Showing papers on "Elasticity (economics) published in 2000"
TL;DR: In this article, a simple model is constructed to predict the size dependence of the effective stiffness of the structural element, and the important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulation of the bulk.
Abstract: Effective stiffness properties (D) of nanosized structural elements such as plates and beams differ from those predicted by standard continuum mechanics (Dc). These differences (D-Dc)/Dc depend on the size of the structural element. A simple model is constructed to predict this size dependence of the effective properties. The important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk. In general, the non-dimensional difference in the elastic properties from continuum predictions (D-Dc)/Dc is found to scale as αS/Eh, where α is a constant which depends on the geometry of the structural element considered, S is a surface elastic constant, E is a bulk elastic modulus and h a length defining the size of the structural element. Thus, the quantity S/E is identified as a material length scale for elasticity of nanosized structures. The model is compared with direct atomistic simulations of nanoscale structures using the embedded atom method for FCC Al and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.
1,648 citations
TL;DR: A review of constitutive models for the finite deformation response of rubbery materials is given in this article, where several recent and classic statistical mechanics and continuum mechanics models of incompressible rubber elasticity are discussed and compared to experimental data.
Abstract: A review of constitutive models for the finite deformation response of rubbery materials is given. Several recent and classic statistical mechanics and continuum mechanics models of incompressible rubber elasticity are discussed and compared to experimental data. A hybrid of the Flory—Erman model for low stretch deformation and the Arruda—Boyce model for large stretch deformation is shown to give an accurate, predictive description of Treloar's classical data over the entire stretch range for all deformation states. The modeling of compressibility is also addressed.
986 citations
TL;DR: The effect of various drugs affecting the integrity of different components of the cytoskeleton on the elasticity of two fibroblast cell lines was investigated by elasticity measurements with an atomic force microscope (AFM).
912 citations
TL;DR: The analysis of the eigenvalues of the elasticity tensor support the hypothesis that breast carcinoma might exhibit an anisotropic elasticity distribution and the surrounding benign tissue appears isotropic.
Abstract: MR elastography is a novel imaging technique for the visualization of elastic properties of tissue. It is expected that this method will have diagnostic value for the clarification of suspicious breast lesions. Low-frequency mechanical waves are coupled into the tissue and visualized via an MR sequence which is phase-locked to the mechanical excitation. Commonly, elasticity is assumed to be isotropic and reconstruction is performed in only two dimensions. The technique is extended to three dimensions such that the entire symmetric elasticity tensor is assessed. This is achieved by measuring different phases of the mechanical wave during one oscillatory cycle. Thereby it is possible to provide information about the anisotropy of the elasticity tensor. Finite-element simulations as well as phantom experiments are performed to demonstrate the feasibility of the method. Initial clinical results of a breast carcinoma are presented. The analysis of the eigenvalues of the elasticity tensor support the hypothesis that breast carcinoma might exhibit an anisotropic elasticity distribution. The surrounding benign tissue appears isotropic. Thereby new and additional diagnostic information is provided which might help in distinguishing between benign and malignant breast diseases.
542 citations
TL;DR: An asymptotic expansion of a design functional with respect to the creation of a small hole is obtained by using an adaptation of the adjoint method and a domain truncation technique for linear elasticity for general functionals and arbitrary shaped holes.
Abstract: The aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole. In this paper, such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique. The method is general and can be easily adapted to other linear PDEs and other types of boundary conditions.
429 citations
TL;DR: In this paper, the authors derived analytical expressions for the velocities of the longitudinal and torsional sound waves in single-walled carbon nanotubes using Born's perturbation technique within a lattice-dynamical model.
