Ab initio predictions of structural and elastic properties of struvite: contribution to urinary stone research

In the present work, we carried out density functional calculations of struvite – the main component of the so-called infectious urinary stones – to study its structural and elastic properties. Using a local density approximation and a generalised gradient approximation, we calculated the equilibrium structural parameters and elastic constants C _ijkl . At present, there is no experimental data for these elastic constants C _ijkl for comparison. Besides the elastic constants, we also present the calculated macroscopic mechanical parameters, namely the bulk modulus (K), the shear modulus (G) and Young's modulus (E). The values of these moduli are found to be in good agreement with available experimental data. Our results imply that the mechanical stability of struvite is limited by the shear modulus, G. The study also explores the energy-band structure to understand the obtained values of the elastic constants.     

First-principles study of phase stability and elastic properties in metastable Ti-Mo alloys with cluster structure

This paper provided a novel approach for evaluating phase stability and elastic properties in metastable Ti–Mo alloys with low Mo content by first-principles combined with cluster structure. In 54-atom body-centered-cubic supercell by substituting Ti atoms with 2–7 Mo atoms (7.1–23.0?wt% Mo), individual cluster structure of β-phase was constructed by ‘-Mo-Ti-Mo-’ cluster unit having the lowest cohesive energy. The distorted supercell was more stable than undistorted one at a low Mo content. With increasing Mo content, the density of state at Fermi level decreased, and bonding electron number increased, indicating β-phase stability was gradually promoted. Tetragonal shear elastic constant (C′?=?(C₁₁?–?C₁₂)/2), shear modulus (G₁₁₁) and anisotropy factor (A?=?C₄₄/C′) exhibited a fluctuation with Mo addition, while the change trend of A was opposite to C′ and G₁₁₁. Calculated Young’s modulus exhibited similar changing trend to the C′, implying that the softening of C′ resulted in low Young’s modulus of β-phase. Measured Young’s modulus exhibited significant difference from calculated one, which was mainly caused by formation of α″-martensite and ω-phase. The values of C′, G₁₁₁ and A were considered to associate with not only elastic properties of β-phase itself but also transition from β-phase to α″-martensite and/or ω-phase.     

Elastic properties of cancellous bone: measurement by an ultrasonic technique

The high degree of porosity of cancellous bone makes elastic property measurement difficult by traditional mechanical testing methods. An ultrasonic technique is described with which mechanical properties of anisotropic, rigid, porous materials, such as cancellous bone, can be measured. The technique utilizes unique piezoelectric transducers operated in a continuous wave mode at a frequency of approximately 50 kHz. Both longitudinal and shear waves can be propagated and received with the transducers allowing both Young's moduli and shear moduli to be determined with the technique. A comparison between moduli measured with the ultrasonic technique and moduli measured with traditional mechanical testing shows the new method to be quite accurate in elastic property determination, (r2 = 0.935, Emech = 1.00E1dt + 23.3 MPa) (r2 = 0.656, Gmech = 1.08 Gult--3.3MPa).     

Anatomical variation of orthotropic elastic moduli of the proximal human tibia

The anatomical variation of orthotropic elastic moduli of the cancellous bone from three human proximal tibiae was investigated using an ultrasonic technique. With this technique, it was possible to measure three orthogonal elastic moduli and three shear moduli from cubic specimens of cancellous bone as small as 8 mm per side. Correlation with mechanical tensile testing has shown this technique to offer a precise measure of cancellous modulus (Eten = 0.94Eult + 144.6 MPa, r2 = 0.96, n = 34). The cancellous bone of the proximal tibia was found to be very inhomogeneous, with the axial modulus ranging between 340 and 3350 MPa. A course map is presented, showing measured Young's moduli as a function of anatomical position. The anisotropy of the cancellous bone, determined by the relative differences between the three orthogonal moduli, was shown to be relatively constant over the entire range of cancellous densities tested. The relationship between the axial elastic modulus and the apparent density was found to be approximately linear, as reported by others for proximal tibial cancellous bone.     

The effect of cross linking density on the mechanical properties and structure of the epoxy polymers: molecular dynamics simulation

Recently, great attention has been focused on using epoxy polymers in different fields such as aerospace, automotive, biotechnology, and electronics, owing to their superior properties. In this study, the classical molecular dynamics (MD) was used to simulate the cross linking of diglycidyl ether of bisphenol-A (DGEBA) with diethylenetriamine (DETA) curing agent, and to study the behavior of resulted epoxy polymer with different conversion rates. The constant-strain (static) approach was then applied to calculate the mechanical properties (Bulk, shear and Young’s moduli, elastic stiffness constants, and Poisson’s ratio) of the uncured and cross-linked systems. Estimated material properties were found to be in good agreement with experimental observations. Moreover, the dependency of mechanical properties on the cross linking density was investigated and revealed improvements in the mechanical properties with increasing the cross linking density. The radial distribution function (RDF) was also used to study the evolution of local structures of the simulated systems as a function of cross linking density.     

