This paper presents a thermodynamically consistent, fully coupled thermo-chemo-mechanical framework governing hydrogen transport, heat conduction, and gradient plasticity. Departing from conventional Helmholtz free-energy formulations, the developed theory utilizes the grand-canonical potential as the primary thermodynamic potential. Microstructural length scale effects are incorporated via the Burgers tensor as a continuum measure of geometrically necessary dislocation (GND) densities. The governing macro- and micro-force balances are established using the principle of virtual power, while the laws of thermodynamics dictate the admissible constitutive equations and dissipation inequalities. Crucially, formulating the hydrogen transport balance in terms of the chemical potential via the grand-canonical approach yields a more computationally efficient governing equation in comparison with traditional concentration-based free-energy models. Under the assumptions of material isotropy and a quadratic grand-canonical potential, the framework reveals an energetic decoupling of the thermal and chemical fields from plastic strain gradients. Furthermore, the formulation provides a unified description of both interstitial and trapped hydrogen populations, establishing a rigorous theoretical foundation for subsequent numerical implementations.
Fiber-reinforced composites have a wide range of structural applications due to their high specific strength and stiffness. However, their limited intrinsic damping restricts their performance in dynamic environments. To address this limitation, viscoelastic layers are integrated within laminates to enhance vibration attenuation. The present study provides a systematic comparative and design-oriented investigation of multilayered viscoelastic configurations incorporated within carbon, glass, and hybrid fiber-reinforced composite plates to enhance energy dissipation and improve vibration control characteristics. Given the relatively small thickness of the plate compared to its in-plane dimensions, the first-order shear deformation theory is employed for modeling. The equations of motion are derived using Hamilton’s principle and solved under multiple boundary conditions using admissible functions and the Differential Quadrature Method. A detailed parametric study is conducted to evaluate the influence of viscoelastic layer spacing, stacking sequence, and fiber orientation on the vibration and damping behavior of the composite plates. The results indicate that the angular orientation of the outermost plies significantly influences the natural frequencies and damping loss factors, whereas the innermost plies exhibit comparatively smaller influence. Furthermore, the study demonstrates that using identical viscoelastic materials in all layers tends to favor either frequency enhancement or damping improvement individually. Therefore, different combinations of frequency-dependent viscoelastic materials are comparatively assessed in symmetric multilayer configurations to achieve an effective balance between modal frequencies and damping performance.
The equilibrium positions of an edge dislocation climbing in a cylindrical nanowire of infinite length embedded in a matrix of infinite extension have been theoretically investigated when a disclination dipole is lying in the nanowire. From a Peach–Koehler force analysis, the stable and unstable equilibrium positions of the edge dislocation have been determined in the nanowire as a function of the disclination strength and shear moduli of the two elastically heterogeneous phases. When the matrix is harder than the nanowire, a stable equilibrium position is reached for the dislocation near the interface with the matrix. When the matrix is softer than the nanowire, a critical ratio between the shear modulus of the nanowire and that of the matrix has been finally determined as a function the disclination strength. Beyond this critical ratio, the climbing dislocation exhibits in the nanowire an unstable and a stable position. Below the critical ratio, no equilibrium position is observed.
We present PI-CANN, an input-convex constitutive artificial neural network for finite-strain hyperelasticity that is trained variationally from full-field kinematics and measured boundary tractions rather than from pointwise stress labels. The network represents the isochoric strain energy as a convex, non-decreasing function of a frame-indifferent invariant set, augmented by a prescribed volumetric term. We make three precise architectural guarantees: (i) the energy is convex in its invariant inputs by construction (non-negative output weights with convex activations), the deformation-gradient ellipticity then being certified a posteriori; (ii) the reference state is energy- and stress-free exactly, because the isochoric invariant inputs are stationary in F at F=I ; and (iii) stresses and tangent moduli are exact derivatives of the learned representation to floating-point precision. We deliberately do not claim that convexity in the isochoric invariants implies polyconvexity in F , since the isochoric invariants are not polyconvex in F ; ellipticity is therefore monitored numerically. Identifiability is analysed through a weak-equilibrium convergence theorem, with L^2 stress convergence promoted to a corollary under explicitly stated richness and constitutive-identifiability hypotheses. On Neo-Hookean, Mooney–Rivlin, Gent and Holzapfel–Gasser–Ogden (HGO) benchmarks the network recovers energy, stress and tangent moduli with relative L^2 errors of 10^-5 – 10^-3 ; it generalises from homogeneous calibration data to an inhomogeneous Cook’s-membrane boundary-value problem (on the correct tapered-trapezoid geometry) with errors of 10^-4 – 10^-3 . Finally we discover a deformation response generated by a three-term Ogden law that lies outside the calibration family, and use the Akaike and Bayesian information criteria (AIC/BIC), with an explicit Gaussian likelihood and a correlation-deflated effective sample size, to select the closest analytical surrogate and to flag the resulting model misspecification. A controlled comparison against four baseline architectures attributes each guarantee to its architectural cause: objectivity to the invariant inputs, an exact reference state to the construction, and certified ellipticity to the hard convexity constraint.
