Related papers: Convergence of a force-based hybrid method for ato…
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the…
Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…
We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for…
Inspired by the blending method developed by [P. Seleson, S. Beneddine, and S. Prudhome, \emph{A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity}, (2013)] for the nonlocal-to-local coupling, we create a symmetric and…
We prove long-time existence of solutions for the equations of atomistic elastodynamics on a bounded domain with time-dependent boundary values as well as their convergence to a solution of continuum nonlinear elastodynamics as the…
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with coarse-grained models away from the defects. Quasicontinuum…
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
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…
We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functional acting on the deformation gradient in the…
We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predictions. We present a range of numerical experiments studying…
In this paper we construct energy based numerical methods free of ghost forces in three dimensional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite…
We present sharp convergence results for the Cauchy--Born approximation of general classical atomistic interactions, for both static and dynamic problems, for small data.
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
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…
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model remains an open problem. In 1D and 2D,…
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…
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based…