Showing papers on "Elasticity (economics) published in 2018"
Book•
07 Aug 2018
TL;DR: In this paper, the plate equations were derived from 3D elasticity by formal expansion from three-dimensional elasticity, and a calculus of variations was used to describe the geometrical rigidity of surfaces.
Abstract: 1. Introduction 2. Three-dimensional elasticity I: RODS 3. Equations for elastic rods 4. Mechanics of the human hair 5. Rippled leaves, uncoiled springs II: PLATES 6. The equations for elastic plates 7. End effects in plate buckling 8. Finite amplitude buckling of a strip 9. Crumpled paper 10. Fractal buckling near edges III: SHELLS 11. Geometric rigidity of surfaces 12. Shells of revolution 13. The elastic torus 14. Spherical shell pushed by a wall Appendix A: Calculus of variations: a worked example Appendix B: Boundary and interior layers Appendix C: The geometry of helices Appendix D: Derivation of the plate equations by formal expansion from 3D elasticity
286 citations
TL;DR: The authors use nanolipogels with tunable moduli to study the effect of particle elasticity on in vitro cellular uptake and in vivo tumor uptake, finding that stiffer particles are not as easily internalized.
Abstract: To date, the role of elasticity in drug delivery remains elusive due to the inability to measure microscale mechanics and alter rheology without affecting chemistry. Herein, we describe the in vitro cellular uptake and in vivo tumor uptake of nanolipogels (NLGs). NLGs are composed of identical lipid bilayers encapsulating an alginate core, with tunable elasticity. The elasticity of NLGs was evaluated by atomic force microscopy, which demonstrated that they exhibit Young’s moduli ranging from 45 ± 9 to 19,000 ± 5 kPa. Neoplastic and non-neoplastic cells exhibited significantly greater uptake of soft NLGs (Young’s modulus 13.8 MPa). In an orthotopic breast tumor model, soft NLGs accumulated significantly more in tumors, whereas elastic NLGs preferentially accumulated in the liver. Our findings demonstrate that particle elasticity directs tumor accumulation, suggesting that it may be a design parameter to enhance tumor delivery efficiency.
269 citations
TL;DR: Using microfocused synchrotron radiation, it is shown that, under strain, the molecules in the crystal reversibly rotate, and thus reorganize to allow the mechanical compression and expansion required for elasticity and still maintain the integrity of the crystal structure.
Abstract: Single crystals are typically brittle, inelastic materials. Such mechanical responses limit their use in practical applications, particularly in flexible electronics and optical devices. Here we describe single crystals of a well-known coordination compound-copper(II) acetylacetonate-that are flexible enough to be reversibly tied into a knot. Mechanical measurements indicate that the crystals exhibit an elasticity similar to that of soft materials such as nylon, and thus display properties normally associated with both hard and soft matter. Using microfocused synchrotron radiation, we mapped the changes in crystal structure that occur on bending, and determined the mechanism that allows this flexibility with atomic precision. We show that, under strain, the molecules in the crystal reversibly rotate, and thus reorganize to allow the mechanical compression and expansion required for elasticity and still maintain the integrity of the crystal structure.
199 citations
TL;DR: In this article, a covalent/supramolecular hybrid construction strategy was proposed to synthesize self-healing elastomers integrating extreme stretchability, relatively high mechanical modulus, and autonomous and rapid selfhealing capability.
Abstract: Stretchable and autonomously self-healable elastomers with wide-ranging tunable mechanical properties have attracted increasing attention in various industries. To date, it continues to be a huge challenge to synthesize self-healing elastomers integrating extreme stretchability, relatively high mechanical modulus, and autonomous and rapid self-healing capability. Herein, we propose a novel covalent/supramolecular hybrid construction strategy, in which the covalent cross-links are responsible for providing high modulus and elasticity, while supramolecular cross-links realize extreme stretchability and rapid self-healing under room temperature depending on the ultrafast exchange kinetics of metal–ligand motifs and multicoordination modes. The representative polyurea hybrid elastomer, CSH-PPG-Zn-0.25, can be stretched more than 180× its original length with the highest Young’s modulus (1.78 ± 0.08 MPa) among reported ultrastretchable materials. CSH-PPG-Zn-0.25 can fully restore mechanical properties of compl...
