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

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Scalable Molecular Dynamics with NAMD

Meshless methods: An overview and recent developments

Analysis of the cup-cone fracture in a round tensile bar

A balanced mechanics-materials approach and coverage of the latest developments in biomaterials and electronic materials, the new edition of this popular text is the most thorough and modern book available for upper-level undergraduate courses on the mechanical behavior of materials To ensure that the student gains a thorough understanding the authors present the fundamental mechanisms that operate at micro- and nano-meter level across a wide-range of materials, in a way that is mathematically simple and requires no extensive knowledge of materials This integrated approach provides a conceptual presentation that shows how the microstructure of a material controls its mechanical behavior, and this is reinforced through extensive use of micrographs and illustrations New worked examples and exercises help the student test their understanding Further resources for this title, including lecture slides of select illustrations and solutions for exercises, are available online at wwwcambridgeorg/97800521866758

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Mechanical Behavior of Materials

Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29° from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.

Numerical simulations of fast crack growth in brittle solids

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from in­itial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical in­clusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through com­plete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry

Alan Needleman

Papers

Analysis of the cup-cone fracture in a round tensile bar

Numerical simulations of fast crack growth in brittle solids

A Continuum Model for Void Nucleation by Inclusion Debonding

A continuum model for void nucleation by inclusion debonding

Overview no. 42 Texture development and strain hardening in rate dependent polycrystals