Abstract: Analytical expressions for the velocities of the longitudinal and the torsional sound waves in single-walled carbon nanotubes are derived using Born's perturbation technique within a lattice-dynamical model. These expressions are compared to the formulas for the velocities of the sound waves in an elastic hollow cylinder from the theory of elasticity to obtain analytical expressions for the Young's and shear moduli of nanotubes. The calculated elastic moduli for different chiral and achiral ~armchair and zigzag! nanotubes using force constants of the valence force field type are compared to the existing experimental and theoretical data. vibration amplitude of several isolated MWNT's was ana- lyzed in a transmission electron microscope to eventually obtain 1.8 TPa for the average Young's modulus. Later on, this technique was applied to measure Young's modulus of isolated SWNT's in the diameter range 1.0 21.5 nm and an average value ^Y&51.2520.35/10.45 TPa was derived. 7 In another experimental approach 8 the MWNT's were pinned to a substrate by conventional lithography and the force was measured at different distances from the pinned point by atomic force microscope ~ATM!. The average Young's modulus for different MWNT's with diameters from 26 to 76 nm was found to be 1.2860.59 TPa. Recently, Young's and shear moduli of ropes of SWNT's were measured by sus- pending the ropes over the pores of a membrane and using ATM to determine directly the resulting deflection of the rope. 9 The theoretical estimation of the elastic moduli was accomplished exclusively by numerical second derivatives of the energy of the strained nanotubes. In the calculation of the elastic moduli of various SWNT's within a simple force- constant model 10 it was found that the moduli were insensi- tive to tube size and helicity and had the average values of ^Y&50.97 TPa and ^G&50.45 TPa. In several works, molecular-dynamics ~MD! simulation algorithms using the Tersoff-Brenner potential for the carbon-carbon interactions were implemented to relax the strained nanotubes and calcu- late their energy. 11-13 For tubes of diameter of 1 nm values for Y of 5.5 TPa ~Ref. 12! and 0.8 TPa ~Ref. 13! were ob- tained. A non-orthogonal tight-binding ~TB! scheme was ap- plied to calculate Young's modulus of several chiral and achiral SWNT's yielding an average value of 1.24 TPa. 14 Recently, the second derivative of the strain energy with re- spect to the axial strain, calculated with a pseudopotential density-functional-theory ~DFT! model for a number of SWNT's, 15 was found to vary slightly with the tube type and to have the average value of 56 eV. In this paper, we choose a different approach to the cal- culation of the elastic properties of SWNT's. Namely, we derive analytical expressions for the elastic ~Young's and shear! moduli of SWNT's using a perturbation technique due to Born 16 within a lattice-dynamical model for nanotubes. 17 This scheme has the advantage that the elastic moduli are consistent with the lattice dynamics of the nanotubes and that each of these moduli is obtained in one calculational step only. The essential features of a model of the lattice dynamics of SWNT's based on the explicit accounting for the helical symmetry of the tubes 17 are summarized in Sec. II A. This model is applied to study of the long-wavelength vibrations in nanotubes using Born's perturbation technique 16 and to obtain analytical expressions for the velocities of the longi- tudinal and the torsional sound waves in SWNT's ~see Sec. II B!. The comparison of these expressions with the formulas from the theory of elasticity for the velocities of these waves in an elastic hollow cylinder allows one to determine the Young's and shear moduli of the nanotubes. The calculated phonon dispersion of a (10,10) nanotube and elastic moduli for various chiral and achiral ~armchair and zigzag! nano- tubes using force constants of the valence force field ~VFF! type 18 are presented in Sec. III and discussed in comparison with the existing experimental and theoretical data.
422 citations
TL;DR: The present study provides a direct determination of pressure without recourse to any prior pressure standard, thus creating a primary pressure scale and improving the commonly used ruby fluorescence pressure scale to 1% accuracy.
Abstract: We have studied the elasticity and pressure-density equation of state of MgO in diamond cells to 55 GPa and have doubled the previous pressure limit of accurate elasticity determinations for crystals. Integrating single-crystal velocity data from Brillouin scattering measurements and density data from polycrystalline x-ray diffraction, we obtained the three principal elastic tensor elements (C(11), C(12), and C(44)) and various secondary elasticity parameters, including single-crystal elastic anisotropy, Cauchy relation, aggregate sound velocities, and Poisson's ratio, as functions of pressure. The present study also provides a direct determination of pressure without recourse to any prior pressure standard, thus creating a primary pressure scale. The commonly used ruby fluorescence pressure scale has thus been improved to 1% accuracy by the new MgO scale.
