Geometric origin of mechanical properties of granular materials

Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list of contacts is known- is established in a quite general context, and the important distinction between isostatic problems under given external loads and isostatic (rigid) structures is presented. Complete rigidity is only guaranteed, on stability grounds, in the case of spherical cohesionless grains. Otherwise, the network of contacts might deform elastically in response to load increments, even though grains are rigid. This sets an uuper bound on the contact coordination number. The approximation of small displacements (ASD) allows to draw analogies with other model systems studied in statistical mechanics, such as minimum paths on a lattice. It also entails the uniqueness of the equilibrium state (the list of contacts itself is geometrically determined) for cohesionless grains, and thus the absence of plastic dissipation. Plasticity and hysteresis are due to the lack of such uniqueness and may stem, apart from intergranular friction, from small, but finite, rearrangements, in which the system jumps between two distinct potential energy minima, or from bounded tensile contact forces. The response to load increments is discussed. On the basis of past numerical studies, we argue that, if the ASD is valid, the macroscopic displacement field is the solution to an elliptic boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and minor errors correcte

Minagkabau and negeri sembilan

214 p.; 24 cm

Symbolic Anthropology in the Netherlands

Indonesi

Symbolic Anthropology in the Netherlands

Indonesi

Determination of Mineral Changes in Human Dental Enamel by Longitudinal Microradiography and Scanning Optical Monitoring and Their Correlation with Chemical Analysis

Both longitudinal microradiography (LMR) and scanning optical monitoring (OM) are non-destructive methods for measuring mineral changes in dental tooth enamel slices with time at 169 locations on the slice. Average calcium losses from four human tooth enamel slices (300-400 micron thickness), etched in HClO4, were determined by LMR and chemical analysis (C). As predicted from theory, LMR and C correlate very well (r = 0.99), but the appearance of a systematic error of unknown source of 30% made with LMR, C, or both could not be avoided. Another, more complex, experiment concerned six human tooth enamel slices of the same thickness which were demineralized in an aqueous buffered acid solution containing Ca and PO4. From this experiment it was found that average calcium loss as measured by C and LMR correlated well with the optical scattering as measured with scanning OM (Spearman rank correlation rs approximately equal to 0.79). It was also found that three-dimensional plots of local calcium loss by LMR and scanning OM as a function of tooth slice surface position show a well-defined tooth-dependent increase due to local demineralization and rather similar behaviour with time. From the experiments it follows that LMR and scanning OM are reliable methods to determine the mineral change in a tooth tissue as a function of local tooth slice surface position and of time and that with LMR and scanning OM time- and position-dependent measurements with an oral device become feasible