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

Electrolytes have been identified as some of the most influential components in the performance of electrochemical supercapacitors (ESs), which include: electrical double-layer capacitors, pseudocapacitors and hybrid supercapacitors. This paper reviews recent progress in the research and development of ES electrolytes. The electrolytes are classified into several categories, including: aqueous, organic, ionic liquids, solid-state or quasi-solid-state, as well as redox-active electrolytes. Effects of electrolyte properties on ES performance are discussed in detail. The principles and methods of designing and optimizing electrolytes for ES performance and application are highlighted through a comprehensive analysis of the literature. Interaction among the electrolytes, electro-active materials and inactive components (current collectors, binders, and separators) is discussed. The challenges in producing high-performing electrolytes are analyzed. Several possible research directions to overcome these challenges are proposed for future efforts, with the main aim of improving ESs' energy density without sacrificing existing advantages (e.g., a high power density and a long cycle-life) (507 references).

A review of electrolyte materials and compositions for electrochemical supercapacitors

https://www.crm.sns.it/media/course/3060/miehe+hofacker+welschinger10.pdf

A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase-field. In this paper, we outline a thermodynamically consistent framework for phase-field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. We start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that Γ-converges for vanishing length-scale parameter to a sharp crack topology functional. This functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase-field. Here, we propose alternative rate-independent and viscous over-force models that ensure the local growth of the phase-field. Next, we define an energy storage function whose positive tensile part degrades with increasing phase-field. With these constitutive functionals at hand, we derive the coupled balances of quasi-static stress equilibrium and gradient-type phase-field evolution in the solid from the argument of virtual power. Here, we consider a canonical two-field setting for rate-independent response and a time-regularized three-field formulation with viscous over-force response. It is then shown that these balances follow as the Euler equations of incremental variational principles that govern the multi-field problems. These principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation, including features such as the symmetry of the monolithic tangent matrices. We demonstrate the performance of the proposed phase-field formulations of fracture by means of representative numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.

Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations

A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

Cracking particles: A simplified meshfree method for arbitrary evolving cracks

A simple and robust three-dimensional cracking-particle method without enrichment

An extended finite element method scheme for a static cohesive crack is developed with a new formulation for elements containing crack tips. This method can treat arbitrary cracks independent of the mesh and crack growth without remeshing. All cracked elements are enriched by the sign function so that no blending of the local partition of unity is required. This method is able to treat the entire crack with only one type of enrichment function, including the elements containing the crack tip. This scheme is applied to linear 3-node triangular elements and quadratic 6-node triangular elements. To ensure smooth crack closing of the cohesive crack, the stress projection normal to the crack tip is imposed to be equal to the material strength. The equilibrium equation and the traction condition are solved by the Newton–Raphson method to obtain the nodal displacements and the external load simultaneously. The results obtained by the new extended finite element method are compared to reference solutions and show excellent agreement. Copyright © 2003 John Wiley & Sons, Ltd.

New crack-tip elements for XFEM and applications to cohesive cracks

SUMMARY A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity. The approach is limited to rate-independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extendednite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks. Copyright ? 2003 John Wiley & Sons, Ltd.

Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

https://ir.canterbury.ac.nz/bitstream/handle/10092/705/12608447_paper8_07.pdf?sequence=1

Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment

Goangseup Zi

Papers

A simple and robust three-dimensional cracking-particle method without enrichment

New crack-tip elements for XFEM and applications to cohesive cracks

Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment

On three-dimensional modelling of crack growth using partition of unity methods