Abstract
This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.
Highlights
Some of the most fascinating problems in all fields of science involve multiple temporal or spatial scales
As typical applications we presented methods for the generation of realistic microstructures of polycrystalline solids in 3D which can be used for finite element methods (FEM) analysis on the macroscale including micro structural details
Results of molecular dynamics (MD) and non-equilibrium MD simulation (NEMD) shock impact simulations employing a multiscale model based on microscopic soft particles were presented and the potential of the model for the description of macroscopic properties of brittle materials was demonstrated
Summary
Some of the most fascinating problems in all fields of science involve multiple temporal or spatial scales. The typical hierarchical structural features of materials have to be taken into account when developing mathematical and numerical models which describe their behavior With this respect, usually one of two possible strategies is pursued: In a “sequential modeling approach” one attempts to piece together a hierarchy of computational approaches in which large-scale models use the coarse-grained representations with information obtained from more detailed, smaller-scale models (“bottom-up” vs “top-down” approach). One attempts to link methods appropriate at each scale together in a combined model, where the different scales of the system are considered concurrently and often communicate with some type of hand-shaking procedure [33,34,35] This approach is necessary for systems, whose behavior at each scale inherently depends strongly on what happens at the other scales, for example dislocations, grain boundary structure, or dynamic crack propagation in polycrystalline materials.
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