Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Publisher Summary This chapter discusses some basic problems in mechanics of elastic solids containing multiple cracks. A number of mathematical aspects that frequently constitute fields of their own (like various numerical techniques) are discussed very briefly in the chapter. The focus is on physically important effects produced by crack interactions and to present results in the simplest form possible. The problems considered in this chapter can be divided into two groups: (1) The impact of interactions on individual cracks, particularly on the stress intensity factors (SIFs), and (2) the effective elastic properties of solids with many cracks. Problems of the first group are, generally, relevant for the fracture-related considerations; solutions are sensitive to the positions of individual cracks. Problems of the second group deal with the volume average quantities; they are relatively insensitive to the information on individual cracks. The chapter discusses, in this connection, whether correlations exist between these two groups of quantities; in particular, whether microcracking can be reliably monitored by measuring changes in the effective elastic moduli.

Elastic Solids with Many Cracks and Related Problems

Cracking and coalescence behavior has been studied experimentally with prismatic laboratory-molded gypsum and Carrara marble specimens containing two parallel pre-existing open flaws. This was done at both the macroscopic and the microscopic scales, and the results are presented in two separate papers. This paper (the first of two) summarizes the macroscopic experimental results and investigates the influence of the different flaw geometries and material, on the cracking processes. In the companion paper (also in this issue), most of the macroscopic deformation and cracking processes shown in this present paper will be related to the underlying microscopic changes. In the present study, a high speed video system was used, which allowed us to precisely observe the cracking mechanisms. Nine crack coalescence categories with different crack types and trajectories were identified. The flaw inclination angle (β), the ligament length (L), that is, intact rock length between the flaws, and the bridging angle (α), that is, the inclination of a line linking up the inner flaw tips, between two flaws, had different effects on the coalescence patterns. One of the pronounced differences observed between marble and gypsum during the compression loading test was the development of macroscopic white patches prior to the initiation of macroscopic cracks in marble, but not in gypsum. Comparing the cracking and coalescence behaviors in the two tested materials, tensile cracking generally occurred more often in marble than in gypsum for the same flaw pair geometries.

Crack Coalescence in Molded Gypsum and Carrara Marble: Part 1. Macroscopic Observations and Interpretation

Crack coalescence in a rock-like material containing two cracks

A two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films. Specific examples are presented for films subject to equi-biaxial residual tensile stress. Single and multiple crack geometries are considered with a view to elucidating some of the crack patterns which are observed to develop. Tendencies for propagating cracks to remain straight or curve are explored as a consequence of crack interaction. The existence of spiral paths is demonstrated.

Crack patterns in thin films

The experimentally known phenomenon that originally collinear mode I cracks seem to avoid each other before coalescence is studied by investigating the stability of straight crack paths. To this end a periodic array of approximately collinear but slightly curved cracks is considered. Stress intensity factors for modes I and II are derived and the growth of originally straight cracks under mode I conditions is studied after introduction of a disturbance that forces the cracks to deviate from a straight path. It is shown that the straight crack path is unstable, i.e. that tip to tip coalescence will not take place.

Why do cracks avoid each other

Even cracks which seem to be favourably oriented for mode II growth might extend in mode I by kinking. The conditions that favour mode I or mode II growth are examined. It is shown that a high confining pressure promotes mode II growth and so does a low ratio between the critical stress intensity factors of modes II and I. Quantitative results are given for different coefficients of friction and confining pressures.

When does a crack grow under mode II conditions

The sign of the T-stress has been widely used for deciding whether directional stability prevails for straight cracks subjected to mode I loading under small scale yielding. However, there is little evidence for the reliability of such a criterion. On the contrary, it is shown that a local criterion is not applicable and that directional stability generally depends on body and load geometry as well as on material parameters, whereas the sign of the T-stress is totally irrelevant in most cases.

The influence of the T-stress on the directional stability of cracks

In this work, the influence of substrate bias voltage on the microhardness, adhesive strength, friction coefficient, and wear rate of AIP Cr2O3 films deposited on AISI 304 stainless steel substrates was investigated systematically. In the meantime, the wear failure mechanism of AIP Cr2O3 films in dry sliding contact was also analyzed and discussed. The results showed that the mechanical properties, adhesive behaviors, and tribological performance of AIP Cr2O3 films were greatly altered by applying a negative bias voltage. With increasing the bias voltage, the hardness, critical load, and tribological performance of AIP Cr2O3 films first were improved gradually, and then were impaired slightly again. When the bias voltage is - 100 V. the Cr2O3 film possessed the highest hardness, the strongest adhesion, and the best wear resistance. The essence of above phenomena was attributed to the variations of microstructure and defect density in the films induced by the substrate bias voltage increase. The main wear failure mechanism of AIP Cr2O3 films is crack initiation and propagation under the high contact stresses, inducing the local film with small area to flake off gradually, and eventually leading to the formation of a wear scar. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

Solveig Melin

Papers

Why do cracks avoid each other

When does a crack grow under mode II conditions

The influence of the T-stress on the directional stability of cracks

Study on nanocrystalline Cr2O3 films deposited by arc ion plating: II. Mechanical and tribological properties

Accurate data for stress intensity factors at infinitesimal kinks