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Metal-coated lattice structures hold significant promise for customizing mechanical properties in diverse industrial applications, including the mechanical arms of unmanned aerial vehicles. However, their intricate geometries pose computational challenges, resulting in time-intensive and costly numerical evaluations. This study introduces a parameterization-based multiscale method to analyze body-centered cubic lattice structures with metal coatings. We establish the validity and precision of our proposed method with a comparative analysis of numerical results at the Representative Volume Element (RVE) scale and experimental findings, specifically addressing both elastic tensile and bending stiffness. Furthermore, we showcase the method’s accuracy in interpreting the bending stiffness of coated lattice structures using a homogenized material-based solid model, underscoring its effectiveness in predicting the elastic properties of such structures. In exploring the mechanical characterization of coated lattice structures, we unveil positive correlations between elastic tensile stiffness and both coating thickness and strut diameter. Additionally, the metal coating significantly enhances the structural elastic bending stiffness multiple times over. The diverse failure patterns observed in coated lattices under tensile and bending loads primarily stem from varied loading-induced stress states rather than external factors. This work not only mitigates computational challenges but also successfully bridges the gap between mesoscale RVE mechanical properties and those at the global structural scale.

Image inpainting is pivotal within the realm of image processing, and many efforts have been dedicated to modeling, theory, and numerical analysis in this research area. In this paper, we propose a curvature-dependent elastic bending total variation model for the inpainting problem, in which the elastic bending energy in the phase-field framework introduces geometric information and the total variation term maintains the sharpness of the inpainting edge, referred to as elastic bending-TV model. The energy stability is theoretically proved based on the scalar auxiliary variable method. Additionally, an adaptive time-stepping algorithm is used to further improve the computational efficiency. Numerical experiments illustrate the effectiveness of the proposed model and verify the capability of our model in image inpainting.

One-dimensional (1D) nanomaterials easily bend due to perturbations from their surroundings or their own behaviors. This phenomenon not only impacts the performances of various devices but has also been employed to develop a variety of new functional devices, in which the bending energies of the nanomaterials determine the device performances. However, measuring the energies of such nanomaterials is extremely difficult. Herein, pseudo-break imaging of 1D nanomaterials has been proposed and realized on individual carbon nanotubes (CNTs), in which a CNT appears to break and has a fracture but is actually intact. This imaging approach provides the values of the bending energies of the CNTs with an accuracy of 1–50 eV. Furthermore, this imaging approach can manipulate the bending shapes and energies of CNTs. This work presents a protocol for bending analysis and manipulation, which are vital to fundamental and applied studies of 1D nanomaterials.

Metallic wire mesh has gained attention as a potential material for lightweight aircraft structures, e.g., a metallic frame of morphing wings, due to its customizable mechanical properties associated with cell structures. However, the relationship between the pattern design of cell structures and the mechanical characteristics of metallic wire mesh remains unclear. The present work aims to investigate the mechanical behavior of asymmetric crosslinked metallic wire mesh with a hybrid Poisson’s ratio pattern, which has the potentials of arbitrary Poisson’s ratios. Two typical designs of cell arrangement for asymmetric crosslinked metallic wire mesh were proposed, namely negative Poisson’s ratio cells (NPRC) and positive Poisson’s ratio cells (PPRC). The in-plane Poisson’s ratio of asymmetric crosslinked metallic wire mesh was calculated based on the Euler beam theory. The effects of hybrid Poisson’s pattern and interwoven joint on mechanical properties, including macroscopic Poisson’s ratio and elastic bending recovery, were analyzed using numerical and experimental methods. The results demonstrate that the analytical Poisson’s ratio obtained from the proposed theoretical model agrees well with the simulation result. The hybrid structure which consisted of NPRC and PPRC could effectively control transverse shrinkage and become one of the most efficient potentials for promising structures with the arbitrary Poisson’s ratio phenomenon.

Present research work is based on the unique properties of isogeometric analysis (IGA) like smarter, faster and cheaper analysis for the thermo-elastic bending of laminated and sandwich composite plates. IGA, based on isoparametric concept, is a breakthrough in the area of structural analysis, which employs non-uniform rational B-spline (NURBS) as a basis function to represent less erroneous geometry. Unlike finite-element method (FEM), increasing the polynomial order in IGA gives higher continuous basis functions naturally and easily with reduced computational cost. A procedure has been developed for thermo-elastic bending analysis of laminated composite plates and sandwich structures using IGA approach. The developed NURBS-based code is validated and computational efficacy of thermo-elastic analysis is investigated. A detailed parametric study has been carried out for the quadratic, cubic and quartic NURBS elements with respect to the variation of temperature. Different types of temperature profiles have been considered. Change of deflections, stresses and moment resultants are analysed with an aim to understand the thermo-elastic behaviour of laminated and sandwich composite plates. Several thermo-elastic numerical examples have been analysed extensively. Obtained numerical results are compared with available literature to show the advantage of current formulation.