410 citations
TL;DR: The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
Abstract: A biphasic mixture model is developed which can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J Elasticity 37:1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A =0.64±0.22 MPa, kz = 3.62 ± .97 × 10−16 m4/N.s, r2 =0.95±0.03), the tensile modulus, compressive Poisson ratio and radial permeability were obtained from unconfined compression (E+Y = 12.75 ± 1.56 MPa, ν− =0.03±0.01, kr =6.06±2.10×10−16 m4/N.s, r2 =0.99±0.00), and the shear modulus was obtained from torsional shear (µ=0.17±0.06 MPa). The model was also employed to successfully predict the interstitial fluid pressure at the center of the cartilage plug in unconfined compression (r2 =0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage which can successfully curvefit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
327 citations
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20 Jan 2000
TL;DR: In this article, the authors describe different types of cyclastic wave propagation, including non-linear ACOUSTIC SURFACE WAVES on CRYSTALS and non-linear wave swarms in MARTENSITIC STRUCTURES.
Abstract: 1. DIFFERENT TYPES OF CRYSTAL 2. DISCRETE AND CONTINUUM DESCRIPTIONS: GENERAL INTRODUCTION 3. ELASTICITY AND ANELASTICITY: CONTINUOUS VIEWPOINT 4. ELASTICITY AND ANELASTICITY: DISCRETE VIEWPOINT 5. COUPLED FIELDS IN ELASTICITY 6. NONLINEAR WAVES IN ELASTIC CHAINS 7. NONLINEAR WAVES IN ELASTIC CRYSTALS WITH A MICROSTRUCTURE 8. NONLINEAR WAVES IN MARTENSITIC STRUCTURES 9. NONLINEAR ACOUSTIC SURFACE WAVES ON CRYSTALS 10. SHOCK WAVES AND PHASE-TRANSITION FRONTS IN THERMOELASTIC CRYSTALS 11. MISCELLANI 12. POSTFACE BY WAY OF CONCLUSION
266 citations
TL;DR: This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching, and fragmentation.
Abstract: We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching, and fragmentation.
233 citations
TL;DR: In this paper, a novel elongational device is used to investigate the capillary thinning process of threads of dilute and semidilute aqueous polymer solutions, and the elasticity of the polymers is dominated by polyacrylamide chains and the effect of branching and topological structure of macromolecules is negligible.
Abstract: A novel elongational device is used to investigate the capillary thinning process of threads of dilute and semidilute aqueous polymer solutions. It is shown that the end regions of the threads do not play an essential role in the thinning process, so that a simple theory describing the self-thinning of the liquid thread is appropriate to describe the experiments with polymer solutions carried out with this device. Aqueous solutions of four different polymers (all polyacrylamide based) are studied using the elongational device. It is shown that the elasticity of the polymers is dominated by polyacrylamide chains and that the effect of branching and topological structure of macromolecules is negligible. The time-dependent decrease of the thread diameter can be divided into two stages. The first is a viscoelastic one where macromolecular coils are stretched by the elongational flow, and the second is a quasi-Newtonian one, where full stretching has already been achieved, resulting in a very high but constant...
TL;DR: The gelation kinetics of gelatin have been exhaustively studied using oscillatory rheometry for six molecular weight distributions, three concentrations, and four temperatures as mentioned in this paper, and all of the data can be superimposed on a single master curve using suitable shift factors.
Abstract: The gelation kinetics of gelatin has been exhaustively studied using oscillatory rheometry for six molecular weight distributions, three concentrations, and four temperatures. Measurements lasted up to 31/2 months, much longer than previous studies. Remarkably, all of the data can be superimposed on a single master curve using suitable shift factors. The existence of a master curve shows that, over the broad range of variables studied, the gelation processes are identical; altering the variables just changes the scaling factors for elasticity and time. Empirically, it is found that neither high nor low molecular weight chains contribute to the elasticity. A statistical network model has been developed, based on Flory's phantom network formalism. It gives reasonable fits to the experimental gel times and is compatible with the observed dependence of elasticity on molecular weight distribution. A second order reaction kinetics model has also been developed which satisfactorily models the early stages of gel...
TL;DR: The present results indicate that the elasticity of tendon structures of VL and MG at high force production levels, which might be assumed to associate with the storage and subsequent release of energy during exercises involving the stretch-shortening cycle, are similar in both sprinters and controls.