Molecular dynamics simulations indicate that deoxyhemoglobin,oxyhemoglobin, carboxyhemoglobin,and glycated hemoglobin under compression and shear exhibit an anisotropic mechanical behavior

We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells, using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhemoglobin (HbO₂), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA_1C). The SMD simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and secondary structure, our simulation results show a significant variation in the mechanical strength in different directions (anisotropy) and also a strength variation among the four different hemoglobin configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures studied possess a soft outer shell and a stiff core based on stiffness.     

Viral capsid equilibrium dynamics reveals nonuniform elastic properties

The long wavelength, low-frequency modes of motion are the relevant motions for understanding the continuum mechanical properties of biomolecules. By examining these low-frequency modes, in the context of a spherical harmonic basis set, we identify four elastic moduli that are required to describe the two-dimensional elastic behavior of capsids. This is in contrast to previous modeling and theoretical studies on elastic shells, which use only the two-dimensional Young's modulus (Y) and the bending modulus (κ) to describe the system. Presumably, the heterogeneity of the structure and the anisotropy of the biomolecular interactions lead to a deviation from the homogeneous, isotropic, linear elastic shell theory. We assign functional relevance of the various moduli governing different deformation modes, including a mode primarily sensed in atomic force microscopy nanoindentation experiments. We have performed our analysis on the T = 3 cowpea chlorotic mottle virus and our estimate for the nanoindentation modulus is in accord with experimental measurements.     

NpH-MD-Simulations of the Elastic Moduli of Cellulose II at Room Temperatue

We have used molecular dynamics modeling to investigate the stucture and mechanical properties of regenerated cellulose fibres. This work is motivated by continued interest in replacing the environmentally hazardous viscose process by alternative spinning methods. An important input parameter for any realistic model of the elastic properties is the stiffness tensor of the crystalline constituent, cellulose II. Conventional molecular mechanics techniques can be used to estimate the elastic reaction of a material with respect to small external stresses or strains, i.e. the compliance and stiffness tensors, and the elastic moduli derived therefrom, at zero temperature. In order to access non-zero temperatures, it is necessary to use either the quasi-harmonic approximation for the vibrational free energy or molecular dynamics (MD) simulations. In the present work, Parrinello-Rahman constant-stress MD was performed to generate trajectories in constant particle number (N), constant external stress tensor (p or t) and constant enthalpy H (NpH or HtN) ensemble. This was found to be less time consuming than working with isothermal conditions, as done by other authors. The fluctuations in kinetic energy and MD cell vectors were then used to calculate adiabatic elastic constants, thermal expansion coefficients and heat capacity. The isothermal elastic constants were found by applying a standard thermodynamic relation. The Youngs modulus along the chain direction, E_l, was determined to be 155 GPa, whereas the values in the perpendicular directions vary between 51 and 24 GPa. These results are of the same order of magnitude as those obtained by Tashiro and Kobayashi [1] with the static (T = 0K) method, but our value of E_l is 5% lower and, unexpectedly, the lateral values are up to six times higher. A strong anisotropy is found for shear along the chains in planes containing the chain axis, the shear modulus ranging from 5 to 20 GPa. Convergence was achieved in the simulations, to the extend that the elastic constants become stationary, but significant internal stresses remain, pointing to shortcomings in the software used. Further work is necessary to resolve these problems, although the major conclusions should be unaffected.     

Phase stability,elastic, anisotropic and thermodynamic properties of HoT2Al20 (T = Ti,V, Cr) intermetallic cage compounds

The structural stability, elastic properties, anisotropy, dynamics stability and thermodynamics properties were explored for pure Al and HoT₂Al₂₀ intermetallics from the first-principles method. The formation enthalpy and phonon frequencies indicate that these HoT₂Al₂₀ intermetallics maintain structural stability. The elastic constants C_ijs and moduli B, G, E and H_v indicate these intermetallics possess higher hardness and the better resistance to deformation. The values of Poisson’s ratio and B/G demonstrate that HoT₂Al₂₀ intermetallics are brittle materials. The anisotropic constants and anisotropic acoustic velocities confirm that HoT₂Al₂₀ intermetallics exhibit anisotropic properties. Importantly, the calculated thermal quantities demonstrate that these new HoT₂Al₂₀ intermetallics possess the better thermodynamic properties at high temperature.     

Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Thermo-mechanical properties of cubic titanium nitride

The equilibrium structure, elastic constants C_ij and thermodynamic functions of cubic titanium nitride (TiN) were calculated within the temperature range of 0–3100 K and under a pressure range 0–60 GPa. Properties were computed using the generalised gradient approximations (GGA) exchange-correlation functional. Calculated mechanical properties (Elastic constants, Young’s modulus and shear modulus) and phonon spectra of TiN obtained via robust DFT-QHA algorithm, were generally in a good agreement with available experimental and theoretical analogous values. In particular, a well-examined quasi-harmonic approximation method implemented in the Gibbs2 code is utilised herein to provide accurate estimation of thermal expansion coefficients, entropies, heat capacity values (at different combinations of temperature/volume/pressure) and Debye’s temperature. Parameters calculated herein shall be useful to elucidate the superior performance of TiN at harsh operational conditions encompassing elevated temperatures and pressures pertinent to cutting machineries and surface coatings.     

The role of particle softness in determining the value of Poisson's ratio for soft sphere solids

The influence of particle softness on the Poisson's ratio of model solids has been investigated. We have used the repulsive inverse power potential (～r ^? n for particle separations, r) between the particles, which is conveniently characterised by one adjustable parameter, ? = 1/n. For large ?, the interaction is soft whereas in the ? → 0 limit the particles approach hard spheres. The pressure and elastic constants of the solid phase have been calculated at various densities with constant temperature molecular dynamics (MD) simulation for a range of the softness parameter in the range, n>12. Density-softness surfaces of these quantities were determined which revealed hitherto unrecorded trends in the behaviour of the elastic moduli and Poisson's ratio. It was found that the pressure and some elastic properties, e.g. the C₁₂ elastic constant and the bulk modulus, manifest a maximum value or ‘ridge’ on this surface. The height of the maximum increases with density and interaction steepness (small ?). The Poisson's ratio varies essentially linearly with softness and is relatively insensitive to density. However, at higher densities and for larger steepness a considerable lowering of the Poisson's ratio is observed. In order to identify possible mechanisms for reducing the value of Poisson's ratio, ν, the fluctuation and Born-Green contributions were analysed. Changes in the Poisson's ratio are mainly determined by the fluctuation contribution which can cause a considerable decrease as well as increase of its value.     

Roles of electrostatic interaction and dispersion in CH···CH,CH···π, and π···π ethylene dimers

The structural, mechanical, electronic, and optical properties of orthorhombic Bi₂S₃ and Bi₂Se₃ compounds have been investigated by means of first principles calculations. The calculated lattice parameters and internal coordinates are in very good agreement with the experimental findings. The elastic constants are obtained, then the secondary results such as bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, anisotropy factor, and Debye temperature of polycrystalline aggregates are derived, and the relevant mechanical properties are also discussed. Furthermore, the band structures and optical properties such as real and imaginary parts of dielectric functions, energy-loss function, the effective number of valance electrons, and the effective optical dielectric constant have been computed. We also calculated some nonlinearities for Bi₂S₃ and Bi₂Se₃ (tensors of elasto-optical coefficients) under pressure.

Changes in the hyperelastic properties of endothelial cells induced by tumor necrosis factor-alpha

Mechanical properties of living cells can be determined using atomic force microscopy (AFM). In this study, a novel analysis was developed to determine the mechanical properties of adherent monolayers of pulmonary microvascular endothelial cells (ECs) using AFM and finite element modeling, which considers both the finite thickness of ECs and their nonlinear elastic properties, as well as the large strain induced by AFM. Comparison of this model with the more traditional Hertzian model, which assumes linear elastic behavior, small strains, and infinite cell thickness, suggests that the new analysis can predict the mechanical response of ECs during AFM indentation better than Hertz's model, especially when using force-displacement data obtained from large indentations (>100 nm). The shear moduli and distensibility of ECs were greater when using small indentations (<100 nm) compared to large indentations (>100 nm). Tumor necrosis factor-α induced changes in the mechanical properties of ECs, which included a decrease in the average shear moduli that occurred in all regions of the ECs and an increase in distensibility in the central regions when measured using small indentations. These changes can be modeled as changes in a chain network structure within the ECs.     

