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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. Static elastic cloaking, low-frequency elastic wave transparency and neutral inclusions

   https://doi.org/10.1098/rspa.2019.0725  

   Norris, Andrew N.; Parnell, William J. (August 2020, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   null (Ed.)

   New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low-frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core–shell composite cylinder as a neutral elastic inclusion. Two types of NI are distinguished, weak and strong with the former equivalent to low-frequency transparency and the classical Christensen and Lo generalized self-consistent result for in-plane shear from 1979. Our introduction of the strong NI is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed ‘unphysical’ materials. The relationships between low-frequency transparency, static cloaking and NIs provide the material designer with options for achieving elastic cloaking in the quasi-static limit. 

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