Abstract: The present study aims to investigate the elasticity of tendon structures of the lower limbs in sprinters and its relation with sprint performance. Subjects were 10 male sprinters and 14 controls whose anthropometric variables and isometric maximum strength were similar. The elongation (L) of the tendon and aponeurosis of vastus lateralis (VL) and medial gastrocnemius muscles (MG) during isometric knee extension and planter flexion, respectively, were determined using a real-time ultrasonic apparatus in vivo, while the subjects developed a gradually increasing torque from zero (relax) to maximal effort (MVC) within 5 s. While sprinters compared with controls showed significantly greater L above 500 N (about 50% of MVC) and higher dL/dF for VL at less than 20% of MVC during knee extension, there were no significant differences between the two groups in L and dL/dF for MG at every 10% of MVC during plantar flexion. Moreover, the average value of dL/dF above 50% of MVC, proposed as the compliance of tendon structures, did not significantly differ between sprinters and controls in either VL or MG. In a regression analysis within sprinters, the compliance of VL was negatively correlated to 100-m sprint time, r=-0.757 (P 0.05). Thus the present results indicate that the elasticity of tendon structures of VL and MG at high force production levels, which might be assumed to associate with the storage and subsequent release of energy during exercises involving the stretch-shortening cycle, are similar in both sprinters and controls. For sprinters, however, the tendon structures of VL are more compliant than that for controls at low force production levels, and its elasticity at high force production levels may influence sprint performance.
11 May 2000
TL;DR: In this paper, the section capacity of very high strength (VHS®) circular tubes under compression was investigated and the reliability of section capacity based on the full effective section model has been verified using a first order second moment (FOSM) approach.
Abstract: This paper investigates the section capacity of very high strength (VHS®) circular tubes under compression. Full-section tensile tests were performed to determine the Young's modulus of elasticity, tensile yield stress and ultimate tensile strength. The modulus of elasticity was found around 200,000 MPa, the tensile yield stress (0.2% proof stress) was around 1350 MPa and the ultimate tensile strength was around 1500 MPa. Twelve stub column tests were carried out. The plate element slenderness varies from 86 to 130. It has been demonstrated that the limits on local buckling in most existing design standards are conservative when applied to VHS circular tubes. The reliability of section capacity based on the full effective section model has been verified using a FOSM (first order second moment) approach.
TL;DR: Budiansky and Rice as discussed by the authors extended the analysis of Knowles and Sternberg (1972) to the case of infinitesimal couple stress elasticity and deduced two conserved integral quantities.
Abstract: Noether’s theorem on invariant variational principles is applied in the case of infinitesimal couple stress elasticity, thereby extending the analysis of Knowles and Sternberg (1972. On a class of conservation laws in linearized and finite elastostatics. Arch. Ration. Mech. Anal. 44, 187–211) beyond the range of classical elasticity. Two conserved integral quantities are deduced which generalize the J -integral and L -integral in the notation of Budiansky and Rice (1973: Budiansky, B. and Rice, J. R. (1973) Conservation laws and energy-release rates. J. Appl. Mech. 40, 201–203 ). An expression for an M -integral is also obtained, but it is demonstrated that there is no corresponding conservation law for this integral. Relationships of the derived path integrals to other similar quantities for couple stress elasticity which have appeared in the literature are discussed.
TL;DR: Preliminary investigations suggest that transient effects in the data are the cause of a significant mismatch between the inversion model, which assumes steady-state conditions, and the actual displacements as measured by a phase contrast MR technique.
Abstract: The determination of the elastic property distribution in heterogeneous gel samples with a finite element based reconstruction scheme is considered. The algorithm operates on small overlapping subzones of the total field to allow for a high degree of spatial discretization while maintaining computational tractability. By including a Maxwellian-type viscoelastic property in the model physics and optimizing the spatial distribution of this property in the same manner as elasticity, a Young's modulus image is obtained which reasonably reflects the true distribution within the gel. However, the image lacks the clarity and accuracy expected based on simulation experience. Preliminary investigations suggest that transient effects in the data are the cause of a significant mismatch between the inversion model, which assumes steady-state conditions, and the actual displacements as measured by a phase contrast MR technique.
