Showing papers on "Elasticity (economics) published in 2015"

Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography.

Abstract: Probing the mechanical properties of tissue on the microscale could aid in the identification of diseased tissues that are inadequately detected using palpation or current clinical imaging modalities, with potential to guide medical procedures such as the excision of breast tumours. Compression optical coherence elastography (OCE) maps tissue strain with microscale spatial resolution and can delineate microstructural features within breast tissues. However, without a measure of the locally applied stress, strain provides only a qualitative indication of mechanical properties. To overcome this limitation, we present quantitative micro-elastography, which combines compression OCE with a compliant stress sensor to image tissue elasticity. The sensor consists of a layer of translucent silicone with well-characterized stress-strain behaviour. The measured strain in the sensor is used to estimate the two-dimensional stress distribution applied to the sample surface. Elasticity is determined by dividing the stress by the strain in the sample. We show that quantification of elasticity can improve the ability of compression OCE to distinguish between tissues, thereby extending the potential for inter-sample comparison and longitudinal studies of tissue elasticity. We validate the technique using tissue-mimicking phantoms and demonstrate the ability to map elasticity of freshly excised malignant and benign human breast tissues.

Bubble dynamics in a viscoelastic medium with nonlinear elasticity

Abstract: In a variety of recently developed medical procedures, bubbles are formed directly in soft tissue and may cause damage. While cavitation in Newtonian liquids has received significant attention, bubble dynamics in tissue, a viscoelastic medium, remains poorly understood. To model tissue, most previous studies have focused on Maxwell-based viscoelastic fluids. However, soft tissue generally possesses an original configuration to which it relaxes after deformation. Thus, a Kelvin–Voigt-based viscoelastic model is expected to be a more appropriate representation. Furthermore, large oscillations may occur, thus violating the infinitesimal strain assumption and requiring a nonlinear/finite-strain elasticity description. In this article, we develop a theoretical framework to simulate spherical bubble dynamics in a viscoelastic medium with nonlinear elasticity. Following modern continuum mechanics formalism, we derive the form of the elastic forces acting on a bubble for common strain-energy functions (e.g. neo-Hookean, Mooney–Rivlin) and incorporate them into Rayleigh–Plesset-like equations. The main effects of nonlinear elasticity are to reduce the violence of the collapse and rebound for large departures from the equilibrium radius, and increase the oscillation frequency. The present approach can readily be extended to other strain-energy functions and used to compute the stress/deformation fields in the surrounding medium.

Mathematical Methods in Elasticity Imaging

Abstract: This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative-based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Elastic coupling between layers in two-dimensional materials

Abstract: Two-dimensional materials, such as graphene and MoS2, are films of a few atomic layers in thickness with strong in-plane bonds and weak interactions between the layers. The in-plane elasticity has been widely studied in bending experiments where a suspended film is deformed substantially; however, little is known about the films' elastic modulus perpendicular to the planes, as the measurement of the out-of-plane elasticity of supported 2D films requires indentation depths smaller than the films' interlayer distance. Here, we report on sub-angstrom-resolution indentation measurements of the perpendicular-to-the-plane elasticity of 2D materials. Our indentation data, combined with semi-analytical models and density functional theory, are then used to study the perpendicular elasticity of few-layer-thick graphene and graphene oxide films. We find that the perpendicular Young's modulus of graphene oxide films reaches a maximum when one complete water layer is intercalated between the graphitic planes. This non-destructive methodology can map interlayer coupling and intercalation in 2D films.

Hierarchical elasticity of bimesogenic liquid crystals with twist-bend nematic phase

Abstract: In 2001, Dozov predicted that twist-bend nematic phase can be spontaneously formed when K33 2, and this phase has recently been discovered in bimesogens. To verify Dozov's hypothesis, we have measured precisely the temperature dependence of the elastic constants of CB7CB in the entire temperature range of nematic phase and in twist-bend nematic phase close to the transition temperature by combing the Freedericksz threshold methods for a twist nematic and an in-plane switching cells. Anomalous changes in K22 and K33 are observed across the phase transition. The elasticity estimated via extrapolation of the data in the high temperature region of the nematic phase seems to fully satisfy Dozov's hypothesis although the elasticity data in the vicinity of the phase transition exhibit opposite trends. This can be explained by the general nature of a hierarchical system where the macroscopic elasticity is governed mostly by the distortion of a higher level structure.

Phase-field elasticity model based on mechanical jump conditions

Abstract: Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition (Johnson and Alexander, J Appl Phys 59(8):2735, 1986).

From Soft Self-Healing Gels to Stiff Films in Suckerin-Based Materials Through Modulation of Crosslink Density and β-Sheet Content

Abstract: Suckerins are block-copolymer-like structural proteins constituting the building blocks of the strong squid sucker-ring teeth. Here, recombinant suckerin-19 is processed into biomaterials spanning a wide range of elasticity, from very soft hydrogels to stiff films with elastic modulus in the gigapascal range. The elasticity is controlled by the interplay between the β-sheet content and induced di-tyrosine crosslinking.

