A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids

Abstract

SUMMARYWe present a multiscale method that couples atomistic models with continuum mechanics. The method is based on an overlapping domain-decomposition scheme. Constraints are imposed by a Lagrange multiplier method to enforce displacement compatibility in the overlapping subdomain in which atomistic and continuum representations overlap. An efficient version of the method is developed for cases where the continuum can be modelled as a linear elastic material. An iterative scheme is utilized to optimize the coupled configuration. Conditions for the regularity of the constrained matrices are determined. A method for computing strain in atomistic models and handshake domains is formulated based on a moving least-square approximation which includes both extensional and angle-bending terms. It is shown that this method exactly computes the linear strain field. Applications to the fracture of defected single-layer atomic sheets and nanotubes are given.

Coordinated buckling of thick multi-walled carbon nanotubes under uniaxial compression

“…To improve the computational affordability without sacrificing accuracy, the fully atomistic models employed are here coarse-grained by a quasicontinuum method based on the finite crystal elasticity theory for curved crystalline monolayers [39][40][41]. Within this theoretical framework, the exponential Cauchy-Born rule was proposed as a way of linking the kinematics at the atomic and continuum scales:…”

Concurrently coupled atomistic and XFEM models for dislocations and cracks

“…Furthermore, we define N ⊆ N and E ⊆ E . The fully atomistic domain is then defined by the set of elements e where w C I = 0 for each node of element e. The definition of w C (x) by (16) implies that w C (x) and w A (x) are piecewise linear since we will adopt linear shape functions N I . The elements E and nodes M of the Lagrange multiplier mesh are chosen to coincide with the displacement field elements E where 0<w C (x)<1.…”

On bridging domain methods to couple particle‐ and finite‐element‐based simulations

“…A proposal to do this was given by Zhang, Khare, Lu and Belytschko in [2]. This Staggered Scheme I separates the computations in the continuum and in the particle domain quite far.…”

“…This is realized in this contribution by using a bridging domain method, introduced e.g. by Xu and Belytschko [1], Zhang, Khare, Lu and Belytschko [2] and Bauman et al [3].…”

“…particle-based domain, a so-called bridging domain is considered, e.g. Xu and Belytschko [1], Zhang, Khare, Lu and Belytschko [2] and Bauman et al [3]. The main goal is to separate the computation of finite element and atomistic domains as much as possible, amongst others, to calculate the different domains on several CPUs.…”