This study presents a closed-form analytical solution for the elastostatic response of long cylindrical shells composed of microstructured materials within the framework of the isotropic relaxed micromorphic continuum. The formulation accounts for microstructural effects by introducing an independent micro-distortion tensor field in addition to the classical displacement field. Under the assumptions of axisymmetric deformation and plane strain conditions, the governing equilibrium equations reduce to a coupled system of ordinary differential equations in the radial coordinate. By introducing suitable auxiliary variables, the system is reformulated into a non-homogeneous modified Bessel equation, which admits an exact analytical solution. Explicit expressions are derived for the radial displacement field and the non-zero components of the micro-distortion tensor. Numerical examples are presented to illustrate the influence of material parameters and the characteristic length on the displacement. The results demonstrate that the relaxed micromorphic model predicts deviations from classical elasticity where microstructural effects are more pronounced. The obtained solution provides valuable physical insight into the mechanics of cylindrical shells and serves as a benchmark for validating numerical implementations of relaxed micromorphic models.

This paper develops and analyzes a nonlocal supercell model for wave propagation in one-dimensional periodic chains that incorporates lumped and distributed masses together with beyond-nearest-neighbor couplings. The formulation advances earlier treatments of nonlocal metasurfaces by explicitly integrating distributed inertia, diatomic asymmetry, and long-range elastic links within a single supercell. The Bloch–Floquet theory is applied to the infinite chain to derive dispersion relations, while a complementary finite-chain formulation establishes the corresponding transmittance spectra. Parametric sweeps reveal how variations in mass ratios, stiffness asymmetry, and nonlocal coupling parameters govern the location, width, and attenuation characteristics of the spectral response. The results show consistent alignment between infinite- and finite-chain analyses, confirming that the proposed framework captures essential dynamic behavior across different structural scales. This unified treatment provides clear design guidance for engineering periodic media with tailored wave transmission properties and establishes a tractable foundation for the development of metamaterial structures aimed at vibration isolation, acoustic manipulation, and broadband attenuation.

Background and Aims:Understanding how the central nervous system generates muscle activation patterns for performing diverse movements remains a significant challenge in motor control. This study aims to evaluate the similarities and combinations of complex multiplanar upper limb movements in relation to the synergies of basic motions, using both experimental and computational approaches. Methods:Three healthy participants performed both proprioceptive neuromuscular facilitation (PNF) patterns and basic upper limb motions. Electromyography (EMG) and kinematic data were recorded simultaneously. A verified musculoskeletal (MS) model, calibrated with computed muscle control (CMC) results and processed EMG data, was used to estimate muscle activations. Muscle synergies and corresponding activation coefficients were extracted using non-negative matrix factorization (NNMF), and variance accounted for (VAF) metrics were applied to determine the optimal number of synergies. Spearman's rank correlation and least squares optimization were employed to assess the similarity and combination of synergy patterns between motion types. Results:Four muscle synergies were identified for both basic and complex movements. A shared synergy with correlation values exceeding 0.5 was observed across both types of movement. The composition of each complex motion synergy usually requires the merging of three basic motion synergies. Conclusions:The findings suggest that complex upper limb movements are constructed through combinations of fundamental motor modules. This supports the concept of modular control in human motor coordination.

Studies on the mechanics of nanomaterials, and nanostructures have driven significant discoveries and advances through multiple approaches, including experimental nanomechanics, computational nanomechanics, and size-dependent continuum theories. However, these approaches have inherent limitations related to measurement uncertainty, computational cost, and the calibration of material parameters. Recent developments in artificial intelligence (AI) have introduced new opportunities to overcome these limitations and reorganize the existing methodologies in nanomechanics. In experimental nanomechanics, machine learning (ML) techniques are increasingly employed for automated image analysis, real-time signal processing, noise reduction, and intelligent control of manipulation. In computational nanomechanics, AI enables the construction of surrogate models and machine learning interatomic potentials (MLIP) that significantly reduce the computational expense of atomistic simulations. The role of AI in size-dependent continuum mechanics was also examined, with an emphasis on the data-driven calibration of internal length-scale parameters, efficient solution strategies for non-local and strain-gradient theories, and the development of variable order nonlocal models. This study reviews recent developments, critically examines existing limitations, and delineates future directions for rigorous and physically consistent integration of AI into nanomechanics. Finally, we show how AI goes beyond being a computational tool to become a transformative force, enabling predictive, efficient, and physically grounded exploration of nanomechanics.

