A goal-oriented adaptive procedure for the quasi-continuum method with cluster approximation
Artikel i vetenskaplig tidskrift, 2015

We present a strategy for adaptive error control for the quasi-continuum (QC) method applied to molecular statics problems. The QC-method is introduced in two steps: Firstly, introducing QC-interpolation while accounting for the exact summation of all the bond-energies, we compute goal-oriented error estimators in a straight-forward fashion based on the pertinent adjoint (dual) problem. Secondly, for large QC-elements the bond energy and its derivatives are typically computed using an appropriate discrete quadrature using cluster approximations, which introduces a model error. The combined error is estimated approximately based on the same dual problem in conjunction with a hierarchical strategy for approximating the residual. As a model problem, we carry out atomistic-to-continuum homogenization of a graphene monolayer, where the Carbon-Carbon energy bonds are modeled via the Tersoff-Brenner potential, which involves next-nearest neighbor couplings. In particular, we are interested in computing the representative response for an imperfect lattice. Within the goal-oriented framework it becomes natural to choose the macro-scale (continuum) stress as the "quantity of interest". Two different formulations are adopted: The Basic formulation and the Global formulation. The presented numerical investigation shows the accuracy and robustness of the proposed error estimator and the pertinent adaptive algorithm.

Cluster approximation

NONLINEAR MECHANICS

DEFORMATION

FORMULATION

Mathematics

Mechanics

Goal-oriented adaptivity

Graphene

ERROR CONTROL

GRAIN-BOUNDARIES

LAYER GRAPHENE

ATOMIC-SCALE

SHEETS

Quasi-continuum

STRENGTH

NANOINDENTATION

Interdisciplinary Applications

Författare

Arash Memarnahavandi

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik

Fredrik Larsson

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik

Kenneth Runesson

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik

Computational Mechanics

0178-7675 (ISSN) 1432-0924 (eISSN)

Vol. 55 617-642

Ämneskategorier

Maskinteknik

Drivkrafter

Hållbar utveckling

DOI

10.1007/s00466-015-1127-4