Imposing the above generic structure on the evolution loop limits the ways to couple two submodels. A coupling amounts to an exchange of data between a pair of operators belonging to the SEL of the two submodels. According to our definitions, the sender of information is either Oi or Of. Note that the SSM can give a quick estimate of the CPU time gained by the scale splitting process when it concerns a mesh-based calculation.
Decompose the surface topography parameter
- Machine learning provides the appropriate tools towards supplementing training data, preventing overfitting, managing ill-posed problems, creating surrogate models, and quantifying uncertainty with the ultimate goal being to explore massive design spaces and identify correlations.
- To further illustrate the fact that the SSM is a powerful way to describe a multi-scale, multi-science problem, let us consider the SSM corresponding to a real problem with more than two submodels.
- The forest–savannah–fire example uses cellular automata to model grasslands that evolve into forests which are occasionally affected by forest fires 19.
- At each step the feature map from the channel-wise encoder is concatenated with previously generated prediction segments and passed through a linear layer to generate the next prediction segment (part).
- As discussed in the next section, only a few couplings seem to occur in these examples.
The surface contact stiffness shows a trend of increasing sharply and then leveling off as the surface contact pressure increases, as demonstrated by Fig. The surface contact stiffness decreases with the surface roughness increases when the surface contact pressure is constant. The surface contact stiffness is more obviously affected by the three-dimensional surface roughness when the contact pressure increases. This is because the ability of the surface to resist deformation decreases with the increase of the three-dimensional surface roughness. In order to explore the influence of different surfaces on contact performance, the surface contact parameters are analyzed under different normal displacements. For a matching node i on the surface of 45 steel materials with unusual processing methods, the contact pressure at the node is pi, which has the following relationship with the contact state at the node3, 30.
Exploring massive design spaces
For the grinding surface, the reconstruction error corresponding to the wavelet basis function of the sym7 is small overall, and the minimum slope of the fitting line is 3.236e–15 according to Eq. Consequently, the sym7 wavelet basis function is determined as the optimal wavelet basis function for the grinding surface. Likewise, for the milling surface, the reconstruction error corresponding to the sym6 wavelet basis function is small overall, and the slope of the fitting line is 2.77e–15 according to Eq. Accordingly, the sym6 wavelet basis function is determined as the optimal wavelet basis function for the milling surface.
Material Science
Beyond its methodological contents, MMSF is operational and supported by a full implementation and execution framework, based on MUSCLE 2 and the idea of DMC and multi-scale parallelism. The MUSCLE 2 middleware offers a powerful, flexible and easy full-stack developer way to couple new or legacy submodels, independently of the programming language used to code them. The second application we briefly discuss here is the suspension fluid example.
The plastic contact area of RS-1 with smaller surface roughness changes rapidly, while the plastic contact area of RS-3 with larger surface roughness changes slowly. 14d–f, the contact area of RS-4, RS-5 and RS-6 increases slowly with the increase of normal displacement. Compared with the surface with larger roughness, the total contact area of the reconstructed milling surface with smaller roughness accounts for a larger proportion. The reconstructed surfaces with different roughness are used to analyze the influence of surface roughness on the contact surface stiffness.
In essence, the number of large-scale systems level tests that were previously used to validate a design was reduced to nothing, thus warranting the increase in simulation results of the complex systems for design verification and validation purposes. The multi-scale analysis is literally the means of the analysis that will combine the behavior or the properties of both structure bodies with different scales. To put into a few words, there are various methods to approach and one of the techniques such as the homogenization method has been well known as a typical method.