A local quasicontinuum method for 3D multilattice crystalline materials: Application to shape-memory alloys
V. Sorkin, R. S. Elliott and E. B. Tadmor
Modelling and Simulation in Materials Science and Engineering, 22, 055001 (2014).

ABSTRACT
The quasicontinuum (QC) method, in its local (continuum) limit, is applied to
materials with a multilattice crystal structure. Cauchy–Born (CB) kinematics,
which accounts for the shifts of the crystal motif, is used to relate atomic
motions to continuum deformation gradients. To avoid failures of CB kinematics,
QC is augmented with a phonon stability analysis that detects lattice period
extensions and identifies the minimum required periodic cell size. This approach
is referred to as Cascading Cauchy–Born kinematics (CCB). In this paper, the
method is described and developed. It is then used, along with an effective
interaction potential (EIP) model for shape-memory alloys, to simulate the
shape-memory effect and pseudoelasticity in a finite specimen. The results of
these simulations show that (i) the CCB methodology is an essential tool that is
required in order for QC-type simulations to correctly capture the first-order
phase transitions responsible for these material behaviors, and (ii) that the
EIP model adopted in this work coupled with the QC/CCB methodology is capable of
predicting the characteristic behavior found in shape-memory alloys.