A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

A multilevel algorithm for force-directed graph drawing

We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force- directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Droplet formation with electromagnetic pulse force

Methods for serial generation of droplets from a liquid jet are shortly reviewed. A method of liquid metal droplet generation based on AC high frequency magnetic field is considered in detail. Numerical model for direct simulation of the time dependent droplet generation process is presented. Computed examples demonstrate the liquid silicon droplet formation for the cases of 500-1500 μm diameter.

Manufacturing of uniformly-sized silicon particles for solar cell from molten metal jet by electromagnetic pinch force

Spherical silicon solar cells are expected to serve as a technology to reduce silicon usage of photovoltaic (PV) power systems[1, 2, 3]. In order to establish the spherical silicon solar cell, a manufacturing method of uniformly sized silicon particles of 1mm in diameter is required. However, it is difficult to mass-produce the mono-sized silicon particles at low cost by existent processes now. We proposed a new method to generate liquid metal droplets uniformly by applying electromagnetic pinch force to a liquid metal jet[4]. The electromagnetic force was intermittently applied to the liquid metal jet issued from a nozzle in order to fluctuate the surface of the jet. As the fluctuation grew, the liquid jet was broken up into small droplets according to a frequency of the intermittent electromagnetic force. Firstly, a preliminary experiment was carried out. A single pulse current was applied instantaneously to a single turn coil around a molten gallium jet. It was confirmed that the jet could be split up by pinch force generated by the current. And then, electromagnetic pinch force was applied intermittently to the jet. It was found that the jet was broken up into mono-sized droplets in the case of a force frequency was equal to a critical frequency[5], which corresponds to a natural disturbance wave length of the jet. Numerical simulations of the droplet generation from the liquid jet were then carried out, which consisted of an electromagnetic analysis and a fluid flow calculation with a free surface of the jet. The simulation results were compared with the experiments and the agreement between the two was quite good.

Mode shape expansion using perturbed force vector approach

A new technique for mode shape expansion in structural dynamic applications is presented based on the perturbed force vector approach. The proposed technique can directly adopt the measured incomplete modal data and include the effect of the perturbation between the analytical and test models. The results show that the proposed technique can provide very accurate expanded mode shapes, especially in cases when significant modelling error exists in the analytical model and limited measurements are available.

Direct measurement of powder flavour adhesion on to a food surface using a novel adhesion tester

The firm adhesion of flavouring particles onto crisp surfaces during coating processes is a major concern in the snack production industry. Detachment of flavouring powders from products during handling and production stages can lead to substantial financial losses for the industry, in terms of variable flavour performance and extended cleaning down time of fugitive particle build-up on process equipment. Understanding the adhesion strength of applied bulk particulates used for flavouring formulations will help analysts to evaluate the efficiency of coating processes and potentially enable them to assess the adhesion strength of newly formulated flavouring powder prior to commitment to full scale plant trials. A rapid prototype of a novel adhesion tester has been designed and constructed. The apparatus operates according to the principle of impact force acting on particles attached to the surface of the food substrate. The main component is a circular plate to which four sample holders are attached and which is subjected to vertical travel down a guide shaft. Several flavouring powders have been tested extensively. By plotting the detachment versus impact force, the difference obtained between adhesion strength of different flavouring powders (which is a strong function of particle size) has been discussed.