Graduate and Postdoctoral Studies
Physics & Astronomy
Multi-scale calculation based on dual domain material point method combined with molecular dynamics
Thursday, February 16, 2017
to 4:00 PM
254 Herman Brown Hall
This dissertation combines the dual domain material point method (DDMP) with molecular dynamics (MD) in an attempt to create a multi-scale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically non-equilibrium state, and conventional constitutive relations are often not available. In this method, the
closure quantities, such as stress, at each material point are calculated from a MD simulation of a group of atoms surrounding the material point. Rather than restricting
the multi-scale simulation in a small spatial region, such as phase interfaces, or crack
tips, this multi-scale method can be used to consider non-equilibrium thermodynamic
effects in a macroscopic domain. This method takes advantage that the material points only communicate with mesh nodes, not among themselves; therefore MD simulations for material points can be performed independently in parallel.
First, using a one-dimensional shock problem as an example, the numerical properties of the original material point method (MPM), the generalized interpolation
material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the DDMP method are investigated. Among these methods, only the DDMP method converges as the number of particles increases, but the large number of particles needed for convergence makes the method very expensive especially in our multi-scale method where we calculate stress in each material point using MD simulation. To improve DDMP, the sub-point method is introduced in this dissertation, which provides high quality numerical solutions with a very small number of
The multi-scale method based on DDMP with sub-points is successfully implemented for a one dimensional problem of shock wave propagation in a cerium crystal. The MD simulation to calculate stress in each material point is performed in GPU
using CUDA to accelerate the computation. The numerical properties of the multi-scale method are investigated as well as the results from this multi-scale calculation are compared with direct MD simulation results to demonstrate the feasibility of the method. Also, the multi-scale method is applied for a two dimensional problem of jet formation around copper notch under a strong impact.