The histopathology of nonsteroidal anti-inflammatory drug-associated colitis

We combined three techniques--mechanical testing, three-dimensional imaging, and finite-element modeling--to distinguish between the contributions of architecture and tissue modulus to mechanical function in human trabecular bone. The objectives of this study were 2-fold. The first was to assess the accuracy of micromechanical modeling of trabecular bone using high-contrast x-ray images of the trabecular architecture. The second was to combine finite-element calculations with mechanical testing to infer an average tissue modulus for the specimen. Specimens from five human L1 vertebrae were mechanically tested along the three anatomic axes. The specimens were then imaged by synchrotron x-ray tomography, and the elastic moduli of each specimen were calculated from the tomographic image by finite-element modeling. We found that 23-microm tomographic images resolved sufficient structural detail such that the calculated anisotropy in the elastic modulus was within the uncertainties of the experimental measurements in all cases. The tissue modulus of each specimen was then estimated by comparing the calculated mean stiffness of the specimen, averaged over the three anatomical directions, with the experimental measurement. The absolute values of the experimental elastic constants could be fitted, again within the uncertainties of the experimental measurements, by a single tissue modulus of 6.6 GPa, which was the average tissue modulus of the five specimens. These observations suggest that a combination of mechanical testing, three-dimensional imaging, and finite-element modeling might enable the physiological variations in tissue moduli to be determined as a function of age and gender.     

Cortical elasticity in aging rats with and without growth hormone treatments

This study quantified the orthotropic elastic changes in cortical bone due to aging as well as determined any elastic changes after acute treatments of growth hormone (GH). Three groups of twenty rats represented three age groups of young adult (9 months), middle age (20 months), and old (31 months) rats. During a ten day period, half of the rats in each age group were given twice-daily doses of recombinant human GH while the remaining half were injected with a vehicle control (saline). The effects of aging and GH on the elastic characteristics of cortical bone were quantified via ultrasonic wave propagation. Propagation velocities of longitudinal and shear waves were measured through cubic cortical specimens from the posterior femoral diaphysis. Density was measured by Archimedes' technique. The normalized, orthotropic elastic properties of Young's moduli (Eii), shear moduli (Gij), and Poisson's ratios (Vij) were calculated and used to compare the groups (where i and j = 1, 2, or 3 reference the radial, circumferential, and longitudinal axes, respectively). Cortical elastic moduli consistently increased with age with the strongest effects demonstrated in radial dependent properties such as E11 (+ 25.3% from 9 to 31 months, p = 0.0004) and G12 (+ 12.6% from 20 to 31 months, p = 0.0419). The ratio of transverse to axial displacement (Poisson's ratio) typically decreased with age (9 to 31 months) as seen in V31 (-24.95%, p = 0.0134) and V32 (-20.7%, p = 0.0015). Overall, a ten day treatment with GH produced no global statistical change in elastic properties (p > 0.05). However, GH did minimize the age related differences that were measured for E22, E33, and V32 between the 9 and 31 month old groups essentially returning old bone to its youthful elastic state. These finding add orthotropic detail to the current understanding of changing cortical elastic properties during aging as well as providing a reference for further studies of GH.     

The effect of porosity on the Poisson's ratio of porous iron

Summary The results are presented of Poisson's ratio measurements performed on porous iron specimens of different porosity. It is shown that, like the other elastic characteristics (moduli E and G), Poisson's ratio change's with increasing porosity of the material.     

Equilibrium-Based Finite-Element Formulation for the Geometrically Exact Analysis of Planar Framed Structures

This paper addresses the development of a hybrid-mixed finite-element formulation for the geometrically exact quasi-static analysis of elastic planar framed structures, modeled using the two-dimensional Reissner beam theory. The proposed formulation relies on a modified principle of complementary energy, which involves, as independent variables, the generalized vectors of stress resultants and displacements and, in addition, a set of Lagrange multipliers used to enforce the stress continuity between elements. The adopted finite-element discretization produces numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the static boundary conditions. It consists, therefore, in a true equilibrium formulation for arbitrarily large displacements and rotations. Furthermore, as it does not suffer from shear locking or any other artificial stiffening phenomena, it may be regarded as an alternative to the standard displacement-based formulation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions are compared with those obtained using the standard two-node displacement-based formulation. Numerical analyses of convergence of the proposed finite-element formulation are also included.     

Penalty-Based Solution for the Interval Finite-Element Methods

A new approach for achieving guaranteed reliable results within the context of finite-element approximation of mechanical systems is developed. A reliable analysis requires that all the sources of uncertainty and errors be accommodated. The appropriateness of a partial differential equation to a given physical problem is beyond the scope of this work. Parameter uncertainty is treated as intervals in this work and guaranteed bounds on the “unknown” true solutions are obtained. In this paper an element-by-element penalty-based interval finite-element analysis of linear elastic structural mechanics and solid mechanics problem is introduced. Material and load uncertainties are handled simultaneously. Presented numerical examples illustrate the ability of the method to maintain very sharp solution enclosures even when the number of the interval parameters or the size of the problems is increased.     

