OUR CURRENT RESEARCH AREAS (PPT PRESENTATION
A1: LINKing AND Unifying Atomistic and Continuum DescriptionS
Historically, atomistic and continuum descriptions offer two fundamentally different approaches to our understanding and description of matter. From the atomistic viewpoint, matter consists of discrete particles; while from the continuum viewpoint, matter is infinitely divisible. The continuum view leads to formulations of field equations of conservation laws. Supplemented by constitutive relations, such as Hooke’s law and Fourier’s law, these conservation equations serve as the governing equations in continuum modeling of materials.
Our research seeks a theoretical formulation that links and unifies the atomistic and continuum descriptions. For this purpose, we have been working on a formalism to extend Irving and Kirkwood’s statistical mechanical theory of transport processes for ensemble-averaged homogenized systems to a concurrent atomistic-continuum description of crystalline materials. The formalism employs the two-level structural description of crystals in Solid State Physics (i.e., crystal structure =lattice +basis) to include the internal degrees of freedom of atoms within each material point in a continuum description. The Theory of Generalized Functions is employed as the mathematical tool to describe physical phenomena involving discontinuous or singular functions and to enable a rigorous solution to the mathematical difficulties in linking discrete and field descriptions.
This formulation offers a unified atomistic-continuum representation of field quantities and conservation laws that are mathematically and physically valid at multiple length and time scales. It has two significances:
- It can serve as an atomistic theory for concurrent atomistic-continuum simulation of coupled microstructural, mechanical, and thermal transport processes under a single set of governing equations.
- It can provide consistent formulas for calculations of field quantities, such as stress and heat flux, in atomistic, coarse-grained atomistic, or concurrent atomistic-continuum simulations of heterogeneous materials or highly nonequilibrium processes.
Selected Publications
A2: Concurrent Atomistic-Continuum Methods and Tools
Development of multiscale methods has been a major focus of simulation-based engineering science in the past decades; yet most of existing multiscale methods are only applicable to static problems. The key challenge is to interface atomistic models with continuum mechanics, since across this interface there is a change in materials description and governing equations, and consequently spurious wave reflections at the numerical interface, rendering most existing multiscale methods powerless in dynamic simulations. Our approach to this problem builds on our theoretical formulation that links and unifies atomistic and continuum representation of conservation laws and field quantifies. Supplemented with an interatomic potential, the conservation equations completely determine the materials behavior in space and time, naturally leading to a concurrent atomistic-continuum (CAC) methodology.
Different from other multiscale tools, CAC represents both the atomic and continuum regions with the exact same governing equations, admits propagation of phonons, cracks, and dislocations in the finite element regions, and can be exercised under steady-state or highly transient conditions to study the interplay of atomic and higher scale structural hierarchy in the dynamics of defects and phonons. Three computer codes that have implemented the CAC formulation with a modified finite element method have been published:
- PyCAC: https://link.springer.com/article/10.1557/jmr.2018.8
- CAC: https://doi.org/10.1016/j.commatsci.2017.11.051
- CAC-in-LAMMPS: https://doi.org/10.1016/j.jcp.2022.111140
A3: Atomistic and Multiscale mechanics
Fracture and plasticity are problems that the society has faced for as long as there have been man-made structures or materials. Historically, classical continuum mechanics has provided the main theoretical and computational tools for understanding fracture or plasticity. However, the mathematical framework that has been developed for continuum mechanics is not well suited to the simulation of discontinuities such as cracks or dislocations, since the governing equations of continuum mechanics are partial differential equations, and the presence of the spatial derivatives requires continuity of the material. Therefore, cracks within a material have to be treated as surface boundaries of the material, and it is very difficult to model dislocations or slips by classical continuum mechanics-based methods.
Moreover, advanced materials are typically complex involving multiple morphological length scales. For example, a polycrystalline material may have an average grain size of 50-100 μm, whereas the average thickness of the grain boundaries may just be a few angstroms to a few nanometers. It is well known that polycrystalline materials are usually stronger and tougher than single crystals. The grain boundaries are what are responsible for the increased strength and toughness because they impede the motion of dislocation or cracks. Therefore, for a simulation to predict the strength or toughness of a polycrystal, it must span multiple length and time scales from the atomic to the meso or macroscale.
Our mechanics research aims to predict and visualize the atomic and multiscale processes that lead to materials phenomena at the meso or macroscale, including nucleation and propagation of cracks and dislocations, as well as their interactions with materials interfaces. We have been using atomistic and multiscale simulations to investigate mechanisms for deformation and failure of multiscale structured materials such as polycrystalline materials, multilayered structures, superlattices, periodically structured metamaterials, etc.
Selected Publications
A4: Coupled defect dynamics and phonon thermal transport
Dislocations are ubiquitous crystallographic defects that form during materials synthesis or during thermal or mechanical processes. Dynamics of atoms in crystals, which are best described in terms of phonons, are inevitably influenced by the interaction between dislocations and phonons. This interaction is the basis for the microscopic description and understanding of many materials phenomena, including plastic flow, internal friction, and thermal resistance. Our understanding of this interaction, however, is limited.
The multiscale dislocation structures in meso-to macroscale materials or heterostructures and consequently the interaction between phonons and dislocations are too complex to be addressed using only today’s nanoscale computational tools such as Density Functional Theory and Molecular Dynamics. State of the art mesoscale simulation tool for thermal transport is the first principle-based BTE (Boltzmann Transport Equation), in which phonons are the fundamental entities, while that for dislocations is the atomisticaly-informed DDD (Discrete Dislocation Dynamics), in which dislocations are the only simulated moving entities. These methods have contributed to our understanding of phonon transport and dislocation dynamics, respectively, but they cannot be coupled in one simulation to study phonon-dislocation interactions. The challenge to addressing the problem of the phonon-dislocation interaction thus lies not only in the disparate length and time scales involved in the physical processes of phonon scattering by dislocations, but also in the dynamically coupled dislocation dynamics and phonon transport, which traditionally belong to two different disciplines.
Our research aims to address this challenge by establishing a multiscale methodology from machine learning of high-fidelity interatomic potentials to concurrent atomistic-continuum simulation of coupled dislocations dynamics and phonon transport. This will enable an accurate description of dislocations in the studies of phonon thermal transport, as well as a visualization of the transient processes of phonon scattering with multiscale details of the physical processes to identify the underlying mechanisms. It is expected that this research will build capabilities to predict physical processes involving collective dynamics of phonons and dislocations across multiple length and time scales, and will establish a fundamental understanding on the physical nature of phonon-dislocation interaction and its effect on phonon thermal transport.