108 citations
TL;DR: In this article, the authors demonstrate a dynamic thermal control of the surface topography of an elastomer prepared as a coating with a pattern of in-plane molecular orientation, which can be used to design coating with functionalities that mimic biological tissues such as skin.
Abstract: Stimuli-responsive liquid crystal elastomers with molecular orientation coupled to rubber-like elasticity show a great potential as elements in soft robotics, sensing, and transport systems. The orientational order defines their mechanical response to external stimuli, such as thermally activated muscle-like contraction. Here we demonstrate a dynamic thermal control of the surface topography of an elastomer prepared as a coating with a pattern of in-plane molecular orientation. The inscribed pattern determines whether the coating develops elevations, depressions, or in-plane deformations when the temperature changes. The deterministic dependence of the out-of-plane dynamic profile on the in-plane orientation is explained by activation forces. These forces are caused by stretching-contraction of the polymer networks and by spatially varying molecular orientation. The activation force concept brings the responsive liquid crystal elastomers into the domain of active matter. The demonstrated relationship can be used to design coatings with functionalities that mimic biological tissues such as skin.
100 citations
TL;DR: Customer elasticity for Incentive Based Demand Response programs is estimated using data from two nation wide surveys and integrated with a detailed residential load model, and a constrained non-negative matrix factorization method is proposed.
98 citations
TL;DR: The continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales, and is demonstrated to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states.
Abstract: Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with [Formula: see text] topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U shape into a V shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal's elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.
92 citations
TL;DR: In this paper, the authors used strain-gradient elasticity to quantitatively describe the behavior of a microstructured solid, and showed that the validity domain (in terms of frequency and wavelength) of this model is sufficiently large to be useful in practical applications.
Abstract: Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the wavelength approaches this characteristic size) important quantities, such as phase and group velocity, deviate considerably from their low frequency/long wavelength values. This well-known phenomenon is called dispersion of waves. Objective of this work is to show that strain-gradient elasticity can be used to quantitatively describe the behaviour of a microstructured solid, and that the validity domain (in terms of frequency and wavelength) of this model is sufficiently large to be useful in practical applications. To this end, the parameters of the overall continuum are identified for a periodic architectured material, and the results of a transient problem are compared to those obtained from a finite element full field computation on the real geometry. The quality of the overall description using a strain-gradient elastic continuum is compared to the classical homogenization procedure that uses Cauchy continuum. The extended model of elasticity is shown to provide a good approximation of the real solution over a wider frequency range.
83 citations
TL;DR: A new adaptable main-chain LCE system was developed with thermally induced transesterification BERs and demonstrates an innovative feature of reprogrammability, where the reversible shape-switching memory of programmed LCEs is readily deleted by free-standing heating as random BER's disrupt the mesogen alignment.
Abstract: Adaptable liquid crystal elastomers (LCEs) have recently emerged to provide a new and robust method to program monodomain LCE samples. When a constant stress is applied with active bond exchange reactions (BERs), polymer chains and mesogens gradually align in the strain direction. Mesogen alignment is maintained after removing the BER stimulus (e.g. by lowering the temperature) and the programmed LCE samples exhibit free-standing two-way shape switching behavior. Here, a new adaptable main-chain LCE system was developed with thermally induced transesterification BERs. The network combines the conventional properties of LCEs, such as an isotropic phase transition and soft elasticity, with the dynamic features of adaptable network polymers, which are malleable to stress relaxation due to the BERs. Polarized Fourier transform infrared measurements confirmed the alignment of polymer chains and mesogens after strain-induced programming. The influence of the creep stress, temperature, and time on the strain amplitude of two-way shape switching was examined. The LCE network demonstrates an innovative feature of reprogrammability, where the reversible shape-switching memory of programmed LCEs is readily deleted by free-standing heating as random BERs disrupt the mesogen alignment, so LCEs are reprogrammed after returning to the polydomain state. Due to the dynamic nature of the LCE network, it also exhibits a surface welding effect and can be fully dissolved in the organic solvent, which might be utilized for green and sustainable recycling of LCEs.
79 citations
03 Jul 2018
TL;DR: In this paper, the authors re-examine a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which br...
Abstract: This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which br...
73 citations
TL;DR: In this paper, a meta-analysis based on a comprehensive and systematic summary of 103 articles is presented in order to identify the influencing factors with a weighed least squares (WLS) linear regression model to evaluate their strength.
