From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals

We present a formalism for coupling a density functional theory-based quantum simulation to a classical simulation for the treatment of simple metallic systems. The formalism is applicable to multiscale simulations in which the part of the system requiring quantum-mechanical treatment is spatially confined to a small region. Such situations often arise in physical systems where chemical interactions in a small region can affect the macroscopic mechanical properties of a metal...

For the numerical simulations of physical and mechanical behaviors of materials at the micro-nano scale, a coupled model with the effect of local quantum is presented in this paper. Unlike traditional methods, the transition region is not needed since the non-local mechanical effects and the constitutive relations are naturally involved by first principle density functional calculations. In order to identify and calculate the mechanical quantities at different scales, some ne...

Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom. The present paper gives a full description of the quasicontinuum method, with special reference to t...

Multiscale modeling of material properties has emerged as one of the grand challenges in material science and engineering. We provide a comprehensive, though not exhaustive, overview of the current status of multiscale simulations of materials. We categorize the different approaches in the spatial regime into sequential and concurrent, and we discuss in some detail representative methods in each category. We classify the multiscale modeling approaches that deal with the tempo...

The most essential concept in concurrent multiscale methods involving atomistic-continuum coupling is how to define the relation between atomistic and continuum regions. A well-known coupling method that has been frequently employed in different concurrent multiscale methods such as Quasicontinuum is the strong compatibility coupling (SCC). Although the SCC is a highly accurate coupling method, it constrains the mesh generation and restricts the reduction of computational cos...

Predicting the structural response of advanced multiphase alloys and understanding the underlying microscopic mechanisms that are responsible for it are two critically important roles modeling plays in alloy development. An alloys demonstration of superior properties, such as high strength, creep resistance, high ductility, and fracture toughness, is not sufficient to secure its use in widespread application. Still, a good model is needed, to take measurable alloy properties,...

Ultra-precision machining of metals, the breaking of nanowires under tensile stress and fracture of nanoscale materials are examples of technologically important processes which are both extremely difficult and costly to investigate experimentally. We describe a multiscale method for the simulation of such systems in which the energetically active region is modelled using a robust tight-binding scheme developed at the Naval Research Laboratory (NRL-TB) and the rest of the sys...

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in system description across the interface between two scales, can be satisfactorily overcome by the proposed method. We propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equatio...

We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of 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 continuum regions. These conditions ensure the accurate passage of large scale information between the atomistic and continuum regions and ...

We discuss how simulations of mechanical properties of materials require descriptions at many different length scales --- from the nanoscale where an atomic description is appropriate, through a mesoscale where dislocation based descriptions may be useful, to macroscopic length scales. In some materials, such as nanocrystalline metals, the range of length scales is compressed and a polycrystalline material may be simulated at the atomic scale. The first part of the paper desc...