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

Influence of Al-doped ZnO Transparent Contacts Deposited by a Spray Pyrolysis Technique on Performance of HIT Solar Cells

AbstractTransparent and conductive Al-doped ZnO (AZO) thin films were deposited by spray pyrolysis and analysed in the aim to improve optical and electrical properties involved in the efficiency of Heterostructure with Intrinsic Thin Layer (HIT) solar cell. X-ray diffraction measurement shows that AZO film grown on glass has (002) preferred orientation. High optical transmittance value of ∼80% in the visible region was observed and the optical band gap was found to be 3.31eV at room temperature. The influence of AZO thin films as transparent conductive oxide TCO on heterojunction with intrinsic thin-layer (HIT) solar cell performance was investigated using software simulation. The beneficial effect of implementing AZO front contact for increasing electrical energy conversion properties of HIT solar cell compared to the reference cell without the AZO layer

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

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

A prototypical model for tensional wrinkling in thin sheets

The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians and engineers. This has been triggered by the growing interest in developing technologies at ever decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. While the most basic buckling instability of uniaxially compressed plates was understood by Euler more than 200 years ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length - a sheet under axisymmetric tensile loads. This geometry, whose first study is attributed to Lam´e, allows us to construct\ud a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that for thin sheets the far-from-threshold regime is expected to emerge under extremely small compressive loads, emphasizing the relevance of our analysis for nanomechanics applications

Modeling flocks with perceptual agents from a dynamicist perspective

Computational simulations of flocks and crowds have typically been processed by a set of logic or syntactic rules. In recent decades, a new generation of systems has emerged from dynamicist approaches in which the agents and the environment are treated as a pair of dynamical systems coupled informationally and mechanically. Their spontaneous interactions allow them to achieve the desired behavior. The main proposition assumes that the agent does not need a full model or to make inferences before taking actions; rather, the information necessary for any action can be derived from the environment with simple computations and very little internal state. In this paper, we present a simulation framework in which the agents are endowed with a sensing device, an oscillator network as controller and actuators to interact with the environment. The perception device is designed as an optic array emulating the principles of the animal retina, which assimilates stimuli resembling optic flow to be captured from the environment. The controller modulates informational variables to action variables in a sensory-motor flow. Our approach is based on the Kuramoto model that describes mathematically a network of coupled phase oscillators and the use of evolutionary algorithms, which is proved to be capable of synthesizing minimal synchronization strategies based on the dynamical coupling between agents and environment. We carry out a comparative analysis with classical implementations taking into account several criteria. It is concluded that we should consider replacing the metaphor of symbolic information processing by that of sensory-motor coordination in problems of multi-agent organizations