Non-linear elastic behavior of light fibrous materials

Light fibrous materials composed of elastic fibers display a non-linear elastic behavior, where the non-linearity is due to the increase in the number of contacts between fibers under compression. Testing glass wool under compression up to 95% shows such a strongly non-linear behavior. A model is proposed to account for the divergence of the compressive stress as the strain approaches a threshold compression , with . Quantitative analysis of the experimental data on glass wool is fully consistent with this result. Received 2 February 1999     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

Processing dependence of Young's modulus of Ti-base nanostructured alloys

The cooling rate and heat treatment dependence of Young's modulus for Ti-base multicomponent nanostructure-dendrite composites exhibits a very different response compared with the monolithic nanostructured or normal grain-sized Ti alloys. With increasing cooling rate, the decrease in the volume fraction of the micrometer-sized β-phase dendrites induces a significant increase in Young's modulus for most of these composites. This increase can cover the decrease in Young's modulus induced by the reduction of grain size of the nanostructured matrix. Heat treatment induces a significant increase in Young's modulus due to the precipitation of intermetallics and/or α-phase in the nanostructured matrix.     

A first principles study of cubic IrO<Subscript>2</Subscript> polymorph

We have studied structural, thermodynamic, elastic, and electronic properties of cubic IrO₂ polymorph via ab initio calculations within the LDA and GGA approximations. Basic physical properties, such as lattice constant, bulk modulus, second-order elastic constants (C_ij), and the electronic band structures are calculated, and compared with available experimental values. We have, also, predicted the Young's modulus, Poison's ratio (ν), Anisotropy factor (A), sound velocities, and Debye temperature.     

Elasticity of BaFCl single crystal under hydrostatic pressure

The sound velocities for longitudinal and transverse waves have been measured in single crystalline BaFCl at room temperature using ultrasonic pulse echo and Brillouin scattering techniques. The complete set of elastic constants is deduced and lead to the bulk moduli values of BaFCl at ambiant conditions (, , ) which are compared with those obtained by a shell model. Moreover, using the ultrasonic technique under pressure, the pressure derivatives of the second order elastic constants at 298 K have been determined up to 0.3 GPa. All moduli increase linearly with pressure in this pressure range, allowing to determine directly and separately the first derivative of the bulk modulus B'₀ = 5.8. These data are used to calculate a Murnaghan equation of state. A detailed comparison is given between our results with those recently obtained by X-ray diffraction on powder or calculated using the local density approximation method. Finally, the anisotropy of BaFCl under pressure is discussed. Received: 19 March 1998 / Revised: 15 May 1998 / Accepted: 19 May 1998     

The elastic behavior of entropic "fisherman's net”

A new formalism is used for a Monte Carlo determination of the elastic constants of a two-dimensional net of fixed connectivity. The net is composed of point-like atoms each of which is tethered to six neighbors by a bond limiting the distance between them to a certain maximal separation, but having zero energy at all smaller lengths. We measure the elastic constants for many values of the ratio between the maximal and actual extensions of the net. When the net is very stretched (), a simple transformation maps the system into a triangular hard disks solid, and we show that the elastic properties of both systems coincide. We also show that the crossover to a Gaussian elastic behavior, expected for the non-stressed net, occurs when the net is looser (). Received 9 February 2000 and Received in final form 14 May 2000     

Hypersonic wave anomalies in Cs3H(SeO4)2 at the transitions above room temperature

The elastic properties of Cs3H ( SeO4 ) ₂ are investigated by Brillouin spectroscopy in the temperature range 20-220 covering the two transitions III II and II I occurring at and , respectively. Phase I is known to be a protonic conductive one. Discontinuities of elastic constants are generally observed at both transitions, implying first orderness. In phases II and I, a slight broadening of the Brillouin lines is detected. The results are discussed in comparison with compounds of the families XHSeO4 (X = NH4, Rb and Cs) and CsH2BO4 (B = As and P) which also undergo a transition to a superionic phase. In the conductive phase, it appears that the lattice anharmonicity is weaker in Cs3H ( SeO4 ) ₂ than in these other compounds. Received 16 October 1998     