Confined liquid crystals (LC) provide a unique platform for technological applications and for the study of LC properties, such as bulk elasticity, surface anchoring, and topological defects. In this work, lyotropic chromonic liquid crystals (LCLCs) are confined in spherical droplets, and their director configurations are investigated as a function of mesogen concentration using bright-field and polarized optical microscopy. Because of the unusually small twist elastic modulus of the nematic phase of LCLCs, droplets of this phase exhibit a twisted bipolar configuration with remarkably large chiral symmetry breaking. Further, the hexagonal ordering of columns and the resultant strong suppression of twist and splay but not bend deformation in the columnar phase, cause droplets of this phase to adopt a concentric director configuration around a central bend disclination line and, at sufficiently high mesogen concentration, to exhibit surface faceting. Observations of director configurations are consistent with Jones matrix calculations and are understood theoretically to be a result of the giant elastic anisotropy of LCLCs.

The phase field approach has become a popular tool in modeling interface motion, microstructure evolution, and more recently the shape transformation of vesicle membranes under elastic bending energy. While it is advantageous to employ phase field models in numerical simulations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes, detecting topological events may also become important for many applications such as those in the simulation of blood cells. Motivated by such considerations, a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events. It can also be used as a control method to avoid unphysical changes of topology due to the numerical methods, should it become necessary for particular practical applications. Through numerical experiments, we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes.

Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. We consider the case in which the elastic interface is clamped at the lateral walls of a closed trough and thus encloses a finite amount of fluid. For a slender film undergoing infinitesimal deformations, the displacement of the elastic surface from its initial equilibrium position obeys a sixth-order (in space) initial boundary value problem (IBVP). To solve this IBVP, we construct a set of odd and even eigenfunctions that intrinsically satisfy the boundary conditions (BCs) of the original IBVP. These eigenfunctions are the solutions of a non-self-adjoint sixth-order eigenvalue problem (EVP). To use the eigenfunctions for series expansions, we also construct and solve the adjoint EVP, leading to another set of even and odd eigenfunctions, which are orthogonal to the original set (biorthogonal). The eigenvalues of the adjoint EVP are the same as those of the original EVP, and we find accurate asymptotic formulas for them. Next, employing the biorthogonal sets of eigenfunctions, a Petrov–Galerkin spectral method for sixth-order problems is proposed, which can also handle lower-order terms in the IBVP. The proposed method is tested on two model sixth-order BVPs, which admit exact solutions. We explicitly derive all the necessary formulas for expanding the quantities that appear in the model problems into the set(s) of eigenfunctions. For both model problems, we find that the approximate Petrov–Galerkin spectral solution is in excellent agreement with the exact solution. The convergence rate of the spectral series is rapid, exceeding the expected sixth-order algebraic rate.

The morphological dynamics, instabilities, and transitions of elastic filaments in viscous flows underlie a wealth of biophysical processes from flagellar propulsion to intracellular streaming and are also key to deciphering the rheological behavior of many complex fluids and soft materials. Here, we combine experiments and computational modeling to elucidate the dynamical regimes and morphological transitions of elastic Brownian filaments in a simple shear flow. Actin filaments are used as an experimental model system and their conformations are investigated through fluorescence microscopy in microfluidic channels. Simulations matching the experimental conditions are also performed using inextensible Euler–Bernoulli beam theory and nonlocal slender-body hydrodynamics in the presence of thermal fluctuations and agree quantitatively with observations. We demonstrate that filament dynamics in this system are primarily governed by a dimensionless elasto-viscous number comparing viscous drag forces to elastic bending forces, with thermal fluctuations playing only a secondary role. While short and rigid filaments perform quasi-periodic tumbling motions, a buckling instability arises above a critical flow strength. A second transition to strongly deformed shapes occurs at a yet larger value of the elasto-viscous number and is characterized by the appearance of localized high-curvature bends that propagate along the filaments in apparent “snaking” motions. A theoretical model for the as yet unexplored onset of snaking accurately predicts the transition and explains the observed dynamics. We present a complete characterization of filament morphologies and transitions as a function of elasto-viscous number and scaled persistence length and demonstrate excellent agreement between theory, experiments, and simulations.

Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. To solve such problems, we first derive a complete set of odd and even orthonormal eigenfunctions — resembling trigonometric sines and cosines, as well as the so-called “beam” functions. These functions intrinsically satisfy boundary conditions (BCs) of relevance to thin-film flows, since they are the solutions of a self-adjoint sixth-order Sturm–Liouville BVP with the same BCs. Next, we propose a Galerkin spectral approach for sixth-order problems; namely the sought function as well as all its derivatives and terms appearing in the differential equation are expanded into an infinite series with respect to the derived complete orthonormal (CON) set of eigenfunctions. The unknown coefficients in the series expansion are determined by solving the algebraic system derived by taking successive inner products with each member of the CON set of eigenfunctions. The proposed method and its convergence are demonstrated by solving two model sixth-order BVPs.