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1. Analysis of the Postbuckling Response of Nonlocal Plates Via Fractional-Order Continuum Theory

   https://doi.org/10.1115/1.4049224  

   Sidhardh, Sai; Patnaik, Sansit; Semperlotti, Fabio (April 2021, Journal of Applied Mechanics)

   null (Ed.)

   Abstract We present a comprehensive study on the postbuckling response of nonlocal structures performed by means of a frame-invariant fractional-order continuum theory to model the long-range (nonlocal) interactions. The use of fractional calculus facilitates an energy-based approach to nonlocal elasticity that plays a fundamental role in the present study. The underlying fractional framework enables mathematically, physically, and thermodynamically consistent integral-type constitutive models that, in contrast to the existing integer-order differential approaches, allow the nonlinear buckling and postbifurcation analyses of nonlocal structures. Furthermore, we present the first application of the Koiter’s asymptotic method to investigate postbifurcation branches of nonlocal structures. Finally, the theoretical framework is applied to study the postbuckling behavior of slender nonlocal plates. Both qualitative and quantitative analyses of the influence that long-range interactions bear on postbuckling response are undertaken. Numerical studies are carried out using a 2D fractional-order finite element method (f-FEM) modified to include a combination of the Newton–Raphson and a path-following arc-length iterative methods to solve the system of nonlinear algebraic equations that govern the equilibrium beyond the critical points. The present framework provides a general foundation to investigate the postbuckling response of potentially any type of nonlocal structure. 

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2. On the role of the microstructure in the deformation of porous solids

   https://doi.org/10.1038/s41524-022-00840-5  

   Patnaik, Sansit; Jokar, Mehdi; Ding, Wei; Semperlotti, Fabio (July 2022, npj Computational Materials)

   Abstract This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure. Then, a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response. The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams. The performance, evaluated both in terms of accuracy and computational efficiency, is directly contrasted with high-fidelity finite element models that fully resolve the pores’ geometry. Results indicate that the reduced-order representation of the porous microstructure, captured by the synthetic variable-order parameter, offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity. 

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3. Analysis of a 3D nonlinear moving boundary problem describing fluid-mesh-sell interaction

   Suncica Canic, Marija Galic (January 2020, Transactions of the American Mathematical Society)

   Abstract. We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the time-dependent Navier- Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap- plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains. 

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4. Strain-mediated magneto-electric interactions in hexagonal ferrite and ferroelectric coaxial nanofibers

   https://doi.org/10.1557/mrc.2020.30  

   Liu, Y.; Zhou, P.; Fu, J.; Iyengar, M.; Liu, N.; Du, P.; Xiong, Y.; Moiseienko, V.; Zhang, W.; Zhang, J.; et al (June 2020, MRS Communications)

   Abstract This report is on the synthesis by electrospinning of multiferroic core-shell nanofibers of strontium hexaferrite and lead zirconate titanate or barium titanate and studies on magneto-electric (ME) coupling. Fibers with well-defined core–shell structures showed the order parameters in agreement with values for nanostructures. The strength of ME coupling measured by the magnetic field-induced polarization showed the fractional change in the remnant polarization as high as 21%. The ME voltage coefficient in H-assembled films showed the strong ME response for the zero magnetic bias field. Follow-up studies and potential avenues for enhancing the strength of ME coupling in the core–shell nanofibers are discussed. 

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5. Dynamic nonlocal passive scalar subgrid-scale turbulence modeling

   https://doi.org/10.1063/5.0106733  

   Seyedi, S. Hadi; Akhavan-Safaei, Ali; Zayernouri, Mohsen (October 2022, Physics of Fluids)

   Extensive experimental evidence highlights that scalar turbulence exhibits anomalous diffusion and stronger intermittency levels at small scales compared to that in fluid turbulence. This renders the corresponding subgrid-scale dynamics modeling for scalar turbulence a greater challenge to date. We develop a new large eddy simulation (LES) paradigm for efficiently and dynamically nonlocal LES modeling of the scalar turbulence. To this end, we formulate the underlying nonlocal model starting from the filtered Boltzmann kinetic transport equation, where the divergence of subgrid-scale scalar fluxes emerges as a fractional-order Laplacian term in the filtered advection–diffusion model, coding the corresponding superdiffusive nature of scalar turbulence. Subsequently, we develop a robust data-driven algorithm for estimation of the fractional (noninteger) Laplacian exponent, where we, on the fly, calculate the corresponding model coefficient employing a new dynamic procedure. Our a priori tests show that our new dynamically nonlocal LES paradigm provides better agreement with the ground-truth filtered direct numerical simulation data in comparison to the conventional static and dynamic Prandtl–Smagorinsky models. Moreover, in order to analyze the numerical stability and assessing the model's performance, we carry out comprehensive a posteriori tests. They unanimously illustrate that our new model considerably outperforms other existing functional models, correctly predicting the backscattering phenomena and, at the same time, providing higher correlations at small-to-large filter sizes. We conclude that our proposed nonlocal subgrid-scale model for scalar turbulence is amenable for coarse LES and very large eddy simulation frameworks even with strong anisotropies, applicable to environmental applications. 

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