Atomistic Continuum Research Articles

Relation between the atomistic picture and continuum mechanics description of detonating solid-state explosives

In the present work, using the molecular-dynamics approach, we examine the initiation and development of detonation, initiated by a pulse of an external force, in a 3-D solid-state explosive. It is found that, prior to the onset of the chemical reaction, the substance passes from crystalline into the liquid state. Based on a mesoscale analysis, we analyze the applicability of main conservation equations, written in their integral, most general form or in the stationary form for the entire computation domain, including the undisturbed region of the crystal, reacting zone, and detonation products, to detonating solid explosives.

A Dynamic Atomistic–Continuum Method for the Simulation of Crystalline Materials

We present a coupled atomistic–continuum method for the modeling of defects and interface dynamics in crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away from defects and interfaces. We propose a new class of matching conditions between the atomistic and the continuum regions. These conditions ensure the accurate passage of large-scale information between the atomistic and the continuum regions and at the same time minimize the reflection of phonons at the atomistic–continuum interface. They can be made adaptive by choosing appropriate weight functions. We present applications to dislocation dynamics, friction between two-dimensional crystal surfaces, and fracture dynamics. We compare results of the coupled method and of the detailed atomistic model.

Hybrid Atomistic–Continuum Formulations and the Moving Contact-Line Problem

We present a hybrid atomistic–continuum computational framework for the treatment of dense fluid problems with emphasis on the coupling of molecular dynamics with continuum (finite element/spectral) methods for problems involving multi-fluid dynamics in the presence of multi-fluid interfaces. The technique is an extension of the single-fluid framework already presented by the author. The well-known moving contact-line problem is used as a validation example. A hybrid solution that employs molecular dynamics close to the walls where molecular effects are important and continuum fluid mechanics in the remainder of the domain (far field region) is obtained. A fully molecular solution of the same problem serves as an exact solution. Various issues related to dense fluid atomistic–continuum techniques are discussed and contrasted to the already existing but less general dilute gas techniques. Numerical considerations are discussed with particular emphasis on efficiency, and a formulation that reduces computational cost is proposed.

Mathematical Modeling in Materials Science and Engineering

During the past two decades, mathematical modeling has been gaining acceptance as a legitimate part of materials science and engineering. However, as common to all relatively new disciplines, we still lack a realistic perspective regarding the uses, limitations, and even the optimal methodologies of mathematical modeling techniques.The term “mathematical modeling” covers a broad range of activities, including molecular dynamics, other atomistic scale systems, continuum fluid and solid mechanics, deformation processing, systems analysis, input-output models, and lifecycle analyses. The common point is that we use algebraic expressions or differential equations to represent physical systems to varying degrees of approximation and then manipulate these equations, using computers, to obtain graphical output.While it is becoming an accepted fact that some kind of mathematical modeling will be needed to make most research programs complete, there is still considerable ambiguity as to what form this should take and what might be the actual usefulness of such an effort.Among the more seasoned and successful practitioners of this art, clear guidelines have emerged regarding the uses and limitations of the mathematical modeling approach. We seek to illustrate these uses through the successful modeling examples presented by some leading practitioners. Some general principles may be worth repeating as an introduction to this interesting collection of articles.

Calculation‐ of Some Defect Parameters in F.C.C. Metals

AbstractThe lattice statics model together with the atomistic continuum model is used for the calculation of relaxation due to a vacancy, the vacancy formation energy and divacancy binding energy in the case of some f.c.c. metals whose phonon dispersion curves are available. Using the measured phonon dispersion relations and the elastic constants as constraints the dynamical matrix is derived considering interactions up to the eighth nearest neighbouring shell. The calculation shows that in all the cases the first twelve nearest neighbours relax towards the vacancy and the magnitude of the displacements of the distant neighbours decreases systematically. The available experimental values of the monovacancy formation energy and divacancy binding energy whereever available, show fairly good agreement. Relations among monovacancy formation energy, melting temperature, and activation energy for self‐diffusion are proposed.