Scale-bridging

Chapter 5 considers the connection between the universal large scale dynamics discussed first and the local specific dynamics discussed in the second step. The dynamics at intermediate length scales bridges the two and we will address the leading mechanism limiting the universal dynamics in flexible polymers. 

To bridge the time-scale gap between microscopic and macroscopic scales and accurately capture dynamic phenomena on the coarsegrained level, systematic time-scale-bridging molecular dynamics was recently introduced by using an alternative MC-MD iteration scheme, which also shows higher calculation efficiency than standard NEMD (Ilg et al, 2009). 

Analysis indicates that large-scale bridging (LSB) is involved and the bridging behavior can be explicitly ascertained from the measured curves.103 For the particular case of a DCB specimen (Fig. 1.38a), the /-integral is explicitly defined in terms of the bending moment, M, and the traction law.13... 

In the paper, the methodology of measuring G c by using DCB specimens in the presence of large-scale bridging is adapted for investigating the delamination in 3D woven composites. 

The delamination of UD composites in the presence of large-scale bridging has been modelled and studied experimentally rather well, and the list of some references can be found in [1, 2]. 

It was shown that, in the presence of large-scale bridging (i.e., when the size of the biidging region is comparable to the crack size), the f -curve is not a material characteristic ind its shape depends on the specimen geometry. In the case of a double-cantilever beam, tht shape of the f -curve depends on the stiffness of specimen arms. 

The first step taken in the attempt to pare down the problem is to exploit the so-called Bom-Oppenheimer approximation. Though this approximation will not enter into our calculations in any material way, it is crucial to our enterprise from a philosophic perspective since it illustrates the way in which degrees of freedom can be unlinked, and thereby, problems can be rendered more tractable. The central physical idea is to separate the nuclear and electronic motions on the basis of the smallness of the ratio m/M, where m is the electron mass and M is that of the relevant nuclei. Indeed, from a multiscale perspective, the Bom-Oppenheimer approximation represents the simplest of cases in which there is a natural separation of scales, upon which may be founded the scale-bridging ansatz. The physical argument that is made is that the electronic motions are so fast relative to the nuclear motions that we may imagine the electrons to respond to an essentially static set of nuclear positions. The outcome of adopting this view is... 

The challenges will involve quantitative ab initio prediction of molecular-level chemistry of thermodynamics and kinetics with no empirical scaling, bridging the gap from the molecular scale to the microscopic (nano- and biological)... 

The common mesoscopic scale of confrontation of the two methods allows for more precise scales bridging and adjust more precisely the rheological parameters for both systems. 

Praprotnik, M., Delle Site, L., and Kremer, K. 2008. Multiscale simulation of soft matter From scale bridging to adaptive resolution. Annual Review of Physical Chemistry 59 545-571. 

Abstract We review recent work on scale-bridging modeling approaches applied to aqueous electrolytes and polyelectrolytes, connecting the local quantum chemical details to classical statistical and thermodynamics properties. We discuss solvation and pairing of ions in water, ways to include solvent degrees of freedom in effective ion-ion interactions, and coarse-grained simulations of polyelectrolytes including dielectric boundary effects. 

Model tests use a small-scale bridge structure to simulate and predict the performance of a full-scale bridge. The equilibrium scour depth is an important parameter, yet requiring a long period to be attained. In such cases, the following procedures are recommended (Guo 2011). 

In the previous chapter, a brief account of the Tacoma Narrows bridge disaster was considered. Tests on scale bridge models are being used today to be sure a proposed structure is not dynamically unstable to excitation due to a Karman Vortex Street that may develop in a high wind. 

Ilg, P., Ottinger, H.C., and Kroger, M. (2009) Systematic time-scale-bridging molecular dynamics applied to flowing polymer melts. Phys. Rev. E, 79, 011802. 

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