1. Sequential and Concurrent Multiscale Modeling of Multiphysics: From Atoms to Continuum

The multiscale and multi-physics approaches reach a new height for modeling and simulation. It opens up a new opportunity to connect engineering applications with basic science. In this work, a more general governing equation of non-equilibrium molecular dynamics, covering thermo-mechanical-electromagnetic coupling effects, has been derived. This theoretical development of classical molecular dynamics provides a solid foundation for our bottom-up sequential multiscale modeling, from which we calculate material properties including the elastic constants, thermal conductivity, specific heat, and thermal expansion coefficients for thermoelasticity. With these preparations, we further present our newly formulated concurrent multiscale theory. The key challenge in constructing a concurrent multiscale theory hinges at the formulation of the interfacial conditions, which determine the communication between the atomic region and genuine continuum region. Our philosophy of concurrent modeling is that we decompose the solution region into two sub-regions in space and utilize the central difference method with different time steps for different sub-regions to march on in time. For sub-regions where critical physical phenomena, such as crack initiation and propagation, occur, we adopt molecular dynamics with small time step to simulate the material behavior with relatively high resolution. For non-critical regions, we adopt finite element method with relatively large time step to reduce the computational effort. The interfacial condition is constructed naturally by anchoring finite element nodes at centroids of groups. Each group is a cluster of atoms simulated by molecular dynamics. In this way, a concurrent multiscale modeling theory from atoms to genuine continuum is constructed. To test the capability of our theory, we conduct crack propagation simulations with different loading conditions. It was observed that the crack that pre-existed in the continuum region can propagate into the critical atomic region without any fracture criterion.