Theory of dynamic crack branching in brittle materials

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of local symmetry are used to determine the cracks paths. The bifurcation is predicted at a given critical speed and at a specific branching angle: both correlated very well with experiments. The curvature of the subsequent branches is also studied: the sign of $T$, with $T$ being the non singular stress at the initial crack tip, separates branches paths that diverge from or converge to the initial path, a feature that may be tested in future experiments. The model rests on a scenario of crack branching with some reasonable assumptions based on general considerations and in exact dynamic results for anti-plane branching. It is argued that it is possible to use a static analysis of the crack bifurcation for plane loading as a good approximation to the dynamical case. The results are interesting since they explain within a continuum mechanics approach the main features of the branching instabilities of fast cracks in brittle materials, i.e. critical speeds, branching angle and the geometry of subsequent branches paths.Comment: 41 pages, 15 figures. Accepted to International Journal of Fractur

Measuring order in the isotropic packing of elastic rods

The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective compressibility. These two quantities may be used to build a statistical framework for packed elastic systems.Comment: 4 pages, 5 figure

A comparative study of crumpling and folding of thin sheets

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly ine cient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the sti ness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We nd that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.Comment: 5 page

Effect of salt stress on some physiological parameters in Atriplex halimus L.

The impact of salinity applied for five weeks followed two provenances of Atriplex halimus L. harvested from Oran (Algeria coast) and Ain Dheb (high plateaus west of Algeria). The analyzed parameters are physiological from the leaves of young plants grown in a greenhouse stored in air-conditioned glass. Two types of salt stress are imposed on plants from the 165th day after sowing for a batch CaCl2 + NaCl to 300 meq and 600 meq.l-1and for the other batch to undiluted water sea with a frequency of watering every other two days. The results of water indicators such as the relative water content (RWC or TRE) showed some fluctuation during the five weeks under the two types of stress. Transpiration (water loss from the excised leaf or RWL) measured after 30, 60 and 120 min at the end of the period of application of stress presents a decline in both sources and types of stress. In addition, the stomatal resistance showed considerable variability for both sources and the type of stress.Keywords: A. halimus L., salt stress NaCl + CaCl2, Seawater, RWC, sweating, stomatal resistance

Evaluating morphological variability of Artemisia herba-alba Asso from western Algeria

This work was interested on the study of the morphological variability of 120 individuals of Artemisia herba-alba Asso coming from three stations in western Algeria , which was assessed through 15 quantitative and qualitative characters. Analysis of variance (ANOVA) and hierarchical cluster analysis (HCA) results showed significant morphological variability inter and intra-population. This phenotypic variability is explained by a high genetic polymorphism determined at another genetic study that we conducted in parallel on individuals of the same site using molecular markers types ISSR.This study also revealed a large variability within A. herba alba which could help investigation on a large collection of individuals and therefore select the most efficient ecotypes for re-introduction this species in steppes and highlands of Algeria.Key words: Artemisia herba-alba Asso; Morphological variability;steppe;Algeria