Mapping forces in a 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterise their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the materials microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems. © 2011 Elsevier Ltd. All rights reserved.

Flexoelectric and elastic coefficients of odd and even homologous bimesogens.

It is known that bimesogenic liquid crystals exhibit a marked "odd-even" effect in the flexoelastic ratio (the effective flexoelectric coefficient to the average elastic coefficient), with the ratio being higher for the "odd-spaced" bimesogens (those with an odd number of alkyl groups in the spacer chain) than their neighboring even-spaced counterparts. To determine the contribution of each property to the flexoelastic ratio, we present experimental results on the flexoelectric and elastic coefficients of two homologous nonsymmetric bimesogens which possess odd and even alkyl spacers. Our results show that, although there are differences in the flexoelectric coefficients, there are substantially larger differences in the effective elastic coefficient. Specifically, the odd bimesogen is found to have both a low splay elastic coefficient and a very low bend elastic coefficient which, when combined, results in a significantly lower effective elastic coefficient and consequently a higher flexoelastic ratio.

The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time. © 2012 Elsevier Ltd. All rights reserved.

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Flexoelectric and elastic coefficients of odd and even homologous bimesogens.

It is known that bimesogenic liquid crystals exhibit a marked "odd-even" effect in the flexoelastic ratio (the effective flexoelectric coefficient to the average elastic coefficient), with the ratio being higher for the "odd-spaced" bimesogens (those with an odd number of alkyl groups in the spacer chain) than their neighboring even-spaced counterparts. To determine the contribution of each property to the flexoelastic ratio, we present experimental results on the flexoelectric and elastic coefficients of two homologous nonsymmetric bimesogens which possess odd and even alkyl spacers. Our results show that, although there are differences in the flexoelectric coefficients, there are substantially larger differences in the effective elastic coefficient. Specifically, the odd bimesogen is found to have both a low splay elastic coefficient and a very low bend elastic coefficient which, when combined, results in a significantly lower effective elastic coefficient and consequently a higher flexoelastic ratio.

Investigation of the poro-elastic response of seabed to solitary

A numerical model is established and validated to study the behavior of porous seabed under solitary wave propagation. Using Biot's poro-elastic theory, the problem is formulated as a two dimensional plane strain problem, and it is modelled using the Finite Element Method. The responses due to the solitary wave are compared with those of linear waves of the same height. It is found that regardless of the wave period, stresses due to solitary waves are generally larger. This indicates a higher potential for shear failure at the seabed under solitary waves. Implications on liquefaction need further investigation. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE).

Adhesive properties of gecko-inspired mimetic via micropatterned carbon nanotube forests

The adhesive properties of the gecko foot have inspired designs of advanced micropatterned surfaces with increased contact areas. We have fabricated micropatterned pillars of vertically aligned carbon nanotube forests with a range of pillar diameters, heights, and spacings (or pitch). We used nanoindentation to measure their elastic and orthogonal adhesion properties and derive their scaling behavior. The patterning of nanotube forests into pillar arrays allows a reduction of the effective modulus from 10 to 15 MPa to 0.1-1 MPa which is useful for developing maximum conformal adhesion. © 2012 American Chemical Society.

Insight into differences in nanoindentation properties of bone.

Nanoindentation provides the ideal framework to determine mechanical properties of bone at the tissue scale without being affected by the size, shape, and porosity of the bone. However, the values of tissue level mechanical properties vary significantly between studies. Since the differences in the bone sample, hydration state, and test parameters complicate direct comparisons across the various studies, these discrepancies in values cannot be compared directly. The objective of the current study is to evaluate and compare mechanical properties of the same bones using a broad range of testing parameters. Wild type C56BL6 mice tibiae were embedded following different processes and tested in dry and rehydrated conditions. Spherical and Berkovich indenter probes were used, and data analysis was considered within the elasto-plastic (Oliver-Pharr), viscoelastic and visco-elastic-plastic frameworks. The mean values of plane strain modulus varied significantly depending on the hydration state, probe geometry and analysis method. Indentations in dry bone analyzed using a visco-elastic-plastic approach gave values of 34 GPa. After rehydrating the same bones and indenting them with a spherical tip and utilizing a viscoelastic analysis, the mean modulus value was 4 GPa, nearly an order of magnitude smaller. Results suggest that the hydration state, probe geometry and the limitations and assumptions of each analysis method influence significantly the measured mechanical properties. This is the first time that such a systematic study has been carried out and it has been concluded that the discrepancies in the mechanical properties of bone measured by nanoindentation found in the literature should not be attributed only to the differences between the bones themselves, but also to the testing and analysis protocols.

Stiffness of sands through a laboratory test database

Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0·01%) to medium (0·5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain γe, up to which the elastic shear modulus is effectively constant at G0; a reference strain γr, defined as the shear strain at which the secant modulus has reduced to 0·5G0; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains γe and γr were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G0 is shown to make predictions that are accurate within a factor of 1·13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G0, should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1·6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

Measurement of the elastic constants of nanometric films

Carbon coatings of thickness down to 2 nanometers are needed to increase the storage density in magnetic hard disks and reach the 100 Gbit/in2 target. Methods to measure the properties of these ultrathin hard films still have to be developed. We show that combining Surface Brillouin Scattering (SBS) andX-ray reflectivity measurements the elastic constants of such films are accessible. Tetrahedral amorphous carbofilms of thickness down to about 2 nm were deposited on Si by an S bend filtered cathodic vacuum arc, achieving a continuous coverage on large areas free of macroparticles. Film thickness and mass density are measured by X-ray reflectivity: densities above 3 g/cm3 are found, indicating a significant sp3 content. The dispersion relations of surface acoustic waves are measured by SBS. We show that for thicknesses above ∼4 nm these waves can be described by a continuum elastic model based on a single homogeneous equivalent film. The elastic constants can then be obtained by fitting the dispersion relations, computed for given film properties, to the measured dispersion relations. For thicknesses of 3 nm or less qualitative differences among films are well measurable, but quantitative results are less reliable. We have thus shown that we can grow and characterise nanometer size tetrahedral amorphous carbon film, which maintain their high density and peculiar mechanical properties down to around 4 nm thickness, satisfying the requirements set for the hard disk coating material.