this can lead to enhancement of the swimming speed, which is physically interpreted as due to asymmetric viscoelastic damping of waves with different frequencies. A change of the swimming direction is also possible. Secondly we consider the affect of fluid-structure interactions. In Chapter 4, we use Taylor’s swimming sheet model to describe an active swimmer immersed in an Oldroyd-B fluid. We solve for the shape of an active swimmer as a balance between the external fluid stresses, the internal driving moments, and the passive elastic resistance. We show that this dynamic balance leads to a generic transition from hindered rigid swimming to enhanced flexible locomotion. The results are physically interpreted as due to a viscoelastic suction increasing the swimming amplitude in a non-Newtonian fluid and overcoming viscoelastic damping. In Chapter 5 we consider peritrichously flagellated bacteria, such as Escherichia coli. The rotation of each motor is transmitted to a flexible rod called the hook which in turns transmits it to a helical filament, leading to swimming. The motors are randomly distributed over the body of the organism, and thus one expects the propulsive forces from the filament to almost cancel out leading to negligible swimming. We show that the transition to swimming is an elasto-hydrodynamic instability arising when the flexibility of the hook is below a critical threshold.

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 work concerns the simulation of viscoelastic behavior of polymer at different states. Viscoelastic modeling of polymer was performed from the solid state to the liquid state via a multiphase approach which is largely used to deal with the fluid structure interaction. To ensure the appreciation of the FSI, viscoelasticity is considered in two parts: an elastic one and viscous other where the main idea is to use a mixed formulation in three fields (u, v, p) (displacement, velocity, pressure), with u and v, represented the primary variables of a strain and a strain rate formulation. We are led to the Navier-Stokes compressible problem with extra-stress, which is solved by using the Mixed Finite Element. The present work contributes some stabilization elements to the numerical simulation of multiphase problem by the monolithic approach.Comparison between the literature and experiments was performed through the validation of an elastic case and the viscoelastic Kelvin-Voigt model in the context of Lagrangian framework as well as Eulerian framework. The extension of the methodology to a visco-hyper-elastic is given through the modeling and validation on material point on the finite elements library CimLib®. Finally, a stabilization scheme of the EVSS type is adopted for viscoelastic Kelvin-Voigt model, hyper-elastic Neo-Hookean model, and also visco-hyper-elastic model which proposed an open door in computational modeling, not only with viscoelasticity but also complex dynamic application.

Ce travail a été effectué dans le cadre du projet Rem3D® dans lequel participent plusieurs entreprises avec l'objectif de développer un logiciel d'injection en 3D par éléments finis. L'objectif est de développer une méthode numérique pour modéliser le comportement viscoélastique des polymères de l'état solide à l'état liquide à travers une approche multiphasique qui est largement utilisé pour traiter le problème de l'interaction fluide-structure (IFS). La philosophie est d'utiliser une formulation mixte de trois champs (u, v, p) (déplacement, vitesse, pression), où u et v représentent les principales variables de déformation et de vitesse de déformation. Nous sommes amenés au problème de Navier-Stokes compressibles avec l'extra-contrainte, qui est résolu en utilisant la méthode des éléments finis mixte. Le présent travail contribue aussi certains éléments de stabilisation pour la simulation numérique des problèmes multiphasiques par l'approche monolithique.Comparaison entre la littérature et l'expérience est accompli par la validation du cas élastique et cas modèle viscoélastique de Kelvin-Voigt dans le lagrangien approche ainsi qu'eulérien approche. L'extension de la méthodologie au modèle visco-hyper-élastique est débuté par la modélisation et la validation au point matériel, puis l'implémentation dans la bibliothèque des éléments finis CimLib®. Enfin, un schéma stabilisation de résolution du type EVSS est adopté pour le modèle viscoélastique de Kelvin-Voigt, le modèle visco-hyper-élastique de Néo-Hookean, et aussi le modèle visco-hyper-élastique qui propose une prometteuse porte ouverte dans la simulation et modélisation, non seulement pour la viscoélasticité, mais aussi pour les applications dynamique complexes. / This work concerns the simulation of viscoelastic behavior of polymer at different states. Viscoelastic modeling of polymer was performed from the solid state to the liquid state via a multiphase approach which is largely used to deal with the fluid structure interaction. To ensure the appreciation of the FSI, viscoelasticity is considered in two parts: an elastic one and viscous other where the main idea is to use a mixed formulation in three fields (u, v, p) (displacement, velocity, pressure), with u and v, represented the primary variables of a strain and a strain rate formulation. We are led to the Navier-Stokes compressible problem with extra-stress, which is solved by using the Mixed Finite Element. The present work contributes some stabilization elements to the numerical simulation of multiphase problem by the monolithic approach.Comparison between the literature and experiments was performed through the validation of an elastic case and the viscoelastic Kelvin-Voigt model in the context of Lagrangian framework as well as Eulerian framework. The extension of the methodology to a visco-hyper-elastic is given through the modeling and validation on material point on the finite elements library CimLib®. Finally, a stabilization scheme of the EVSS type is adopted for viscoelastic Kelvin-Voigt model, hyper-elastic Neo-Hookean model, and also visco-hyper-elastic model which proposed an open door in computational modeling, not only with viscoelasticity but also complex dynamic application.