A MULTISCALE VISION-ILLUSTRATIVE APPLICATIONS FROM BIOLOGY TO ENGINEERING

Abstract

Modeling and simulation have quickly become equivalent pillars of research along with traditional theory and experimentation. The growing realization that most complex phenomena of interest span many orders of spatial and temporal scales has led to an exponential rise in the development and application of multiscale modeling and simulation over the past two decades. In this perspective, the associate editors of the International Journal for Multiscale Computational Engineering and their co-workers illustrate current applications in their respective fields spanning biomolecular structure and dynamics, civil engineering and materials science, computational mechanics, aerospace and mechanical engineering, and more. Such applications are highly tailored, exploit the latest and ever-evolving advances in both computer hardware and software, and contribute significantly to science, technology, and medical challenges in the 21st century.

Keywords: applications of modeling to life and physical sciences; biology; computer simulations; engineering; machine learning; multiscale modeling; structural mechanics.

FIG. 1:

The volume of papers and citation-weighted papers from the SCOPUS database with the query words “multiscale” or “multiscaling” in article title, key words, and abstract

FIG. 2:

The 20 scientific disciplines and journals associated with most of the multiscale papers in Fig. 1

FIG. 3:

Multiscale areas relevant to biology. Reproduced from the 2009 DOE report Schlick and Department of Energy (2010)

FIG. 4:

The DNA folding problem. (Left) In eukaryotic cells, the DNA wraps around nucleosomes to form fibers, genes, and chromosomes, at various levels of condensation, taken from Bascom and Schlick (2017). (Right) The different levels of DNA folding can be studied by a variety of computational and experimental tools, but connection strengths (arrow color) are weaker for some levels and along the upper diagonal arrow, taken from Ozer et al. (2015).

FIG. 5:

Mesoscale chromatin model. Coarse-grained beads for the DNA linkers, flexible histone tails, and linker-histone units are combined with a charged irregular surface model for the nucleosome core.

FIG. 6:

Recent mesoscale chromatin model applications. (a) The differentiation state of the cell is correlated to clutch patterns, as illustrated here for neural cells at increasing differentiation from top to bottom (Portillo-Ledesma et al., 2021). (b) Chromatin unfolds upon including acetylated tails in the chromatin mesoscale model (Collepardo-Guevara et al., 2015). (c) Chromatin compartmentalization is directed by the interactions between same-type tails (Rao et al., 2017). (d) A loss of linker histone produces a looser fiber that can be easily transcribed, up regulating certain genes (Yusufova et al., 2021).

FIG. 7:

Bone phases depending on osteoporosis stage (cf. Laboratoires Servier, 2019) and corresponding RVEs

FIG. 8:

Microscale simulation results of a coarse and fine mesh (left and right resp.) (a) Left: σ_xy [GPa], right: D [A s/m²]. Effective Young’s modulus E_eff against cortical bone volume fraction ρ_b for different RVEs (b).

FIG. 9:

Simulation results of the femur bone model for the degenerated (top) and healthy RVE (bottom), t = 25. Left: σ_xy [GPa], right: D [A s/m²].

FIG. 10:

Simulation results of the femur bone model for the degenerated (top) and healthy RVE (bottom), t = 50. Left: H [A/m], right: J [A/m²].

FIG. 11:

Schematics of the VMS method

FIG. 12:

Turbulent flow around immersed sphere at Reynold’s number Re = 10,000

FIG. 13:

Density stratified Plane Couette flow

FIG. 14:

Interfacial kinematic models, progressive interfacial failure, and the VMDG method

FIG. 15:

Sparse multiresolution grid and numerical solution at t = 133.902 μs obtained using p = 8 and ε = 10⁻². (a) MRWT solution of the density field ρ. The grid points are colored according to their resolution level j. (b) MRWT solution of the velocity field $\Vert \overrightarrow{v}{\Vert }_2$. The maximum velocity is approximately 568 m/s. The reader is referred to the online version of this article for clarity regarding the color in this figure. Results are taken from Harnish et al. (2021).

FIG. 16:

Turbine engine disk: (a) prototype engine disk, (b) angular segment of the disk blade simulated in ABAQUS, and (c) von Mises stress contours at the end of the simulation using microstructure MS1

FIG. 17:

Extruded microstructure simulations. Inverse pole figure maps and pole figures of the electron back-scattered diffraction (EBSD) images of two extruded microstructures. (a) MS1. (b) MS2 showing crystallographic orientations.

FIG. 18:

Time history of (a) maximum tensile principal stress, effective plastic strain, and (b) nucleation probability at a critical point C in Fig. 16(c)

FIG. 19:

Wave propagation in viscoelastic and elastic composites as predicted by direct numerical simulation and the asymptotic homogenization models demonstrating the combined attenuating effects of Bragg scattering and viscous damping. The data associated with these results are initially published in Hu and Oskay (2018).

FIG. 20:

Wave propagation in an elastic waveguide predicted by the spectral variational multiscale approach at a fraction of the direct numerical simulation. The results are reprinted from Hu and Oskay (2020).

FIG. 21:

Number of articles published with the phrase “Multiscale Concrete” in the text per Google Scholar

FIG. 22:

Elevation of the pier for the elevated railway in Monterrey, México. The loads represent the bearings of the superstructure beam.

FIG. 23:

Reduced-order methods for infinitesimal (top) and arbitrary size (bottom) RVEs

FIG. 24:

Pier cap. (a) Finite-element mesh of the RVE and its partitions shown in colors. (b) Finite-element mesh of the reinforcement, prestressing, and stirrups.

FIG. 25:

Load versus displacement curve for the pier cap and its corresponding design loads

FIG. 26:

Distribution of location and alignment of short steel fibers: (a) all fibers, (b) θ ∈ [0, π/12], (c) θ ∈ [π/6, π/4], and (d) θ ∈ [π/3, π/12]

FIG. 27:

Finite-element unit cell of a single discontinuous fiber slice

FIG. 28:

Four-point bending test: (a) model schematics (units: mm) and (b) comparison of single-scale, sliced statistical ROH (multiscale) and experimental results