TL;DR: A method for measuring three-dimensional mechanical displacement and strain fields using stimulated echo MRI to provide a method for remotely palpating and elastically quantitating manually inaccessible tissues.
Abstract: This article presents a method for measuring three-dimensional mechanical displacement and strain fields using stimulated echo MRI. Additional gradient pulses encode internal displacements in response to an externally applied deformation. By limiting the mechanical transition to the stimulated echo mixing time, a more accurate static displacement measurement is obtained. A three-dimensional elasticity reconstruction within a region of interest having a uniform shear modulus along its boundary is performed by numerically solving discretized elasticity equilibrium equations. Data acquisition, strain measurements and reconstruction were performed using a silicone gel phantom containing an inclusion of known elastic properties. A comparison between two-dimensional and three-dimensional reconstructions from simulated and experimental displacement data shows higher accuracy from the three-dimensional reconstruction. The long-term objective of this work is to provide a method for remotely palpating and elastically quantitating manually inaccessible tissues.
TL;DR: In this paper, the deformation of capsules with circular, elliptical, and biconcave shapes, and the rheological and statistical properties of their infinitely dilute and moderately dense suspensions are investigated by dynamical simulation using the method of interfacial dynamics for Stokes flow.
Abstract: The simple shear flow of homogeneous suspensions of two-dimensional capsules enclosed by elastic membranes is studied in the limit of vanishing Reynolds number, in the special case where the viscosity of the fluid enclosed by the capsules is equal to the viscosity of the ambient fluid. The deformation of capsules with circular, elliptical, and biconcave unstressed shapes, and the rheological and statistical properties of their infinitely dilute and moderately dense suspensions are investigated by dynamical simulation using the method of interfacial dynamics for Stokes flow. In a preliminary investigation, the behavior of solitary capsules suspended in an infinite fluid is studied as a function of the dimensionless membrane elasticity number expressing the capsule deformability or the strength of the shear flow. It is found that a critical elasticity number above which a capsule exhibits continued elongation does not exist, and an equilibrium configuration is reached no matter how large the shear rate, in agreement with previous results for three-dimensional flow. A correspondence is established between the elasticity numbers for two- and three-dimensional flow at which the capsules undergo the same degree of deformation. Simulations of pairwise capsule interceptions reveal behavior similar to that exhibited by liquid drops with uniform surface tension. Because of strong hydrodynamic interactions in two-dimensional Stokes flow, the concept of hydrodynamic diffusivity in the limit of infinite dilution is ill-defined in the absence of fluid inertia. Dynamical simulations of doubly periodic monodisperse suspensions with up to 50 capsules distributed in each periodic cell at areal fractions of 0.25 and 0.40 provide information on the effective rheological properties of the suspension and on the nature of the statistical properties of the particle motion. The character of the flow is found to be intermediate between that of liquid drops and rigid particles, and this is attributed to the membrane deformability and to the ability of the interfaces to perform tank-treading motion. The results are compared with rheological measurements of blood flow with good agreement.
TL;DR: In this article, the difference between parameter uncertainty and elasticity analyses of a deterministic matrix model was evaluated using the Short-tailed Shearwater (Puffinus tenuirostris) as a case study.
TL;DR: In this article, the transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain.
Abstract: The transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain. The particle Reynolds number is supposed to be very small and the problem is solved numerically by means of the boundary integral method. In the case of a sudden start of flow, the time response of the capsule can be approximated by an exponential function, and is thus characterized by only two parameters: the equilibrium deformation D∞ and the characteristic response time τs. The respective influence of viscosity ratio, membrane elasticity, and initial particle geometry is analyzed. The dynamic response of the capsule subjected to periodic variations of the rate of strain is also studied. The response time τs appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions.
TL;DR: This paper first reviews existing frontier results, extends them formally to the nonfrontier case and then analyzes how the scale elasticity behaves, to provide mathematical characterizations of the Data envelopment analysis (DEA)-based scale elasticITY that is computable for both frontier and non frontier units.
TL;DR: There are two formalisms for two-dimensional deformations of a general anisotropic elastic material: the Lekhnitskii formalism and the Stroh formalism.
