V. Sorkin, R. S. Elliott and E. B. Tadmor
Modelling and Simulation in Materials Science and Engineering, 22, 055001 (2014).
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.