Measuring the viscoelastic properties of human platelets with the atomic force microscope

We have measured force curves as a function of the lateral position on top of human platelets with the atomic force microscope. These force curves show the indentation of the cell as the tip loads the sample. By analyzing these force curves we were able to determine the elastic modulus of the platelet with a lateral resolution of approximately 100 nm. The elastic moduli were in a range of 1-50 kPa measured in the frequency range of 1-50 Hz. Loading forces could be controlled with a resolution of 80 pN and indentations of the platelet could be determined with a resolution of 20 nm.     

Steel Hexagonal Honeycomb Core Equivalent Elastic Moduli for Bridge Deck Sandwich Panels

Glass fiber-reinforced polymer (GFRP) materials possess inherently high strength-to-weight ratios, but their effective elastic moduli are low relative to civil engineering (CE) construction materials. While elastic modulus may be comparable to that of some CE materials, the lower shear modulus adversely affects stiffness. As a result, serviceability issues are what govern GFRP deck design in the CE bridge industry. An innovative solution to increase the stiffness of a commercial GFRP reinforced-sinusoidal honeycomb sandwich panel was proposed; this solution would completely replace the GFRP honeycomb core with a hexagonal honeycomb core constructed from commercial steel roof decking. The purpose of this study was to perform small-scale tests to characterize the steel hexagonal honeycomb core equivalent elastic moduli in an effort to simplify the modeling of the core. The steel core equivalent moduli experimental results were compared with theoretical hexagonal honeycomb elastic modulus equations from the literature, demonstrating the applicability of the theoretical equations to the steel honeycomb core. Core equivalent elastic modulus equations were then proposed to model and characterize the steel hexagonal honeycomb as applicable to sandwich panel design. The equivalent honeycomb core will enable an efficient sandwich panel stiffness design technique, both for structural analysis methods (i.e., hand calculations) and finite-element analysis procedures.     

Two Finite-Element Discretizations for Gradient Elasticity

We present and compare two different methods for numerically solving boundary value problems of gradient elasticity. The first method is based on a finite-element discretization using the displacement formulation, where elements that guarantee continuity of strains (i.e., C1 interpolation) are needed. Two such elements are presented and shown to converge: a triangle with straight edges and an isoparametric quadrilateral. The second method is based on a finite-element discretization of Mindlin’s elasticity with microstructure, of which gradient elasticity is a special case. Two isoparametric elements are presented, a triangle and a quadrilateral, interpolating the displacement and microdeformation fields. It is shown that, using an appropriate selection of material parameters, they can provide approximate solutions to boundary value problems of gradient elasticity. Benchmark problems are solved using both methods, to assess their relative merits and shortcomings in terms of accuracy, simplicity and computational efficiency. C1 interpolation is shown to give generally superior results, although the approximate solutions obtained by elasticity with microstructure are also shown to be of very good quality.     

Complementary Energy Based Formulation for Torsional Buckling of Columns

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions.     

Elastic properties of human supraorbital and mandibular bone

Elastic constants, including the elastic modulus, the shear modulus, and Poisson's ratio, were measured on human craniofacial bone specimens obtained from the supraorbital region and the buccal surfaces of the mandibles of unembalmed cadavers. Constants were determined using an ultrasonic wave technique in three directions relative to the surface of each sample: 1) normal, 2) tangential, and 3) longitudinal. Statistical analysis of these elastic constants indicated that significant differences in the relative proportions of elastic properties existed between the regions. Bone from the mandible along its longitudinal axis was stiffer than bone from the supraorbital region. Directional differences in both locations demonstrated that cranial bone was not elastically isotropic. It is suggested that differences in elastic properties correspond to regional differences in function.     

Effective elastic moduli of fiber-matrix interphases in high-temperature composites

This article describes a theoretical model and an experimental method for determination of interphasial elastic moduli in high-temperature composites. The interphasial moduli are calculated from the ultrasonically measured composite modulivia inversion of multiphase micromechanical models. Explicit equations are obtained for determination of interphasial stiffnesses for an interphase model with spring boundary conditions and multiphase fiber. The results are compared with the exact multiphase representation. The method was applied to ceramic and intermetallic matrix composites reinforced with SiC SCS-6 fibers. In both composites, the fiber-matrix interphases include approximately 3-μm-thick carbon-rich coatings on the outer surface of the SiC shell. Although the same fiber is used in both composite systems, experimental results indicate that the effective interphasial moduli in these two composite systems are very different. The interphasial moduli in intermetallic matrix composites are much greater than those in ceramic matrix composites. After taking the interphase microstructure into account, we found that the interphasial moduli measured for the intermetallic matrix composites are very close to the estimated bulk moduli of the pyrolytic carbon with SiC particle inclusions. Our analysis shows that the lower effective interphasial moduli in the reaction-bonded Si₃N₄ (RBSN) ceramic matrix composites are due to imperfect contact between the interphasial carbon and the porous matrix and to thermal tension forces which slightly unclamp the interphase. Thus, measured interphase effective moduli give information on the quality of mechanical contact between fiber and matrix. Possible errors in the interphasial moduli determined are analyzed and the results show that these errors are below 10 pct. In addition, the use of the measured interphasial moduli for assessment of interphasial damage and interphase reactions is discussed.     