Elastic anomalies and orientational glass transition in Na(CN) Cl mixed crystals. A Brillouin spectroscopic study

High performance Brillouin spectroscopy (BS) has been used to study the elastic properties (static and dynamic) of the orientational glassy state of Na(CN)_xCl_1-x samples ). The temperature behaviour of the elastic properties reveals a more complex scenario for the orientational glass transition than generally believed. The shear elastic constant shows the well-known c ₄₄ ( T ) anomaly, indicated by a minimum, found in other cyanide mixed crystals. The results obtained for the hypersonic attenuation are in clear contradiction with the dynamic character of the c ₄₄ ( T )-minimum. The temperature behaviour of the longitudinal elastic constant c₁₁ of very dilute Na(CN)_xCl_1-x samples shows two striking features: i) Similar to the anomalous temperature behaviour of c ₄₄ ( T ), lowering the temperature c ₁₁ ( T ) first decreases, goes through a minimum and then rises again. The minimum takes place at a temperature above the temperature, , where c ₄₄ ( T ) reaches its minimum value. ii) A kink-like anomaly of c ₁₁ ( T ) is observed at lower temperatures. This second anomaly is similar to the classical one observed in canonical glasses at their glass transition temperature . Received 8 April 1999 and Received in final form 3 June 1999     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Molecular dynamics simulations of thermodynamics,elastic constants and solid solution strengths for Mg-Gd alloys

The thermal and mechanical properties of Mg-Gd intermetallics MgGd, MgGd₂ and MgGd₃ are studied using a modified analytical embedded atom method. Calculated results agree well with the available experimental data and other theoretical results. The results on the elastic constants suggest that thermal softening behavior is observed as the temperature increases and the bulk moduli of ordered phases are larger than that of elemental Mg above 300 K. The heat capacities of MgGd, Mg₂Gd and Mg₃Gd are 22.91, 23.04 and 23.09 J mol K^-1, respectively, at 300 K. Furthermore, the addition of Gd gives rise to an increase of c/a. With the same content of Gd, the ratio c/a remains unchanged with increasing temperature, whereas this phenomenon does not occur in pure Mg, which indicates that the temperature-independent c/a restrains the occurrence of non-basal slip and twinning. Hence the addition of Gd can enhance the strength of Mg, in good agreement with experimental observation.     

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints. Received: 28 November 1997 / Received in final form and accepted: 31 March 1998     

Determination of silicone coating Young's modulus using atomic force microscopy

The polymerisation degree of thin polymer coatings was checked by following the variation of their local mechanical properties. Atomic force microscope (AFM) was used in an indentation mode to investigate the mechanical characteristics of silicone coatings on polycarbonate substrates. The evolution of Young's modulus of the silicone coatings was determined as a function of the polymer annealing time. We have used a relative method to measure Young's moduli, which involves a calibration step with a set of reference polymers. No variation was observed for the modulus of silicone coatings annealed during more than 40 min at 130 °C. This result indicates that over-heating does not modify the mechanical properties of the coating.     

Metastability of a circular o-ring due to intrinsic curvature

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997     

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na_0.5Li_0.5, Na_0.5K_0.5, Na_0.5Rb_0.5 and Na_0.5Cs_0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru-Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C₁₁, C₁₂, C₄₄, C₁₂-C₄₄, C₁₂/C₄₄ and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.     