This study investigates wave attenuation in a bi-coupled periodic chain composed of two unequal masses interconnected through beam elements and longitudinal springs. The baseline configuration is first examined to characterize its inherent dispersion behavior. To enhance its attenuation performance, diagonal springs are introduced between non-adjacent nodes, and their influence is evaluated through a spectral element formulation. Dispersion analysis based on the invariance-plane approach and complex wavenumber evolution shows that a single diagonal spring produces a distinct Bragg-type attenuation band, whereas incorporating two diagonal springs fundamentally alters the dispersion topology by inducing branch merging and the formation of a fully complex band. This geometric coupling mechanism results in a substantial widening of the attenuation region. Frequency-response functions computed for finite chains, and validated through numerical simulation and experimental measurements, confirm the transition from dual propagating modes to mixed propagation-attenuation behavior and ultimately to complete evanescence. Parametric studies reveal that increasing the diagonal stiffness from 6 & times; 103 to 1 & times; 104 N/m widens the bandgap by approximately 60% in the single-spring configuration and nearly 80% in the dual-spring system; variations in mass ratio produce comparable trends, while beam-width changes primarily shift the bandgap location. Collectively, the analytical, numerical, and experimental results establish diagonal geometric coupling as a robust and previously unreported strategy for tunable broadband vibration suppression in periodic mechanical systems.

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential equations. To obtain an analytical solution, modified Bessel functions are utilized and closed-form solutions for the displacement and microdistortion are obtained. We show how certain limit cases (classical linear elasticity), which are naturally included in the relaxed micromorphic model, can be efficiently achieved. Furthermore, numerical results are calculated and the effects of various parameters are examined. The results can be used to calibrate and check corresponding finite element codes.

The development of musculoskeletal models aims to facilitate the evaluation of muscle function and coordination during daily activities. These models are validated using surface electromyography (EMG) data to ensure accurate representation of neuromuscular activation patterns. After validation, dominant muscles in each phase of motion are identified through non-negative matrix factorization (NNMF) and inverse kinematics (IK) approaches. The study considers three specific motions: flexion/extension, abduction/adduction, and shrugging. Using the NNMF approach, four synergies are identified for the flexion and abduction motions, while two synergies are identified for the shrugging motion. Given the high degrees of freedom (DOF) in the shoulder complex, the IK approach is employed to detect the major DOF involved in each movement. Therefore, the dominant muscles associated with the major DOF are determined based on the literature. This study investigates how the central nervous system generates muscle activation patterns to coordinate complex joint movements, a challenge in motor control. The results show high conformity between muscle coordination and the dominant muscles identified by the IK and NNMF approaches, confirming the validity of using NNMF to describe muscle coordination strategies. Based on the findings, a simplified musculoskeletal model (SMM) is proposed for predicting joint angles in the upper limbs of prostheses and robotic applications. This model incorporates identified synergy modules and key joint DOF for the three basic motions, reflecting the underlying principles of motor control for efficient movement execution.

This paper investigates wave propagation in coated sphere-filled composites using the reduced micromorphic model. Composite materials with coated spheres dispersed in a matrix exhibit unique mechanical properties, making them suitable for various engineering applications. The study focuses on the ability of the reduced micromorphic model to predict dispersion curves and bandgap in these composites. The main novelty of this work lies in the analytical derivation of dispersion relations and the frequency-dependent effective mass density of the composite in the framework of the reduced micromorphic model, which has not been previously explored in the context of coated sphere-filled composites. The model’s applicability is validated by comparing results for three different composites with existing literature. This investigation aims to enhance the understanding of wave propagation in complex materials and provide a robust framework for future research.

Fatigue life prediction of orthopedic screws against applied impulsive loads during the treatment period is of great importance. In this study, the fatigue bending life of Cortical and Cancellous screws under cyclic bending loads are evaluated by using both experimental tests and numerical simulations. In the experimental tests, various impulsive loads are perpendicularly applied to the screw axis at the middle of threaded area until to observe the crack. Besides, the Fatemi-Socie model is utilized to obtain the life of the screws by using the finite element method. It is observed that the numerical results are in good agreement with those predicted by the experimental tests. Furthermore, the results reveal that the Cortical screws have a longer fatigue life than the Cancellous screws with similar diameters.

Carbon nano-onions (CNOs)-reinforced nanocomposites are one of the most attractive materials due to their excellent performance in many fields of applications. This review paper aims to provide a systematic, albeit selective, survey of innovative developments in CNO-derived nanocomposites. First, molecular structure, fabrication and purification methods, and various applications of the CNOs are briefly described. Their unique physical properties make them ideal nanofillers for matrices to enhance the final nanocomposite features. Therefore, an overview of the current literature discussing the synthesis of polymeric and inorganic nanocomposites is presented. Then, various computational tools that can be used for simulating and modeling the CNOs and their nanocomposites are introduced. Experimental studies pertinent to the mechanical properties of the CNOs-reinforced nanocomposites are presented, and the effects of the CNOs on the mechanical properties of nanocomposites are reviewed. Next, novel applications of these nanocomposites in the emerging fields of biomedical engineering, energy storage devices, and nano-sensing technologies are also detailed. This article would be inspirational and give new insights by providing valuable, up-to-date, and essential background information to develop new concepts and applications of these carbon-based nanocomposites.