TL;DR: In this article, the broad contents of classical physics (only classical mechanics, electromagnetism, and elementary thermodynamics) are missing, and only classical mechanics and electromagnetic properties are included.
Abstract: Discovering this book was really a pleasant surprise. On the one hand, the broad contents of classical physics (only classical mechanics, electromagnetism and elementary thermodynamics are missing)...
TL;DR: In this paper, a series of long-term creep experiments on coal-and carbonate-rich shale samples from unconventional gas reservoirs were carried out to investigate creep over both relatively short-term (4-h) and long-time periods.
Abstract: We carried out a series of long-term creep experiments on clay- and carbonate-rich shale samples from unconventional gas reservoirs to investigate creep over both relatively short-term (4-h) and long-term (4-week) periods. Results from each set of experiments were compared to evaluate the ability to predict the long-term behavior of reservoir rocks using relatively short-term creep experiments. The triaxial deformation experiments were performed in a time-cycling pattern, which included a series of four stages of loading, creep, unloading and recovery experiments conducted over different time spans. The loading conditions (tens of MPa) reflect current reservoir conditions and were far below the strength of the samples. Experiments were conducted on both horizontal and vertical shale samples to address anisotropy introduced by the bedding. A power-law model was fitted to the creep data to predict the long-term behavior of shale samples. Regardless of the applied loading history, results of the experiments show that the shale samples follow a single trend representing their creep behavior through time. We show that the simple power-law model is capable of describing creep over multiple time periods. Additionally, the value of the creep compliance factor is consistent over different creep testing periods and it is possible to characterize the behavior of these samples from relatively short-term (1 day) creep experiments.
TL;DR: In this paper, the authors developed a model that is able to provide estimates for irradiation-induced stresses and strains on a macroscopic scale, using information about the distribution of radiation defects produced by high-energy neutrons in the microstructure of materials.
Abstract: Predicting strains, stresses and swelling in nuclear power plant components exposed to irradiation directly from the observed or computed defect and dislocation microstructure is a fundamental problem of fusion power plant design that has so far eluded a practical solution. We develop a model, free from parameters not accessible to direct evaluation or observation, that is able to provide estimates for irradiation-induced stresses and strains on a macroscopic scale, using information about the distribution of radiation defects produced by high-energy neutrons in the microstructure of materials. The model exploits the fact that elasticity equations involve no characteristic spatial scale, and hence admit a mathematical treatment that is an extension to that developed for the evaluation of elastic fields of defects on the nanoscale. In the analysis given below we use, as input, the radiation defect structure data derived from ab initio density functional calculations and large-scale molecular dynamics simulations of high-energy collision cascades. We show that strains, stresses and swelling can be evaluated using either integral equations, where the source function is given by the density of relaxation volumes of defects, or they can be computed from heterogeneous partial differential equations for the components of the stress tensor, where the density of body forces is proportional to the gradient of the density of relaxation volumes of defects. We perform a case study where strains and stresses are evaluated analytically and exactly, and develop a general finite element method implementation of the method, applicable to a broad range of predictive simulations of strains and stresses induced by irradiation in materials and components of any geometry in fission or fusion nuclear power plants.
TL;DR: Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, two surface-elastic constants are measured that quantify the linear dependence of the surface stress of a soft polymer gel on its strain.
Abstract: Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched substrate, we measure two surface-elastic constants that quantify the linear dependence of the surface stress of a soft polymer gel on its strain. With these two parameters, one can predict surface stresses for general deformations of the material in the linear-elastic limit.
29 Aug 2018
TL;DR: Li et al. as discussed by the authors demonstrated a method to map the in-plane Young's modulus of mono-and bi-layer MoS2 on a substrate with high spatial resolution, which provided a convenient, robust and accurate means to map 2D materials.
