Multiscale modelling strategies

In terms of cyclic plasticity, Shenoy et al. [139, 140], Wang et al. [137], and McDowell [141] performed hierarchical multiscale modeling of Ni-based superalloys employing internal state variable theory. Fan et al. [142] performed a hierarchical multiscale modeling strategy for three length scales. 

An essential part of a successful multiscale modelling strategy will be to use several scales in one simulation, where the decisions about the required level of modelling are taken by the computer and not by human intervention. This will require considerable computer science input. Despite this increasing complexity appropriate modelling will remain important, i.e. distilling the essentials of behaviour at each length scale. 

VAN DER HoEF, M. A., VAN SiNT AnNALAND, M., DeEN, N. G. KUIPERS, J. A. M. 2008 Numerical simulation of dense gas-solid fluidized beds a multiscale modeling strategy. Annual Review of Fluid Mechanics 40, Al-10. 

Van der Hoef MA, Van Sint Annaland M, DeenNG, Kuipers JAM Numerical simulation of dense gas-sobd fluidized beds a multiscale modeling strategy, Annu Rev Fluid Mech 40 47-70, 2008. 

We begin by introducing and briefiy discussing the specific computational methods we have used in the present work to implement our multiscale modeling strategy for bcc transition metals. 

J.B. Bassingthwaighte et al., Strategies and tactics in multiscale modeling of cell-to-organ systems, Proceedings of the IEEE, vol. 94 pp. 819-830 (2006)... 

Fio. 4. Types of multiscale modeling and solution strategies. Hybrid models (one model at each scale) apply well when there is separation of scales (onion or nested-type models). When there is lack of separation of scales, mesoscale models need to be developed where the same technique (e.g., MD or MC) is accelerated. Alternatively, multigrid (heterogeneous) hybrid models can be employed where the unresolved degrees of freedom are determined from a finer scale model and passed to a coarser scale model. 

Systems approach borrowed from the optimization and control communities can be used to achieve various other tasks of interest in multiscale simulation. For example, Hurst and Wen (2005) have recently considered shear viscosity as a scalar input/output map from shear stress to shear strain rate, and estimated the viscosity from the frequency response of the system by performing short, non-equilibrium MD. Multiscale model reduction, along with optimal control and design strategies, offers substantial promise for engineering systems. Intensive work on this topic is therefore expected in the near future. 

In multiscale modeling approaches the microscopic behavior of a system is linked by a compression operator to the macroscopic state variable. The strategy is then to use the microscopic model to provide necessary information for extracting the macroscale behavior of the system. Such a combined macro-microscale technique is supposed to be much more efficient than solving the full microscopic... 

There are numerous coupled atomistic-continuum modeling strategies, for example, peridynamics, a family of quasi-continuum (QC) methods, finite element adaptive techniques (FEAt), coupling-of-length scales (CLS) method, and coupled atomistic-and-discrete-dislocalion (CADD) method. The grand challenge of multiscale modeling is to connect atomic-scale processes to mesoscale and bulk continuum models. 

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