Research Topic


[Equilibrium Map] Topic: Cascading Cauchy-Born FEM

Team: Jiadi Fan, Ryan Elliott, Ellad Tadmor

Collaboration: Third Wave Systems, Inc.

Funding: MnDRIVE, University of Minnesota

Figure: A CCB FEM simulation of a shape-memory cycle. The colors correspond to in-plane shear highlighting the phase transformations occurring in the material. In the top row, an austenite specimen is initially cooled to create a random microstructure of martensite. It is then sheared, which causes phase transformations to align the martensitic variants. In the second row, the specimen is heated above its transformation temperature and recovers the original austenite phase returning to its original shape. Thus the material exhibits "memory". Figure taken from Sorkin et al. (2014) (see below).


Description: 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). The result is a finite deformation (nonlinear) finite element formulation that uses an atomist-based constitutive relation capable of modeling phase transformations. The methodology is currently being extended to study applications of interest.


Publications: