Computational Methods for Structure-Property Relations in Heterogeneous Materials

The overall theme of the research is focused on the behavior of heterogeneous functional and structural materials; more specifically, on new computational methods for the prediction of structure-property relations in settings that existing methods cannot handle. Under this theme, there are three distinct though related projects: (1) Grain Evolution with Experimentally-derived Interface Properties. Threshold dynamics model is applied to simulate 3D isotropic grain growth with experiment data. The simulations use the reconstructed microstructures from experiment of a nickle sample before annealing as the input, and try to match the experimentally observed microstructures at different anneal states. Statistical analyses on both simulated and observed microstructures are conducted and compared. While the isotropic simulations are validated to promote grain growth isotropically, it cannot fully reproduce the observed microstructures. Possible reasons for

the mismatch are studied and presented. (2) Modeling of Dislocation Dynamics in Metals. The 3D Phase Field Dislocation Dynamics (PFDD) model is extended to body-centered cubic (BCC) metals by accounting for the dependence of the Peierls barrier on the line-character of the dislocation. Simulations of the expansion of a dislocation loop belonging to the f110g h111i slip system are presented with direct comparison to Molecular Statics (MS) simulations. The extended PFDD model is able to capture the salient features of dislocation loop expansion predicted by MS simulations. The model is also applied to simulate the motion of a straight screw dislocation through kinkpair

motion. Furthermore, PFDD formulation is adapted to use non-orthogonal grids that are constructed with lattice primitives. Simulations with the non-orthogonal grids show improved performance when comparing to the rotated grids used before. A test with two dislocation loops on two non-coplanar slip planes annihilating each other demonstrates the advantages of using the non-orthogonal grids.

(3) Computational Methods for High-contrast Composites. This project applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various fixed-point methods to solve the problem on the periodic unit cell. These have proven extremely powerful in a range of problems ranging from image-based modeling to dislocation plasticity. However, the fixed-point iterations can converge

very slowly, or not at all, if the elastic properties have high contrast, such as in the case of voids. The reasons for slow, or lack of convergence, are examined in terms of a variational perspective. In particular, when the material contains regions with zero or very small stiffness, there is lack of uniqueness, and the energy landscape has flat or shallow directions. Therefore, in this work, the fixed-point iteration is replaced by the RPM iteration. The RPM uses the fixed-point iteration to adaptively identify the subspace on which fixed-point iterations are unstable, and performs Newton iterations only on the unstable subspace, while

fixed-point iterations are performed on the complementary stable subspace. This combination of efficient fixed-point iterations where possible, and expensive but well-convergent Newton iterations where required, is shown to lead to robust and efficient convergence of the method. In particular, RPM-FFT converges well for a wide range of choices of the reference medium, while usual fixed-point iterations are usually sensitive to this choice.