Multi-scale Modeling in Material Science
Multi-scale modeling and simulation in material science is a new booming area in recent years. On the one hand it is an important computing and research method in the design and development of new materials as well as the optimization of existing materials, on the other hand, it brings up many new problems for researchers, especially mathematicians and computational scientific workers. We plan to conduct the following studies.
The scale-span research of lattice mechanical interface instability: there exist a variety of different interfaces, such as grain boundaries, phase boundaries, magnetic domain walls, and two-phase material interface et al. The structure and dynamics of the interface have a great influence on the preparation and some properties, like toughness, of materials. Traditionally, this problem can be studied by using continuous medium interface stability and interfacial wave theory, but the continuum theory cannot reveal the interfacial characteristics and mechanism in atomic scale. We plan to combine atomic-scale dislocation theory of interfacial interactions and continuous medium interface wave theory to come up with a corresponding cross-scale mathematical model, which can be used to study interface, especially the mechanism of grain boundary instability. For this problem, series of molecular dynamics simulation conducted by Professor Jin Zhaohui reveal a wealth of phenomena (like dislocation emission and interface migration) and prompt the atomic scale mechanisms that may exist. The model we propose will verify the results of molecular dynamics simulation and make quantitative prediction to the properties of materials.
The design and analysis of atomic continuous coupling method and its application in research of the defect nature: In many material problems, the results need to reach atomistic simulation accuracy near the defect, for example, the crack tip, the grain boundaries, dislocations, vacancies, etc. However, these localized defects can usually affect a much larger area through long-range elasticity. Materials scientists have come up with many cross-scale calculation methods to get the solutions of these multi-scale models by using atomic model near localized defects, while continuum model near uniform deformation. In recent years, the numerical analysis of the atomic / continuum coupling method help sort out the relationship between the different methods and the causes of error. We plan to study the coupling method and apply it to the numerical simulation of defects study, including the above-mentioned molecular dynamics simulation of interface issues, so we can study the systems that are close to the macro-scale.
Research Fellow Zhang Lei’s research interests are in the design of multi-scale methods and numerical analysis, including the numerical homogenization method of multi-scale inhomogeneous media, and the design and analysis of atomic / continuum coupling methods. Zhang Lei first designed a compatible energy coupling method in the two-dimensional general atoms / continuum interface, and gave the error estimates and the rigorous mathematical proof. Professor Jin Zhaohui’s research interests are in multi-scale material modeling and simulation, mechanical properties of nano-materials, phase change (melting, glass transition, collective / cooperative dynamics in condensate) and so on. Professor Jin Zhaohui has done a series of important work in interfacial dynamics, such as grain boundaries and dislocations’ interactions.