This study presents a simple analytical model to investigate wave propagation in 2D carbon nano-onions (CNOs) and nitrogen-doped carbon nano-onions (N-CNOs) lattices. Furthermore, the dispersion relationships of the waves and bandgaps in these lattices are derived based on Bloch's theorem. The CNOs and N-CNOs lattices are modeled as infinite 2D mass-in-mass structures accurately assembled using linear springs. The Lennard-Jones potential energy is employed to obtain equivalent spring constants. A key finding of this research is the identification of bandgaps within all lattice structures, signifying regions where wave propagation is prohibited. The existence of these bandgaps offers potential for the advancement of adjustable nano-scale metamaterials.

Fullerenes, as single crystals, present exceptional mechanical and physical properties due to their hollow spherical molecular structure consisting of carbon atoms connected by covalent bonds. The idea of linking these allotropes of carbon to create monolayer networks has now been accomplished experimentally. The question that remains to be answered is if these synthesized single-layered nanosheets of fullerene present comparable properties with graphene monolayers. To answer this important question and to estimate the full tensile stress-strain behavior of quasi-tetragonal as well as quasi-hexagonal configurations of C60 planar networks, several Molecular Dynamics simulations are performed in this work by using a new REAXFF and the AIREBO-M potential. Various mechanical properties, such as Young's modulus, Poisson's ratio, ultimate tensile strength, ultimate tensile strain, and fracture energy at failure of C60 monolayers of several sizes, are computed and compared with the results reported in the literature. Furthermore, a comprehensive discussion is made regarding the significant influence of the adopted potential on the numerical predictions of the elastic mechanical and fracture behavior of the fullerene nanosheets. This study presents novel findings on the mechanical properties of fullerene monolayers using advanced molecular dynamics simulations. Employing specialized ReaxFF and AIREBO-M potentials, it offers new insights into the stiffness, tensile strength, and fracture mechanisms of these materials, providing significant contributions to the field of nanomaterials research. image

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses. The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix. The inclusions are idealized by lumped masses, and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses. Additionally, the model is capable of depicting the wave propagation in bi-material bars, wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses. The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered, and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method (LPM). Next, a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique. The subsequent use of the second-order method of multiple scales (MMS) facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form. The novelties of the present study consist of (i) considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains; (ii) developing the second-order LPM for the wave propagation in the discrete chains; and (iii) deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses. Finally, a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models. These parameters include the ratio of the spring mass to the lumped mass, the nonlinear stiffness coefficient of the spring, and the wave amplitude.

Metamaterial composites are a rapidly developing field of engineered materials. These materials are typically created by incorporating periodic inclusions, such as coated spheres, into a matrix. It has been shown that the reduced micromorphic model enables the analysis of the static and dynamic behaviors of metamaterial composites. Based on the reduced micromorphic model, a novel approach for estimating the effective bulk modulus of metamaterial composites is proposed. Utilizing the reduced micromorphic model, a hydrostatic compression test is simulated to derive a closed-form expression for the effective bulk modulus. The material coefficients of the reduced micromorphic model are identified according to the elastic properties of all phases of the composite, and the obtained numerical results are compared with those reported in the literature. Additionally, this study examines the influences of various physical parameters on the effective bulk modulus.

In this paper, the effects of initial curvature and lattice core shape on the bending vibration of sandwich beams are investigated. The three-dimensional (3D) sandwich beam is simulated by combining a two-dimensional (2D) cross-sectional analysis with a one-dimensional (1D) nonlinear beam analysis. The sandwich beam is composed of two identical isotropic faces covering a lattice core. Four different lattice core structures are used to take into account the effect of core unit cell shape on the dynamic properties of the sandwich beam. The nonlinear governing equations of the sandwich beam are Discretized using a time-space scheme. Numerical results show that the lattice unit cell shape affects both in-plane and out of plane stiffness values and hence changes the dynamic behavior of the beam. Furthermore, it is observed that by changing the density ratio of the beam, modes veer away from each other at a specific value of density ratio for specific unit cell types. Moreover, the initial curvature of the beam is shown to affect the dynamics of the beam especially lower modes. Finally, it is obtained that the dynamics of the beam is different when it is initially curved or curved due to an applied end follower moment.

A combination of chirality, anti-chirality, and re-entrant lattice pattern is proposed to form a new two-dimensional meta-structure, and a comprehensive parametric study is conducted by using experimental and numerical analysis. The proposed structure can undergo larger deformations without significant stress concentrations. Based on the verified finite element model, the effects of various geometrical parameters on the in-plane mechanical response of the structure are investigated. Results show that the thickness of the structure is the most dominant factor in affecting the Young modulus while other parameters can alter Poisson's ratio. In addition, the proposed structure exhibits tunable negative/near-zero Poisson's ratios.