Anisotropy and inter-condyle heterogeneity of cartilage under large-strain shear

We were the first to examine the mechanical responses of skeletally mature bovine femoral cartilage under large-strain simple shear (up to ±20%) using a multiaxial shear testing device. Since shear loading is critical in both tissue failure and chondrocyte responses, we aimed to probe (1) anisotropy with respect to the split-line direction (principal alignment of the collagen fibers near the articulating surface), (2) heterogeneity between femoral condyles, and (3) the influence of local cartilage thickness. We harvested a total of 48 cuboid cartilage specimens from four bovine knee joints. With each specimen we applied shear strains both parallel and perpendicular to the local split-line direction at a rate of 75 μm/min and calculated the peak-to-peak shear stresses, shear strain–energy dissipation densities, and peak effective shear moduli. The Wilcoxon signed rank test revealed that the medial condyle was anisotropic in some mechanical measures at applied shear strains above 5%, while the lateral condyle was mechanically isotropic at all applied shear strains. The Kruskal–Wallis test revealed no significant differences in the median mechanical behavior of the lateral and medial condyles. Spearman׳s rank correlations revealed statistically significant negative monotonic correlations among thickness and most of our mechanical measures for both lateral and medial condyles at most applied strains and directions of applied shear. These results suggest that large-strain analyses account for nonlinear, anisotropic and location-dependent effects not fully realized at small strains. Our findings may inspire new experiments and models that consider anisotropy and heterogeneity of cartilage in ways previously ignored.     

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone.

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.     

Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone

Mechanical properties of bones are largely determined by their microstructure. The latter comprises a large number of diverse pores. The present paper analyzes a connection between structure of the porous space of the osteonal cortical bone and bone's overall anisotropic elastic moduli. The analysis is based on recent developments in the theory of porous materials that predict the anisotropic effective moduli of porous solids in terms of pores' shapes, orientations and densities. Bone's microstructure is modeled using available micrographs. The calculated anisotropic elastic constants for porous cortical bone are, mostly, in agreement with available experimental data. The influence of each of the pore types on the overall moduli is examined. The results of the analysis can also be used to estimate the extent of mineralization (hydroxyapatite content) if the overall porosity and the effective moduli are known and, vice versa, to estimate porosity from the measured moduli and the extent of mineralization.     

The elastic anisotropy of bone

In modeling the anisotropic properties of hydroxyapatite (HAp), Katz found that two kinds of phenomenological relationships held among the elastic stiffness coefficients. Firstly, there are three linear combinations--(c11 + c22 + c33), (c44 + c55 + c66), (c12 + c13 + c23)--which arise naturally when computing the isotropic averages of anisotropic crystal systems over all possible spatial orientations. Secondly, the degree of elastic anisotropy in such crystal systems is characterized by two specific factors: (a) the ratio of the linear compressibility along the unique axis to that perpendicular to it, (c11 + c12 - 2c23)(c33 - c13); and (b) the ratio of the two shear moduli, c44/c66. There have been a number of experiments in recent years which have used either mechanical methods or ultrasonic techniques to measure the anisotropic elastic properties of bovine and human cortical bone. Analyses of data from these experiments show that the above relationships also play a significant role in characterizing the elastic anisotropy in bone.     

Structural, mechanical and electronic properties of nano-fibriform silica and its organic functionalization by dimethyl silane: a SCC-DFTB approach

Self-consistent-charge density-functional tight-binding (SCC-DFTB) approximated method was employed to investigate the structural, mechanical and electronic properties of the zigzag and armchair nano-fibriform silica (SNTs) and their outer surface organic modified derivatives (MSNTs) with internal radii in the range of 8 to 36 Å. The strain energy curves showed that the nanotubes structures are energetically more stable compared to the respective sheet structures. External hydroxyl dihedral angles in silica nanotubes have small influence, about 0.5 meV.atom^?1, in the strain energy curve tendency of those materials favoring the zigzag chirality. The chemical modification of outer surface of SNTs by dimethyl silane group affects their relative stability favoring the armchair chirality in approximately 2 meV.atom^?1. MSNTs have axial elastic constants, Young’s moduli, determined at the harmonic approximation, around 100 GPa smaller than the respective SNTs. The Young’s moduli of zigzag and armchair SNTs are in the range of 150–195 GPa and 232–260 GPa, respectively. And for the zigzag and armchair MSNTs these values are in the range of 77–89 and 110–140 GPa, respectively. The SNTs and MSNTs were characterized as insulators with band gaps around 8–10 eV.

Correlation between sagging and shear elasticity in pectin, gelatin and polyacrylamide gels

The relationship between the height of gels determined by a sag test and their elastic shear modulus (G′) has been both investigated experimentally and simulated using a finite element analysis for the inhomogeneous deformation of gels due to gravity. It was assumed in the simulations that gels can be modeled as incompressible linear elastic materials. General relationships between the sag of gels and their elastic modulus were obtained from the simulations for slip and no-slip conditions. The relationships were tested experimentally on pectin, gelatin and polyacrylamide gels with a range of concentrations and rigidities. The good agreement between the predictions and the results shows that these gels can be modeled accurately as incompressible elastic materials. A standard 150° SAG pectin gel, which sags 23.5% in the SAG test, has G′ moduli of 429 and 379 Pa under slip and no-slip conditions, respectively.