Elastic constants of transversely isotropically porous (TIP) materials

We derive formulas describing the dependence of the elastic characteristics of multicapillary materials on the capillary porosity. The investigated materials are classified as transversely isotropic, and the anisotropy in their properties is the result of the directionality of the capillary pores. Analysis of the dependences obtained has shown that the elasticity moduli of these materials may be calculated using formulas suggested for reinforced materials, in which the elastic constants of the fibers are assumed to be equal to zero. We derive a relation between the Poisson's ratios and the capillary porosity.Institute of Problems of Materials Science, National Academy of Sciences of the Ukraine, Kiev. Translated from Poroshkovaya Metallurgiya, No. 5–6, pp. 104–109, May–June, 1994.     

Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models

Three variations of a polymer chain model for the human erythrocyte cytoskeleton are used in large deformation simulations of microscopic membrane patches. Each model satisfies an experimental observation that the contour length of the spectrin tetramers making up the erythrocyte cytoskeleton is roughly square root of 7 times the end-to-end distance of the tetramer in vivo. Up to modest stress, each brushy cytoskeletal network behaves, consistently, like a low-temperature, planar network of Hookean springs, with a model-dependent effective spring constant, keff, in the range of 20-40 kBT/s(o)2, where T is the temperature and s(o) is the force-free spring length. However, several features observed at large deformation distinguish these models from spring networks: 1) Network dimensions do not expand without bound in approaching a critical isotropic tension (square root of 3 keff) that is a characteristic limit of Hookean spring nets. 2) In surface compression, steric interactions among the chain elements prevent a network collapse that is otherwise observed in compression of planar triangulated networks of springs. 3) Under uniaxial surface tension, isotropy of the network disappears only as the network is stretched by more than 50% of its equilibrium dimensions. Also found are definitively non-Hookean regimes in the stress dependence of the elastic moduli. Lastly, determinations of elastic moduli from both fluctuations and stress/strain relations prove to be consistent, implying that consistency should be expected among experimental determinations of these quantities.     

Analysis of the micropipet experiment with the anisotropic outer hair cell wall

The outer hair cell makes both passive and active contributions to basilar membrane mechanics. The outer hair cell mechanics is strongly coupled to the elastic properties of the cell lateral wall. The lateral wall experiences both in-plane deformations and bending under physiological and experimental conditions. To characterize the outer hair cell wall, the model of an orthotropic cylindrical shell is used. The elastic constants of the wall are estimated by solving a set of three equations based on the analyses of three independent experiments. The first equation is derived from a new interpretation of the micropipet experiment; the other two are obtained from the axial loading and the osmotic challenge experiments. The two Young's moduli corresponding to the longitudinal and circumferential directions and two Poisson's ratios are estimated. The longitudinal, circumferential, and mixed modes of the bending stiffness are also estimated. The sensitivity of the derived constants to the variation of the cell axial stiffness, which has been measured by several independent groups, is examined. The new estimates are also compared with results obtained by using the assumption of the wall isotropy.     

Decomposition of aluminium-magnesium solid solutions studied by ultrasonic measurements of elastic properties and electron microscopy

The variations of elastic moduli during the pre-precipitation and precipitation phenomena occurring in AlMg alloys are studied by means of ultrasonic measurements. The results obtained in polycrystals are compared with those obtained in single crystals and it is found that the shear elastic moduli are affected, whilst the bulk modulus is invariable during these structural changes. Furthermore the shear moduli increase in the case of pre-precipitation [Guinier-Preston (G.P.) zones]and decrease during the precipitation of β′ and β phases. Using a structural model of G.P. zones elaborated from crystallographic results, the propagation analysis shows that the ultrasonic velocity increases proportionally to the fractional volume of the zones. Subsequently this ultrasonic method is used to study the formation of G.P. zones at temperatures above 20°C and the results are discussed in relation to transmission electron microscopy observations. The existence of a miscibility gap is confirmed and its limits are specified. Further, the investigation of the G.P. zone formation in the vicinity of the miscibility gap limits has shown that the decomposition and the resulting structure are very different in this region from that occurring inside the miscibility gap. G.P. zones are always internally ordered.     

