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

Some materials may naturally form discontinuities such as cracks as a result of deformation. As an aid to the modeling of such materials, a new framework for the basic equations of continuum mechanics, called the "peridynamic" formulation, is proposed. The propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived. Material stability and its connection with wave propagation is investigated. It is demonstrated by an example that the reformulated approach permits the solution of fracture problems using the same equations either on or off the crack surface or crack tip. This is an advantage for modeling problems in which the location of a crack is not known in advance.

https://digital.library.unt.edu/ark:/67531/metadc664843/m2/1/high_res_d/1895.pdf

Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

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

In a numerical micromechanical study of void nucleation, a framework is used where constitutive relations are specified independently for the matrix, the void-nucleating particles and the interface. Plane strain analyses are carried out for a doubly periodic array of circular cylindrical particles. The particles are taken to be rigid and the elastic-plastic deformations of the matrix are described in terms of continuum crystalline plasticity, using a planar crystal model that allows for three slip systems. Comparison is made with void-nucleation predictions based on a corresponding flow theory of plasticity with isotropic hardening. The crystal model can give rise to shear localization at the particle-matrix interface and shear localization, which leads to large localized strains in the matrix, is found to inhibit decohesion. The role of the triaxiality of the stress state in determining whether decohesion or localization occurs first is investigated. A parameteric study is also carried out for a crystal matrix using two descriptions of the interface shear behaviour; one is periodic in the shear displacement across the interface, while the other allows for shear decohesion.

https://iopscience.iop.org/article/10.1088/0965-0393/1/2/001/pdf

Void nucleation by inclusion debonding in a crystal matrix

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.

Numerical simulations of dynamic crack growth along an interface

Large thermal mismatch stress can be introduced in 3D-Integration structures employing Through-Silicon-Via (TSV). The stress distribution in silicon and interconnect is affected by the via diameter and layout geometry. The TSV induced stress changes silicon mobility and ultimately alters device performance. The mobility and performance change differs in nand p- silicon and is a function of the distance to the TSV. In addition, the TSV induced stress acts on the barrier layer, the landing pad, the interconnects, and the dielectrics. The interactions with defects may lead to crack nucleation and growth, and compromise the structure reliability. Furthermore, the material choice that reduces silicon stress for less impact on performance may increase stresses in other regions where reliability is of concern. This paper studies these effects and their dependence on various integration configurations.

Performanace and reliability analysis of 3D-integration structures employing Through Silicon Via (TSV)

Dynamic fracture is investigated for two-dimensional notched solids under tension using million atom systems. Brittle material and ductile material are modeled through the choice of interatomic potential functions which are Lennard-Jones and embedded-atom potentials, respectively. Numerical calculations are carried out on the IBN SP parallel computer and molecular dynamics is implemented using a spatial-decomposition algorithm. Many recent laboratory findings occur in our simulation experiments. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. For rapid brittle fracture, the dynamic instability of the crack growth is observed as the crack velocity approaches one-third of the Rayleigh wave speed. At higher crack velocity, the crack either follows a wavy path or branches and the anisotropy due to the large deformation at the crack tip plays the governing role in determining the crack path. Limited comparison of rapid brittle fracture process with the rapid ductile fracture process is made.

Xiaopeng Xu

Papers

Numerical simulations of fast crack growth in brittle solids

Void nucleation by inclusion debonding in a crystal matrix

Numerical simulations of dynamic crack growth along an interface

Performanace and reliability analysis of 3D-integration structures employing Through Silicon Via (TSV)

A molecular dynamics investigation of rapid fracture mechanics