Nonlinear behavior of gelatin networks reveals a hierarchical structure

We investigate the strain hardening behavior of various gelatin networks-namely physical gelatin gel, chemically cross-linked gelatin gel, and a hybrid gel made of a combination of the former two-under large shear deformations using the pre-stress, strain ramp, and large amplitude oscillations shear protocols. Further, the internal structures of physical gelatin gels and chemically cross-linked gelatin gels were characterized by small angle neutron scattering (SANS) to enable their internal structures to be correlated with their nonlinear rheology. The Kratky plots of SANS data demonstrate the presence of small cross-linked aggregates within the chemically cross-linked network whereas, in the physical gelatin gels, a relatively homogeneous structure is observed. Through model fitting to the scattering data, we were able to obtain structural parameters, such as the correlation length (ξ), the cross-sectional polymer chain radius (Rc) and the fractal dimension (df) of the gel networks. The fractal dimension df obtained from the SANS data of the physical and chemically cross-linked gels is 1.31 and 1.53, respectively. These values are in excellent agreement with the ones obtained from a generalized nonlinear elastic theory that has been used to fit the stress-strain curves. The chemical cross-linking that generates coils and aggregates hinders the free stretching of the triple helix bundles in the physical gels.

Rheological characterization of EVA and HDPE polymer modified bitumens under large deformation at 20 º C

Large amplitude oscillatory shear (LAOS) coupled with Fourier transform rheology (FTR) was used for the first time to characterize the large deformation behavior of selected bituminous binders at 20 C. Two polymer modified bitumens (PMB) containing recycled EVA and HDPE and two unmodified bitumens were tested with LAOS-FTR. The LAOS-FTR response of all binders was compared at same frequency, at same Deborah number (by tuning the frequency to the relaxation time of each binder) and at same phase shift angle d (by tuning the frequency to the one corresponding to d = 50 in the SAOS response of each sample). In all the approaches, LAOS-FTR results allowed to differentiate between all the nonlinear mechanical characteristics of the tested binders. All binders show LAOS-FTR patterns reminiscent from colloidal dispersions and emulsions. EVA PMB was less prone to strain-induced microstructural changes when compared to HDPE PMB which showed larger values of nonlinear FTR parameters for the range of shear strains tested in LAOS.

Method of determining a geophysical-scale sea ice rheology from laboratory measurements

We present a methodology that allows a sea ice rheology, suitable for use in a General Circulation Model (GCM), to be determined from laboratory and tank experiments on sea ice when combined with a kinematic model of deformation. The laboratory experiments determine a material rheology for sea ice, and would investigate a nonlinear friction law of the form τ ∝ σ n⅔, instead of the more familiar Amonton's law, τ = μσn (τ is the shear stress, μ is the coefficient of friction and σ n is the normal stress). The modelling approach considers a representative region R containing ice floes (or floe aggregates), separated by flaws. The deformation of R is imposed and the motion of the floes determined using a kinematic model, which will be motivated from SAR observations. Deformation of the flaws is inferred from the floe motion and stress determined from the material rheology. The stress over R is then determined from the area-weighted contribution from flaws and floes

Rheology and Microfluidic flows of a cationic surfactant and hydrotropic salt mixture

Thesis (Ph.D.)--University of Washington, 2016-08

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Molecular Variations In Aromatic Cosolutes: Critical Role In The Rheology Of Cationic Wormlike Micelles.

Wormlike micelles formed by the addition to cetyltrimethylammonium bromide (CTAB) of a range of aromatic cosolutes with small molecular variations in their structure were systematically studied. Phenol and derivatives of benzoate and cinnamate were used, and the resulting mixtures were studied by oscillatory, steady-shear rheology, and the microstructure was probed by small-angle neutron scattering. The lengthening of the micelles and their entanglement result in remarkable viscoelastic properties, making rheology a useful tool to assess the effect of structural variations of the cosolutes on wormlike micelle formation. For a fixed concentration of CTAB and cosolute (200 mmol L(-1)), the relaxation time decreases in the following order: phenol > cinnamate> o-hydroxycinnamate > salicylate > o-methoxycinnamate > benzoate > o-methoxybenzoate. The variations in viscoelastic response are rationalized by using Mulliken population analysis to map out the electronic density of the cosolutes and quantify the barrier to rotation of specific groups on the aromatics. We find that the ability of the group attached to the aromatic ring to rotate is crucial in determining the packing of the cosolute at the micellar interface and thus critically impacts the micellar growth and, in turn, the rheological response. These results enable us for the first time to propose design rules for the self-assembly of the surfactants and cosolutes resulting in the formation of wormlike micelles with the cationic surfactant CTAB.

Interaction Between Fiscal And Monetary Policy In A Dynamic Nonlinear Model.

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.

Rheology of decane/water and triglyceride/water emulsions stabilized by β-casein and sodium caseinate

β-Casein and sodium caseinate stabilized emulsions were produced and had their rheological properties investigated as a function of the nature of the oil phase, ionic strength and pH. Oil phases of distinct structural characteristics, namely decane and vegetable oil of high triglyceride content, were assayed. The former was much more effectively emulsified than the latter. Effects of pH and ionic strength were minor. Emulsion rheological properties were strikingly distinct in each case, with viscoelastic, solid-like structures being formed with decane (G' >> G"), differently from what is observed for samples containing triglycerides as the oil phase, in which viscoelasticity was not even apparent. The relevance of the spatial features of the oil phase structure in the development of the emulsion viscoelastic character is discussed. Factors responding for the system distinct behaviour possibly reside at the emulsion droplet interface, unapproachable by optical microscopy, rather than on aspects related to particle size or shape.

Rheology of decane/water and triglyceride/water emulsions stabilized by 'beta'-casein and sodium caseinate

Emulsões estabilizadas por 'beta'-caseína e sódio caseinato tiveram suas propriedades reológicas investigadas em função da natureza da fase oleosa, da força iônica e do pH. Fases oleosas de características estruturais distintas, a saber, decano e óleos vegetais de alto teor triglicerídico, foram ensaiadas. A emulsificação dos sistemas contendo decano foi significativamente mais efetiva do que aquela das amostras contendo triglicérides. Efeitos de pH e força iônica mostraram-se relativamente pouco importantes sobre a capacidade emulsificante da proteína. As propriedades reológicas foram marcadamente distintas em cada caso, com estruturas de caráter sólido (G' G") sendo produzidas com decano, diferentemente do que foi observado para amostras contendo triglicérides, nas quais a viscoelasticidade não foi nem mesmo aparente. A relevância de aspectos espaciais da estrutura da fase oleosa no desenvolvimento do caráter viscoelástico é discutida. Propõe-se que os fatores responsáveis pelo comportamento distinto observado residam possivelmente na interface gotícula/meio dispersante, inacessível por microscopia óptica, e guardam pouca relação com tamanho ou forma da gotícula.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.