Structural, electronic and elastic properties of the cubic CaTiO3 under pressure: A DFT study

Abstract: Using highly accurate FP-LAPW method with GGA approximation structural, electronic and elastic properties of cubic CaTiO3 have been calculated from 0-120 GPa range of pressure. It is observed that lattice constant, bond length and anisotropy factor decrease with increase in pressure. Also the brittle nature and indirect band-gap of the compound become ductile and direct band-gap respectively at 120 GPa. Moduli of elasticity, density of the material, Debye temperature and wave elastic wave velocities increase with increase in pressure. Spin dependent DOS’s plots show invariant anti-ferromagnetic nature of the compound under pressure. Our calculated results are in good agreement with available theoretical and experimental results.

Strain gradient elasticity with geometric nonlinearities and its computational evaluation

Abstract: The theory of linear elasticity is insufficient at small length scales, e.g., when dealing with micro-devices. In particular, it cannot predict the “size effect” observed at the micro- and nanometer scales. In order to design at such small scales an improvement of the theory of elasticity is necessary, which is referred to as strain gradient elasticity. There are various approaches in literature, especially for small deformations. In order to include geometric nonlinearities we start by discussing the necessary balance equations. Then we present a generic approach for obtaining adequate constitutive equations. By combining balance equations and constitutive relations nonlinear field equations result. We apply a variational formulation to the nonlinear field equations in order to find a weak form, which can be solved numerically by using open-source codes. By using balances of linear and angular momentum we obtain the so-called stress and couple stress as tensors of rank two and three, respectively. Since dealing with tensors an adequate representation theorem can be applied. We propose for an isotropic material a stress with two and a couple stress with three material parameters. For understanding their impact during deformation the numerical solution procedure is performed. By successfully simulating the size effect known from experiments, we verify the proposed theory and its numerical implementation. Based on representation theorems a self consistent strain gradient theory is presented, discussed, and implemented into a computational reality.

Critical Assessment 16: Anisotropy in metals

Abstract: Sources of anisotropy in metals are discusssed as well as ways of interpreting and modelling this behaviour. A number of case studies are presented relating to mechanical and magnetic properties.

Effect of fluid rheology on particle migration in a square-shaped microchannel

Abstract: The effect of fluid rheology on particle migration induced by fluid viscoelasticity in a square-shaped microchannel is reported. Three water polymer solutions of PolyEthylene Oxyde at different concentrations, corresponding to different elasticity and degree of shear thinning, are prepared and rheologically characterized. Experiments are carried out for a wide range of flow rates, and the particle distributions over the channel cross section are reconstructed by combining particle tracking measurements and numerical simulations of the fluid velocity profile. The particle distributions show that the migration direction strongly depends on the fluid rheology. Specifically, when particles explore the constant viscosity region of the suspending liquids, they are focused around the channel centerline. Such an effect is more and more pronounced as the flow rate increases. On the other hand, for particles suspended in a shear-thinning fluid, a different scenario appears: At low flow rates, i.e., in the constant viscosity region, particles still migrate toward the channel centerline, while at high flow rates, i.e., in the shear thinning region, the migration reverts direction and the particles are driven toward the corners of the channel cross section. Those experimental observations elucidate the relevant and competing role of elasticity and shear thinning, with obvious implications in designing microfluidic devices for particle manipulation. Finally, our results highlight the weak effect of inertia on particle migration as compared to viscoelastic effects, even for low elastic suspending liquids.

A Fully Gradient Model for Euler-Bernoulli Nanobeams

Abstract: A fully gradient elasticity model for bending of nanobeams is proposed by using a nonlocal thermodynamic approach. As a basic theoretical novelty, the proposed constitutive law is assumed to depend on the axial strain gradient, while existing gradient elasticity formulations for nanobeams contemplate only the derivative of the axial strain with respect to the axis of the structure. Variational equations governing the elastic equilibrium problem of bending of a fully gradient nanobeam and the corresponding differential and boundary conditions are thus provided. Analytical solutions for a nanocantilever are given and the results are compared with those predicted by other theories. As a relevant implication of applicative interest in the research field of nanobeams used in nanoelectromechanical systems (NEMS), it is shown that displacements obtained by the present model are quite different from those predicted by the known gradient elasticity treatments.

Undulatory swimming in non-Newtonian fluids

Abstract: We numerically investigate the effects of non-Newtonian fluid properties, including shear thinning and elasticity, on the locomotion of Taylor’s swimming sheet with arbitrary amplitude. Our results show that elasticity hinders the swimming speed, but a shear-thinning viscosity in the absence of elasticity enhances the speed. The combination of the two effects, modelled using a Giesekus constitutive equation, hinders the swimming speed. We find that the swimming speed of an infinitely long waving sheet in an inelastic shear-thinning fluid has a maximum, whose value depends on the sheet undulation amplitude and the fluid rheological properties. The power consumption, on the other hand, follows a universal scaling law.