Abstract: Elasticity is a fundamental mechanical property of two-dimensional (2D) materials, and is critical for their application as well as for strain engineering. However, accurate measurement of the elastic modulus of 2D materials remains a challenge, and the conventional suspension method suffers from a number of drawbacks. In this work, we demonstrate a method to map the in-plane Young’s modulus of mono- and bi-layer MoS2 on a substrate with high spatial resolution. Bimodal atomic force microscopy is used to accurately map the effective spring constant between the microscope tip and sample, and a finite element method is developed to quantitatively account for the effect of substrate stiffness on deformation. Using these methods, the in-plane Young’s modulus of monolayer MoS2 can be decoupled from the substrate and determined as 265 ± 13 GPa, broadly consistent with previous reports though with substantially smaller uncertainty. It is also found that the elasticity of mono- and bi-layer MoS2 cannot be differentiated, which is confirmed by the first principles calculations. This method provides a convenient, robust and accurate means to map the in-plane Young’s modulus of 2D materials on a substrate. A robust and accurate determination of the in-plane Young’s modulus of 2D materials can be accomplished directly on the supporting substrate. A team led by Jiangyu Li at the Shenzhen Institutes of Advanced Technology and University of Washington developed a method to map the in-plane Young’s modulus of 2D materials supported on a substrate with high spatial resolution. Considering the case of mono- and by-layered MoS2, bimodal atomic force microscopy (AFM) was used in combination to the finite element method to map the effective spring constant between the AFM tip and the sample, whist also accounting for the effect of the substrate. The in-plane Young’s modulus of monolayer MoS2 was found to be 265 ± 13 GPa, with less than 5% uncertainty, whereas that of bilayer MoS2 is indistinguishable from the monolayer counterpart.
TL;DR: In this article, the authors constructed an autoregressive distribution lag model to study the elasticity of natural gas demand in various sectors of China and found that the demand for natural gas is complementary to coal in industrial and power generation sectors, which is different from developed countries.
TL;DR: In this paper, the problem of reconstructing the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map is considered and an exact reconstruction procedure is given.
Abstract: We consider the problem of reconstructing of the boundary of an unknown inclusion together with its conductivity from the localized Dirichlet-to-Neumann map. We give an exact reconstruction procedure and apply the method to an inverse boundary value problem for the system of the equations in the theory of elasticity.
TL;DR: This study investigates the elastic and fracture properties of three different surface topologies with 3D graphene foams: P (primitive), D (diamond), and G (gyroid), called Schwarzites, and provides a systematic understanding of the relation between TPMS topologies and their mechanical properties, including failure mechanisms of graphene foam.
Abstract: The mechanics of triply periodic minimal surfaces (TPMSs) with three-dimensional (3D) graphene foams are systematically studied to understand the effects of structure and size on the mechanical properties, for example, elasticity, strength, and fracture. The design of lightweight open-shell porous solid materials with TPMSs has shown excellent and tunable load-bearing properties. However, fracture properties and their relations with surface topologies are largely unknown. Utilizing reactive molecular dynamics simulations, here we investigate the elastic and fracture properties of three different surface topologies with 3D graphene foams: P (primitive), D (diamond), and G (gyroid), called Schwarzites. Models with different lattice sizes are utilized to derive power laws, which can connect the properties along different sizes to shed light on the multiscale mechanics of TPMSs. Our study provides a systematic understanding of the relation between TPMS topologies and their mechanical properties, including fai...
01 Aug 2018
TL;DR: In this paper, the authors proposed a method for simultaneously optimizing both the piezoelectric and mechanical properties of wurtzite piezolectric materials based on the AlN wurtZite and alloyed with one or two end-members from the set BN, YN, CrN, and ScN.
Abstract: Methods and materials are disclosed for simultaneously optimizing both the piezoelectric and mechanical properties of wurtzite piezoelectric materials based on the AlN wurtzite and alloyed with one or two end-members from the set BN, YN, CrN, and ScN.
TL;DR: In this article, the authors consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space.
Abstract: We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.
TL;DR: In this paper, a family of virtual element schemes based on the Hellinger-Reissner variational principle is presented, and a convergence and stability analysis is rigorously developed.
23 Jan 2018
TL;DR: In this paper, a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity has been proved for generalized special functions of bounded deformation (G S B D ).
TL;DR: This technique, unlike other methods, can provide an elasticity image in less than a millisecond, thus opening the possibility of studying dynamic cellular processes and elucidating new mechanocellular properties, and represents a tractable option for interrogating biomechanical properties of diverse cell types.