TL;DR: Evaluated viscoelastic behavior of turkey tendons and self-assembled collagen fiber models and the molecular basis for tendon deformation concluded that elastic energy storage in tendons involves direct stretching of the collagen triple-helix, nonhelical ends, and cross-links between the molecules and is unaffected by mineralization.
TL;DR: The results show the potentiality of US technique to separate information on bone density and elasticity that X‐ray‐based densitometric methods do not provide.
Abstract: Ultrasound (US) waves are mechanical vibrations that are applied to a material--bone tissue--in order to study its properties, that is, density, elasticity, and structure. In this study we evaluated in which way density and elasticity of the spongy bone influenced the transmission of 1.25 MHz US pulses. Twelve cylindrical specimens (diameter, 8 mm; height, 5 mm) excised from phalanxes of pig were decalcified with 0.5 M EDTA for different times (0, 2, and 5 days). During these periods, the samples underwent the following investigations: US transmission, density, and elasticity measurements. To assess the homogeneity of decalcification, the cross-sections of some samples were microradiographed. A detailed analysis of the US signal received was performed using velocity, Fourier analysis, and some parameters typical of signal processing technique. A good correlation was found between US velocity and density (r2 = 0.70); a lower correlation was found between velocity and elasticity (r2 = 0.59). If density and elasticity are considered simultaneously, the correlation with the US velocity improves significantly (r2 = 0.84). Fourier analysis enabled us to observe a shift of the main frequency toward lower values as the decalcification process advanced. We also observed that in the regressions weighted for density, US velocity correlated poorly with elasticity (r2 = 0.16), whereas signal processing parameters maintain a good correlation with elasticity (ultrasound peak amplitude [UPA], r2 = 0.48; slope, r2 = 0.62). In this study, it has been observed that when using a signal processing technique to analyze US pulses, it is possible to identify some parameters that are related in different ways to density and to elastic properties of bone. Our results show the potentiality of US technique to separate information on bone density and elasticity that X-ray-based densitometric methods do not provide.
TL;DR: In this article, the authors consider the problem of microstructural evolution in binary alloys in two dimensions, where both the precipitates and the matrix are taken to be elastically anisotropic, with different elastic constants.
TL;DR: An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks using the exact Poissonian statistics to describe the microscopic geometry of the network, which depends on the network density and fiber dimensions.
Abstract: An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks. These networks are commonly used as basic models of heterogeneous fibrous structures such as paper. Using the exact Poissonian statistics to describe the microscopic geometry of the network, the tensile modulus can be expressed by a single-parameter function. This parameter depends on the network density and fiber dimensions, which relate the macroscopic modulus to the relative importance of axial and bending deformations of the fibers. The model agrees well with simulation results and experimental findings. We also discuss the possible generalizations of the model.
TL;DR: The topography and elasticity of living and fixed astrocytes cultured from the rat cerebra were studied quantitatively by atomic force microscopy and showed that images observed by AFM should be carefully examined in consideration of the force introduced to specimens and the elasticity to find out the real surface topography.
Abstract: The topography and elasticity of living and fixed astrocytes cultured from the rat cerebra were studied quantitatively by atomic force microscopy (AFM). Ridge-like structures reflecting F-actin beneath the cell membrane were prominent in the contact-mode images of living astrocytes. Many of these ridges became unclear after fixation (2% glutaraldehyde). In addition, the ridge-like structures were invisible in the topography of living cells observed at zero-loading force in the force mapping mode, which is considered to show the real cell surface not pressed down by an AFM tip. The topography of fixed cells observed both in the contact mode and at zero-loading force in the force mapping mode was similar to that of living cells observed at zero-loading force in the force mapping mode, although some deformed areas were detected in the fixed cells. The elasticity map images of living astrocytes showed that the cell membrane above the nucleus was softer (2-3 kPa) than the surroundings, and that the cell membrane above F-actin was stiffer (10-20 kPa) than the surroundings. In the elasticity map images of fixed astrocytes, on the other hand, the elasticity of the cells was found to be relatively uniform (200-700 kPa) irrespective of the inner structures of cells. These results show that images observed by AFM should be carefully examined in consideration of the force introduced to specimens and the elasticity of specimens to find out the real surface topography.