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Abstract: The dilatancy is as important property of rock-type (granular, frictional, cohesive, and dilatant) materials as the internal friction, but it is generally ill-constrained and is rarely taken into account in applications, being set to zero. Theoretical analysis shows that the dilatancy factor β strongly affects the onset of the deformation instability (localization). Numerical models confirm this but also reveal that evolution of this instability, resulting in the deformation localization bands and fractures observed in the experiments, is defined by the evolution of the constitutive parameters and notably of β with inelastic strain and mean stress σ. Therefore for the modelling of instability and rupture of rock-like materials, the knowledge (at least to a first approximation) of function β( , σ) and of how it can vary from one material to another is necessary. We constrain these functions from a large original experimental data set obtained for Granular Rock Analogue Material (GRAM1) as well as for hard rocks, Tavel and Solnhofen limestones, from the published data. All data are from axisymmetric compression tests conducted under different confining pressures. The data processing has shown that in spite of very different (orders of magnitude) values of elastic modulii and strengths, the aspect of the β( , σ) functions for all the three materials is similar: For all the materials β reduces with σ and increases with until certain value after which it reduces approaching zero. At intermediate σ values, β changes a sign from negative to positive with . A relatively simple analytical expression of β( , σ) grasping this behaviour is proposed. [Copyright &y& Elsevier]

In this communication, the authors study diffraction patterns calculation under convergent illumination. We analyze known fast algorithms using the Fourier transform and the fractional Fourier transform (FRT). We show that interference between convergent phase factor and the kernel of the different numerical Fresnel transformation may impose serious restrictions on the range of distances, where diffraction patterns can be accurately calculated. We review free space diffraction patterns calculation algorithms. In that case, the FRT provides a unified algorithm for the calculation of amplitude patterns in all the range of distances. On the contrary, we show below that, when convergent illumination is used, none of the algorithms is capable of providing a unified framework of calculation for the entire region of interest from object to focus. [Copyright &y& Elsevier]

Subpixel techniques are commonly used to increase the spatial resolution in tracking tasks. Object tracking with targets of known shape permits obtaining information about object position and orientation in the three-dimensional space. A proper selection of the target shape allows us to determine its position inside a plane and its angular and azimuthal orientation under certain limits. Our proposal is demonstrated both numerical and experimentally and provides an increase the accuracy of more than one order of magnitude compared to the nominal resolution of the sensor. The experiment has been performed with a high-speed camera, which simultaneously provides high spatial and temporal resolution, so it may be interesting for some applications where this kind of targets can be attached, such as vibration monitoring and structural analysis. [ABSTRACT FROM AUTHOR]