A unifying variational framework for stress gradient and strain gradient elasticity theories

Abstract: Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int J Solids Struct 51, 1809–1818, (2014)) in the form of higher order boundary compatibility equations, are here revisited and reinterpreted with the aid of a discrete model of the body's boundary layer The reasons why the latter conditions need to be relaxed for beam and plate structural models are explained

A microstructure- and surface energy-dependent third-order shear deformation beam model

Abstract: A new non-classical third-order shear deformation model is developed for Reddy–Levinson beams using a variational formulation based on Hamilton’s principle. A modified couple stress theory and a surface elasticity theory are employed. The equations of motion and complete boundary conditions for the beam are obtained simultaneously. The new model contains a material length scale parameter to account for the microstructure effect and three surface elastic constants to describe the surface energy effect. Also, Poisson’s effect is incorporated in the new beam model. The current non-classical model recovers the classical elasticity-based third-order shear deformation beam model as a special case when the microstructure, surface energy and Poisson’s effects are all suppressed. In addition, the newly developed beam model includes the models considering the microstructure dependence or the surface energy effect alone as limiting cases and reduces to two existing models for Bernoulli–Euler and Timoshenko beams incorporating the microstructure and surface energy effects. To illustrate the new model, the static bending and free vibration problems of a simply supported beam loaded by a concentrated force are analytically solved by directly applying the general formulas derived. For the static bending problem, the numerical results reveal that both the deflection and rotation of the simply supported beam predicted by the current model are smaller than those predicted by the classical model. Also, it is observed that the differences in the deflection and rotation predicted by the two beam models are very large when the beam thickness is sufficiently small, but they are diminishing with the increase in the beam thickness. For the free vibration problem, it is found that the natural frequency predicted by the new model is higher than that predicted by the classical beam model, and the difference is significant for very thin beams. These predicted trends of the size effect at the micron scale agree with those observed experimentally.

Prediction of mechanical properties - modulus of rupture and modulus of elasticity - of five tropical species by nondestructive methods

Abstract: This paper analyzes the usability of different dynamic moduli of elasticity and wood density for the prediction of mechanical properties – static modulus of elasticity and modulus of rupture – in samples with grain deflection from the longitudinal direction. Five tropical hardwoods (Afzelia bipindensis, Intsia bijuga, Millettia laurentii, Astronium graveolens and Microberlinia brazzavillensis) with different grain characteristics were used for this purpose. The fiber deflection was caused by the presence of interlocked grain or the working process. The three nondestructive techniques used in this study – longitudinal and flexural resonance method and ultrasound method – provided higher values of modulus of elasticity than the static bending test, but close correlation was observed between these variables. The weakest correlation was found for the ultrasound method which is probably caused by its measuring mechanism. The prediction of the modulus of rupture is less accurate when the dynamic modulus of elasticity is compared with the static modulus of elasticity; on the other hand, it was still good in comparison with the density model, which is inapplicable when grain deflection occurs in wood. In the wood of Zebrano where the interlocked grain was strongly developed, almost all of the correlation coefficients showed the lowest values and the prediction of modulus of rupture by nondestructive techniques was unsatisfactory.

Alignment and nonlinear elasticity in biopolymer gels.

Abstract: We present a Landau-type theory for the nonlinear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the nonlinear elastic behavior of these materials to fiber alignment induced by strain. We suggest an application to contact guidance of cell motility in tissue. We compare our theory to simulation of a disordered lattice model for biopolymers. We treat homogeneous deformations such as simple shear, hydrostatic expansion, and simple extension, and obtain good agreement between theory and simulation. We also consider a localized perturbation which is a simple model for a contracting cell in a medium.

Convergence of a Cell-Centered Finite Volume Discretization for Linear Elasticity

Abstract: We show convergence of a cell-centered finite volume discretization for linear elasticity. The discretization, termed the MPSA method, was recently proposed in the context of geological applications, where cell-centered variables are often preferred. Our analysis utilizes a hybrid variational formulation, which has previously been used to analyze finite volume discretizations for the scalar diffusion equation. The current analysis deviates significantly from the previous in three respects. First, additional stabilization leads to a more complex saddle-point problem. Second, a discrete Korn's inequality has to be established for the global discretization. Finally, robustness with respect to the Poisson ratio is analyzed. The stability and convergence results presented herein provide the first rigorous justification of the applicability of cell-centered finite volume methods to problems in linear elasticity.

Elasticity of Crystalline Molecular Explosives

Abstract: Crystalline molecular explosives are key components of engineered explosive formulations. In precision applications a high degree of consistency and predictability is desired under a range of conditions to a variety of stimuli. Prediction of behaviors from mechanical response and failure to detonation initiation and detonation performance of the material is linked to accurate knowledge of the material structure and first stage of deformation: elasticity. The elastic response of pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), and cyclotetramethylene tetranitramine (HMX), including aspects of material and measurement variability, and computational methods are described in detail. Experimental determinations of elastic tensors are compared, and an evaluation of sources of error is presented. Furthermore, computed elastic constants are also compared for these materials and for triaminotrinitrobenzene (TATB), for which there are no measurements.