A priori error analysis of two force-based atomistic/continuum models of a periodic chain

作者：Makridakis Charalambos; Ortner Christoph^*; Sueli Endre

来源：Numerische Mathematik, 2011, 119(1): 83-121.

DOI：10.1007/s00211-011-0380-5

The force-based quasicontinuum (QCF) approximation is a non-conservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a new concept of atomistic stress. Moreover, we formulate a new atomistic/continuum coupling mechanism based on coupling stresses instead of forces and extend the a priori analysis to this new method. We show that the new method has several theoretical advantages over the original QCF method.

• 出版日期2011-9