Application of Periodic Domains in Multiscale Simulations of Large MaterialDeformation

Many multiscale simulations use periodic computational domains to consider lower length scale physics and to calculate closure quantities, such as the stress, to drive the macroscopic continuum level calculations. For materials undergoing large or extreme deformations, the computation domains often become highly distorted and need to be reinitialized. Reinitialization causes the loss of history information and accuracy of the simulation.

To avoid this difficulty, we introduce a method (Wang and Zhang, CMAME, 374, 2021; Barclay and Zhang, JCP, 435, 2021) by decomposing the velocity gradient matrix into an upper triangular part and an antisymmetric part representing a pure rotation. We show that the upper triangular part can always be accommodated by a cuboid domain, and the antisymmetric part can be canceled by performing the simulation in a rotating frame of reference. In this way, the domain reinitialization is avoided. Numerical examples are presented to show advantages of this method.