相关论文: Atomistic-Continuum Coupling by Homogenization
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…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…
This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled…
Atomic-scale phase-field modeling formulates the probability densities of atomic vibrations as Gaussian distributions and derives a free energy functional using variational Gaussian theory and interatomic potentials. This framework permits…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of…
The quasicontinuum method was originally introduced to bridge across length scales -- from atomistics to significantly larger continuum scales -- thus overcoming a key limitation of classical atomic-scale simulation techniques while solely…
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…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
Atomistic theory holds the promise for the ab initio development of superalloys based on the fundamental principles of quantum mechanics. The last years showed a rapid progress in the field. Results from atomistic modeling enter…
The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries, occurs when the lattice configuration loses stability, that is, when an eigenvalue of the Hessian of the lattice energy functional becomes…
We study a force-based hybrid method that couples atomistic models with nonlinear Cauchy-Born elasticity models. We show that the proposed scheme converges quadratically to the solution of the atomistic model, as the ratio between lattice…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical…
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…
In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphisation requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
We study the behavior of atomistic models in general dimensions under uniaxial tension and investigate the system for critical fracture loads. We rigorously prove that in the discrete-to-continuum limit the minimal energy satisfies a…