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1. Stieltjes functions and spectral analysis in the physics of sea ice

   https://doi.org/10.5194/npg-30-527-2023  

   Golden, Kenneth M; Murphy, N Benjamin; Hallman, Daniel; Cherkaev, Elena (November 2023, Nonlinear Processes in Geophysics)

   Abstract. Polar sea ice is a critical component of Earth’s climate system. As a material, it is a multiscale composite of pure ice with temperature-dependent millimeter-scale brine inclusions, and centimeter-scale polycrystalline microstructure which is largely determined by how the ice was formed. The surface layer of the polar oceans can be viewed as a granular composite of ice floes in a sea water host, with floe sizes ranging from centimeters to tens of kilometers. A principal challenge in modeling sea ice and its role in climate is how to use information on smaller-scale structures to find the effective or homogenized properties on larger scales relevant to process studies and coarse-grained climate models. That is, how do you predict macroscopic behavior from microscopic laws, like in statistical mechanics and solid state physics? Also of great interest in climate science is the inverse problem of recovering parameters controlling small-scale processes from large-scale observations. Motivated by sea ice remote sensing, the analytic continuation method for obtaining rigorous bounds on the homogenized coefficients of two-phase composites was applied to the complex permittivity of sea ice, which is a Stieltjes function of the ratio of the permittivities of ice and brine. Integral representations for the effective parameters distill the complexities of the composite microgeometry into the spectral properties of a self-adjoint operator like the Hamiltonian in quantum physics. These techniques have been extended to polycrystalline materials, advection diffusion processes, and ocean waves in the sea ice cover. Here we discuss this powerful approach in homogenization, highlighting the spectral representations and resolvent structure of the fields that are shared by the two-component theory and its extensions. Spectral analysis of sea ice structures leads to a random matrix theory picture of percolation processes in composites, establishing parallels to Anderson localization and semiconductor physics and providing new insights into the physics of sea ice. 

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2. Quasiperiodic Composites: Multiscale Reiterated Homogenization

   https://doi.org/10.1109/MetaMaterials.2019.8900926  

   Cherkaev, E.; Guenneau, S.; Hutridurga, H.; Wellander, N. (September 2019, 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   With recent technological advances, quasiperiodic and aperiodic materials present a novel class of metamaterials that possess very unusual, extraordinary properties such as superconductivity, unusual mechanical properties and diffraction patterns, extremely low thermal conductivity, etc. As all these properties critically depend on the microgeometry of the media, the methods that allow characterizing the effective properties of such materials are of paramount importance. In this paper, we analyze the effective properties of a class of multiscale composites consisting of periodic and quasiperiodic phases appearing at different scales. We derive homogenized equations for the effective behavior of the composite and discover a variety of new effects which could have interesting applications in the control of wave and diffusion phenomena. 

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3. Order to disorder in quasiperiodic composites

   https://doi.org/10.1038/s42005-022-00898-z  

   Morison, David; Murphy, N. Benjamin; Cherkaev, Elena; Golden, Kenneth M. (December 2022, Communications Physics)

   Abstract From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here. 

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4. Effect of the Print Bed Temperature on Void Distribution within the Microstructure of Short Carbon Fiber Reinforced/ABS Manufactured via Large Area Additive

   Neshat Sayah and Douglas E. Smith (October 2023, Proceedings 2023 International Solid Freeform Fabrication Symposium)

   Short carbon fiber-reinforced polymer composite structures produced using Large Area Additive Manufacturing (LAAM) have garnered significant attention due to the design flexibility, energy savings, and materials selection associated with this process. However, the physical and mechanical properties of the additively manufactured composite parts often fall below expectations due to void formation between printed beads and within the microstructure of individual beads. This study aims to investigate the effect of bed temperature on the microstructure within the beads of two-layer Short Carbon Fiber reinforced Acrylonitrile Butadiene Styrene (SCF/ABS) beads manufactured via the LAAM system. This study employs high-resolution 3D micro-computed tomography (μCT) to evaluate the void shape and distribution within the microstructure of composite parts printed at various bed temperatures. The results of this study demonstrate substantial variation in the void volume fraction among four bead sets deposited at different print bed temperatures. Moreover, within each part, a noticeable discrepancy in void volume fraction is observed between the top and bottom bead of the two-bead test samples. Preliminary results indicate that increasing the bed temperature from 25°C to 75°C reduces void volume fraction within the microstructure of the composite parts. However, an opposite trend emerges when the bed temperature is further increased to 100°C, increasing void volume fraction, which needs further investigation to understand. This study also evaluated the void shapes through the calculation of their sphericity. The preliminary results reveal that as the bed temperature increases from 25°C to 75°C, the voids exhibit higher sphericity within the printed parts as the interconnected voids decrease. 

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5. Scaling of relaxation and excess entropy in plastically deformed amorphous solids

   https://doi.org/10.1073/pnas.2000698117  

   Galloway, K. Lawrence; Ma, Xiaoguang; Keim, Nathan C.; Jerolmack, Douglas J.; Yodh, Arjun G.; Arratia, Paulo E. (May 2020, Proceedings of the National Academy of Sciences)

   When stressed sufficiently, solid materials yield and deform plastically via reorganization of microscopic constituents. Indeed, it is possible to alter the microstructure of materials by judicious application of stress, an empirical process utilized in practice to enhance the mechanical properties of metals. Understanding the interdependence of plastic flow and microscopic structure in these nonequilibrium states, however, remains a major challenge. Here, we experimentally investigate this relationship, between the relaxation dynamics and microscopic structure of disordered colloidal solids during plastic deformation. We apply oscillatory shear to solid colloidal monolayers and study their particle trajectories as a function of shear rate in the plastic regime. Under these circumstances, the strain rate, the relaxation rate associated with plastic flow, and the sample microscopic structure oscillate together, but with different phases. Interestingly, the experiments reveal that the relaxation rate associated with plastic flow at time t is correlated with the strain rate and sample microscopic structure measured at earlier and later times, respectively. The relaxation rate, in this nonstationary condition, exhibits power-law, shear-thinning behavior and scales exponentially with sample excess entropy. Thus, measurement of sample static structure (excess entropy) provides insight about both strain rate and constituent rearrangement dynamics in the sample at earlier times. 

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