MCG simulations with a realistic heart-torso model

Magnetocardiograms (MCG's) simulated with a high-resolution heart-torso model of an adult subject were compared with measured MCG's acquired from the same individual. An exact match of the measured and simulated MCG's was not found due to the uncertainties in tissue conductivities and cardiac source positions. However, general features of the measured MCG's were reasonably represented by the simulated data for most, but not all of the channels. This suggests that the model accounts for the most important mechanisms underlying the genesis of MCG's and may be useful for cardiac magnetic field modeling under normal and diseased states. MCG's were simulated with a realistic finite-element heart-torso model constructed from segmented magnetic resonance images with 19 different tissue types identified. A finite-element model was developed from the segmented images. The model consists of 2.51 million brick-shaped elements and 2.58 million nodes, and has a voxel resolution of 1.56 x 1.56 x 3 mm. Current distributions inside the torso and the magnetic fields and MCG's at the gradiometer coil locations were computed. MCG's were measured with a Philips twin Dewar first-order gradiometer SQUID-system consisting of 31 channels in one tank and 19 channels in the other.     

Effects of Edge-Stiffening Elements and Diaphragms on Bridge Resistance and Load Distribution

This research investigates the effects of barriers, sidewalks, and diaphragms (secondary elements) on bridge structure ultimate capacity and load distribution. Simple-span, two-lane highway girder bridges with composite steel and prestressed concrete girders are considered. The finite-element method is used for structural analysis. For the elastic range, typical secondary elements can reduce girder distribution factors (GDF) between 10 and 40%, depending on stiffness and bridge geometry. For the inelastic response, steel is modeled using von Mises yield criterion and isotropic (work) hardening. Concrete is modeled with a softening curve in compression with the ability to crack in tension. At ultimate capacity, typical secondary elements can reduce GDF an additional 5 to 20%, and bridge system ultimate capacity can be increased from 1.1 to 2.2 times that of the base bridge without secondary elements, depending on bridge geometry and secondary-element dimensions.     

Stress-Induced Anisotropic Gma x of Sands and Its Measurement

Anisotropy in elastic shear modulus Gma x exists in most soils as the result of either anisotropic soil fabric or anisotropic stress conditions. This paper presents a theoretical and experimental study on the anisotropy in a Gma x of sand due to a K0 stress condition. Elastic shear moduli of two types of sand in multiple stress planes under a K0 condition were measured using bender elements. Stress-induced anisotropy in Gma x of the sands during loading and unloading processes and the important influential factors were investigated. An empirical relationship for the estimation of K0 was proposed based on the experimental data. Shear moduli in nonprincipal stress planes were measured and compared with the results from the theory. The influence of stress cycles on Gma x in multiple stress planes was studied.     

Multigrid Preconditioner for Unstructured Nonlinear 3D FE Models

Multigrid and multigrid-preconditioned conjugate-gradient solution techniques applicable for unstructured 3D finite-element models that may involve sharp discontinuities in material properties, multiple element types, and contact nonlinearities are developed. Their development is driven by the desire to efficiently solve models of rigid pavement systems that require explicit modeling of spatially varying and discontinuous material properties, bending elements meshed with solid elements, and separation between the slab and subgrade. General definitions for restriction and interpolation operators applicable to models composed of multiple, displacement-based isoparametric finite-element types are proposed. Related operations are used to generate coarse mesh element properties at integration points, allowing coarse-level coefficient matrices to be computed by a simple assembly of element stiffness matrices. The proposed strategy is shown to be effective on problems involving spatially varying material properties, even in the presence of large variations within coarse mesh elements. Techniques for solving problems with nodal contact nonlinearities using the proposed multigrid methods are also described. The performance of the multigrid methods is assessed for model problems incorporating irregular meshes and spatially varying material properties, and for a model of two rigid pavement slabs subjected to thermal and axle loading that incorporates nodal contact conditions and both solid and bending elements.     

Simple Formulation for the Flexure of Plates on Nonlinear Foundation

Plates resting on an elastic medium are normally analyzed in a simplified way using the linear Winkler foundation approach. Nevertheless, plates resting on layered medium with vast differences in their moduli exhibit nonlinear behavior under pressure. The present technical note deals with a nonlinear finite-element procedure to analyze plates with linear strain displacement relations resting on a nonlinear elastic media. The coupled problem is formulated using the total potential energy (TPE) concept. The nonlinear foundation stiffness matrices have been derived using the Taylor expansion of the TPE at equilibrium and a symbolism of grouping the energy contributions. The nonlinear foundation stiffness matrices derived in the present technical note have been demonstrated to yield results that agree well with published results in the literature. A brief parametric study on the effects of nonlinearity of the foundation is also presented using the proposed foundation stiffness matrices.