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1. Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents

   https://doi.org/10.3390/fluids5040189  

   Xie, Xuping; Nolan, Peter J.; Ross , Shane D.; Mou , Changhong; Iliescu, Traian (December 2020, Fluids)

   null (Ed.)

   There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote α-ROM and λ-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the α-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs’ accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis. 

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2. Method for the biomechanical analysis of aqueous veins and perilimbal sclera by three-dimensional photoacoustic imaging and strain field calculation

   https://doi.org/10.1038/s41598-021-01458-1  

   Ni, Linyu; Riesterer, John; Wang, Huaizhou; Berry, Layla; Blackburn, Kara; Chuang, Jonathan; Kim, Wonsuk; Xu, Guan; Moroi, Sayoko E.; Argento, Alan (December 2021, Scientific Reports)

   Abstract A method motivated by the eye’s aqueous veins is described for the imaging and strain calculation within soft biological tissues. A challenge to the investigation of the biomechanics of the aqueous vein—perilimbal sclera tissue complex is resolution of tissue deformations as a function of intraocular pressure and the subsequent calculation of strain (a normalized measure of deformation). The method involves perfusion of the eye with a contrast agent during conduction of non-invasive, optical resolution photoacoustic microscopy. This imaging technique permits three-dimensional displacement measurements of tracked points on the inner walls of the veins which are used in a finite element model to determine the corresponding strains. The methods are validated against two standard strain measurement methods. Representative porcine globe perfusion experiments are presented that demonstrate the power of the method to determine complex strain fields in the veins dependent on intraocular pressure as well as vein anatomy. In these cases, veins are observed to move radially outward during increases in intraocular pressure and to possess significant spatial strain variation, possibly influenced by their branching patterns. To the authors’ knowledge, these are the only such quantitative, data driven, calculations of the aqueous vein strains available in the open literature. 

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3. COMPARING THE MESOSCALE AND MICROSCALE MECHANICAL PROPERTIES OF RAT LUNG TISSUE USING COMPUTATIONAL MODELING

   https://doi.org/10.1142/S0219519423500756  

   DIMBATH, ELIZABETH; GEORGE, STEPHANIE; BRÁS, LISANDRA DE; VADATI, ALEX (September 2023, Journal of Mechanics in Medicine and Biology)

   Current literature reports a wide range of stiffness values and constitutive models for lung tissue across different spatial scales. Comparing the reported lung tissue stiffness values across different spatial scales may provide insights into how well those mechanical properties and the proposed constitutive models represent lung tissue’s mechanical behavior. Thus, this study applies in silico modeling to compare and potentially bridge the differences reported in lung tissue mechanical properties at different length scales. Specifically, we predicted the mesoscale mechanical behavior of rat lung tissue based on in situ and in vitro microscale test data using finite element (FE) analysis and compared those computational predictions to the reported data using mesoscale uniaxial experiments. Our simulations showed that microscale-based stiffness values differed from the mesoscale data in the simulated strain range of 0–60%, with the atomic force microscopy (AFM)-based data overestimating the mesoscale data above 15% strain. This research demonstrates that computational modeling can be used as an informative and guiding tool to investigate and potentially bridge the differences in reported lung tissue material properties across length scales. 

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4. Recent In Situ Experimental and Theoretical Advances in Severe Plastic Deformations, Strain-Induced Phase Transformations, and Microstructure Evolution under High Pressure

   https://doi.org/10.2320/matertrans.MT-MF2022055  

   Levitas, Valery I. (January 2023, MATERIALS TRANSACTIONS)

   Severe plastic deformations (SPD) under high pressure, mostly by high-pressure torsion, are employed for producing nanostructured materials and stable or metastable high-pressure phases. However, they were studied postmortem after pressure release. Here, we review recent in situ experimental and theoretical studies of coupled SPD, strain-induced phase transformations (PTs), and microstructure evolution under high pressure obtained under compression in diamond anvil cell or compression and torsion in rotational diamond anvil cell. The utilization of x-ray diffraction with synchrotron radiation allows one to determine the radial distribution of volume fraction of phases, pressure, dislocation density, and crystallite size in each phase and the main laws of their evolution and interaction. Coupling with the finite element simulations of the sample behavior allows the determination of fields of all components of the stress and plastic strain tensors and volume fraction of high-pressure phase and provides a better understanding of ways to control occurring processes. Atomistic, nanoscale and scale-free phase-field simulations allow elucidation of the main physical mechanisms of the plastic strain-induced drastic reduction in phase transformation pressure (by one to two orders of magnitude), the appearance of new phases, and strain-controlled PT kinetics in comparison with hydrostatic loading. Combining in situ experiments with multiscale theory potentially leads to the formulation of methods to control strain-induced PT and microstructure evolution and designing economic synthetic paths for the defect-induced synthesis of desired high-pressure phases, nanostructures, and nanocomposites. 

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5. Quasi three-dimensional deformable blade element and unsteady vortex lattice reduced-order modeling of fluid–structure interaction in flapping wings

   https://doi.org/10.1063/5.0129128  

   Schwab, R.; Reade, J.; Jankauski, M. (December 2022, Physics of Fluids)

   Flapping, flexible insect wings deform under inertial and fluid loading. Deformation influences aerodynamic force generation and sensorimotor control, and is thus important to insect flight mechanics. Conventional flapping wing fluid–structure interaction models provide detailed information about wing deformation and the surrounding flow structure, but are impractical in parameter studies due to their considerable computational demands. Here, we develop two quasi three-dimensional reduced-order models (ROMs) capable of describing the propulsive forces/moments and deformation profiles of flexible wings. The first is based on deformable blade element theory (DBET) and the second is based on the unsteady vortex lattice method (UVLM). Both rely on a modal-truncation based structural solver. We apply each model to estimate the aeromechanics of a thin, flapping flat plate with a rigid leading edge, and compare ROM findings to those produced by a coupled fluid dynamics/finite element computational solver. The ROMs predict wing deformation with good accuracy even for relatively large deformations of 25% of the chord length. Aerodynamic loading normal to the wing's rotation plane is well captured by the ROMs, though model errors are larger for in-plane loading. We then perform a parameter sweep to understand how wing flexibility and mass affect peak deflection, mean lift and average power. All models indicate that flexible wings produce less lift but require lower average power to flap. Importantly, these studies highlight the computational efficiency of the ROMs—compared to the convention modeling approach, the UVLM and DBET ROMs solve 4 and 6 orders of magnitude faster, respectively. 

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