Temporal and spatial correlations in a viscoelastic model of heterogeneous faults

We study the temporal and spatial correlations in a one-dimensional model of a heterogeneous fault zone, in the presence of viscoelastic effects. As a function of dynamical weakening and of dissipation, the system exhibits three different “phases": one in which there are no time correlations between the events, a second, in which there are “Omori's law” type temporal correlations, and a third, runaway phase with quasiperiodic system size events. Received 30 May 2000 and Received in final form 7 September 2000     

Strong anisotropic nematic order in liquid crystal polymers: [4] a quasi-elastic neutron scattering study

From quasi-elastic neutron scattering experiments performed in glassy, nematic and isotropic phases, the dynamics of oriented samples of strong anisotropic side-on fixed liquid crystal polymers have been analysed. Using the selective deuteration method, we are able to attribute motions to specific parts of the molecule in the parallel and perpendicular orientations. The motions of the whole macromolecule decrease as soon as the temperature decreases below the isotropic-nematic transition. Nevertheless, the motions of the polymer backbone, compared to the whole polymer dynamics, are systematically reduced, even in the isotropic phase. Moreover, an anisotropy of the motions is revealed, with a reduction in the direction parallel to the orientation. An harmonic character of the vibrational processes is also evidenced. We conclude that the anisotropy of the dynamic corroborates the anisotropy of conformation of the macromolecule (so-called jacketed structure). Received: 29 October 1997 / Revised: 22 January 1998/ Accepted: 11 May 1998     

Mechanical properties of carbon nanotubes

A variety of outstanding experimental results on the elucidation of the elastic properties of carbon nanotubes are fast appearing. These are based mainly on the techniques of high-resolution transmission electron microscopy (HRTEM) and atomic force microscopy (AFM) to determine the Young’s moduli of single-wall nanotube bundles and multi-walled nanotubes, prepared by a number of methods. These results are confirming the theoretical predictions that carbon nanotubes have high strength plus extraordinary flexibility and resilience. As well as summarising the most notable achievements of theory and experiment in the last few years, this paper explains the properties of nanotubes in the wider context of materials science and highlights the contribution of our research group in this rapidly expanding field. A deeper understanding of the relationship between the structural order of the nanotubes and their mechanical properties will be necessary for the development of carbon-nanotube-based composites. Our research to date illustrates a qualitative relationship between the Young’s modulus of a nanotube and the amount of disorder in the atomic structure of the walls. Other exciting results indicate that composites will benefit from the exceptional mechanical properties of carbon nanotubes, but that the major outstanding problem of load transfer efficiency must be overcome before suitable engineering materials can be produced. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 29 July 1999     

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO4

Transverse and pseudo-transverse elastic waves have been studied in several scattering geometries in order to investigate the temperature dependences of C E ₆₆ and C E ₁₄ over the range 300-1100 K, including the transitions near 860 K. These results complete those on C E ₄₄ we have obtained in a previous work. All these constants display discontinuities at the lock-in transition. In the phase, the results are analysed in term of lowest order couplings between strains (e) and the order parameter (Q). The main features are described by the lowest order biquadratic e2Q2 coupling, in particular for C E ₄₄ in a large temperature range. However, it appears that a contribution of the next coupling term arises for C E ₆₆ below K and that the first two lowest order terms have to be taken into account even just below the lock-in transition in the case of C E ₁₄ . The temperature dependence of Q has been deduced and it can be well described in the framework of Landau's theory. Received: 2 October 1997 / Received in final form: 3 December 1997 / Accepted: 29 January 1998     

Homogeneous and inhomogenous polyacrylamide gels as observed by small angle neutron scattering: A connection with elastic properties

Small angle neutron scattering of polyacrylamide solutions and gels is presented for different polymer and cross link concentrations. The gels are analyzed in connection with their elastic properties. For less than 11% of polymer concentration and for small cross link contents , it was found that the gels are no more heterogeneous than the solutions. This corresponds to the range of where the elastic modulus increases with . For larger cross link contents when the elastic modulus decreases if increases, the sample appears to be strongly heterogeneous with a large size distribution of the inhomogeneities. The results are compared with the recent model of Oshmyan and Benguigui of the elastic properties of the polyacrylamide gels. Thus a relation can be proposed between the observation of the inhomogeneities by scattering and the mechanical properties Received 30 December 1997 and Received in final form 26 June 1998