Abstract: Elasticity is a fundamental cellular property that is related to the anatomy, functionality, and pathological state of cells and tissues. However, current techniques based on cell deformation, atomic force microscopy, or Brillouin scattering are rather slow and do not always accurately represent cell elasticity. Here, we have developed an alternative technique by applying shear wave elastography to the micrometer scale. Elastic waves were mechanically induced in live mammalian oocytes using a vibrating micropipette. These audible frequency waves were observed optically at 200,000 frames per second and tracked with an optical flow algorithm. Whole-cell elasticity was then mapped using an elastography method inspired by the seismology field. Using this approach we show that the elasticity of mouse oocytes is decreased when the oocyte cytoskeleton is disrupted with cytochalasin B. The technique is fast (less than 1 ms for data acquisition), precise (spatial resolution of a few micrometers), able to map internal cell structures, and robust and thus represents a tractable option for interrogating biomechanical properties of diverse cell types.
TL;DR: In this article, an experimental setup to introduce follower tangential forces at the end of an elastic rod was designed, realized, validated, and tested, in which the follower action is produced by exploiting Coulomb friction on an element (a freely-rotating wheel) in sliding contact against a flat surface (realized by a conveyor belt).
Abstract: Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck’s and Pfluger’s columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of the rod in the latter case), have attracted, and still attract, a thorough research interest. In this field, the most important issue is the validation of the model itself of follower force, a nonconservative action which was harshly criticized and never realized in practice for structures with diffused elasticity. An experimental setup to introduce follower tangential forces at the end of an elastic rod was designed, realized, validated, and tested, in which the follower action is produced by exploiting Coulomb friction on an element (a freely-rotating wheel) in sliding contact against a flat surface (realized by a conveyor belt). It is therefore shown that follower forces can be realized in practice and the first experimental evidence is given for both the flutter and divergence instabilities occurring in the Pfluger’s column. In particular, load thresholds for the two instabilities are measured and the detrimental effect of dissipation on the critical load for flutter is experimentally demonstrated, while a slight increase in load is found for the divergence instability. The presented approach to follower forces discloses new horizons for testing self-oscillating structures and for exploring and documenting dynamic instabilities possible when nonconservative loads are applied.
TL;DR: In this paper, a pine-tree forest environment was used to study the properties of the ambient and induced seismic wavefield that propagates in the ground and in trees, where the dense collection of trees behaves as subwavelength coupled resonators for surface seismic waves.
Abstract: We report on a seismic metamaterial experiment in a pine-tree forest environment where the dense collection of trees behaves as subwavelength coupled resonators for surface seismic waves. For the METAFORET experiment, more than 1000 seismic sensors were deployed over a 120 m × 120 m area to study the properties of the ambient and induced seismic wavefield that propagates in the ground and in trees. The goal of the experiment was to establish a link between seismic-relevant scales and microscale and mesoscale studies that pioneered the development of metamaterial physics in optics and acoustics. The first results of the METAFORET experiment show the presence of frequency band gaps for Rayleigh waves associated with compressional and flexural resonances of the trees, which confirms the strong influence that a dense collection of trees can have on the propagation of seismic waves.
TL;DR: The strain-dependent, nonlinear variation of Young's modulus of the sponge provides a unique opportunity as a variable stiffness stress sensor that operates over a wide stress range (0-10 kPa) with a high maximum sensitivity (0.572 kPa-1).
Abstract: Soft conductive materials should enable large deformation while keeping high electrical conductivity and elasticity. The graphene oxide (GO)-based sponge is a potential candidate to endow large deformation. However, it typically exhibits low conductivity and elasticity. Here, the highly conductive and elastic sponge composed of GO, flower-shaped silver nanoparticles (AgNFs), and polyimide (GO-AgNF-PI sponge) are demonstrated. The average pore size and porosity are 114 µm and 94.7%, respectively. Ag NFs have thin petals (8-20 nm) protruding out of the surface of a spherical bud (300-350 nm) significantly enhancing the specific surface area (2.83 m2 g-1 ). The electrical conductivity (0.306 S m-1 at 0% strain) of the GO-AgNF-PI sponge is increased by more than an order of magnitude with the addition of Ag NFs. A nearly perfect elasticity is obtained over a wide compressive strain range (0-90%). The strain-dependent, nonlinear variation of Young's modulus of the sponge provides a unique opportunity as a variable stiffness stress sensor that operates over a wide stress range (0-10 kPa) with a high maximum sensitivity (0.572 kPa-1 ). It allows grasping of a soft rose and a hard bottle, with the minimal object deformation, when attached on the finger of a robot gripper.