This paper investigates the nonlinear vibration response of fractional viscoelastic functionally graded nanobeams by incorporating Chen–Yao’s surface elasticity theory. Material properties are assumed to vary according to a power-law distribution through the thickness. Under Euler–Bernoulli and von Kármán nonlinear beam assumptions, fractional Kelvin–Voigt viscoelasticity and Chen–Yao surface model are fully coupled. Hamilton’s principle derives governing equations for transverse and axial motions, which are discretized via Galerkin scheme and solved using the Adams predictor–corrector method. Parametric simulations on silicon–gold nanobeams analyze the roles of initial displacement, slenderness ratio, damping, fractional order, gradient index, and surface parameters. Unlike existing weakly coupled models, this work establishes a strongly coupled theoretical framework and reveals competitive coupling behaviors among multiple physical fields, whose action law is described as follows: Surface stiffness hardening restrains the damping capacity of fractional memory effects during large-amplitude nonlinear vibration.
This study presents an extension to the theory for analytically analyzing the eigenfunctions and frequency equation of a taut cable with an intermediate point support. The equations of motion for the free vibration of the two-span cable, along with the corresponding boundary and continuity conditions, are established to define the eigenvalue problem and derive simple analytical expressions for the modal properties. Examination of the obtained spectrum reveals “localized modes”—in which only one span exhibits significant vibration amplitudes—“global modes”—in which the vibration of the cable extends across both spans—and “degenerate modes”—where there is more than one independent eigenfunction for a natural frequency. In a numerical example, the analytical results are confirmed by a comparison with finite element solutions obtained with computation endowed with commercial software (ABAQUS).
The asymptotic expansion method (AEM) is a useful approach for deriving enriched beam models from the full 3D mechanical problem. First developed for straight prismatic beams, it makes it possible to obtain sectional modes able to represent classical beam behavior together with local three-dimensional effects. In this paper, an overview is presented for two extensions of the AEM to more complex beam geometries: curved beams and tapered beams. In the curved beam case, the formulation accounts for the effect of curvature through a curvilinear description of the geometry, which leads to additional coupling effects in the mechanical response. In the tapered beam case, the variation in the cross section along the beam length generates correction modes that enrich the classical Saint-Venant solution. The main ideas of both formulations are summarized, highlighting the geometrical description, the asymptotic procedure, and the form of the resulting displacement and stress modes. The comparison shows that the same AEM framework can be adapted to different geometrical configurations, while the additional modes remain strongly linked to the considered geometric effect.
An analytical model is developed in this study to describe thermoelastic damping (TED) in circular cross-section micro/nanobeam resonators, for the first time, within the framework of Eringen-type nonlocal-dual-phase-lag heat conduction (NDPL_Eringen) theory. Considering one-dimensional heat conduction along the thickness direction of micro/nanobeams, the coupled thermoelastic governing equation is formulated within the NDPL_Eringen theory framework. The temperature field function is solved using the Galerkin method, upon which the analytical TED formula is established utilizing the energy definition approach. Silicon (Si) and gold (Au) are adopted in the numerical simulation to examine the influences of key parameters including the cross‑section radius and the nonlocal thermal length parameter (lQ) on the TED spectra. Results indicate that the developed TED model exhibits excellent convergence and universality. When comparing with the Tzou-type NDPL (NDPL_Tzou) TED model, the NDPL_Eringen model predicts nearly identical TED values at low frequencies but predicts smaller values at high frequencies. In addition, the influence of lQ on TED depends on the cross-section radius and vibration frequency. In the range of high frequencies, increasing lQ can reduce the NDPL_Eringen TED but enhance NDPL_Tzou TED. Furthermore, increasing the cross-section radius will make the nonlocal thermal size‑dependent effect less pronounced.
This study develops a frictionless thermoelectro-mechanical adhesive contact model for a rigid spherical indenter interacting with a thermoelectric thin film bonded to a rigid substrate. Thermoelectric and elastic frequency–response functions are derived from the coupled constitutive equations and boundary conditions using a double Fourier transform. The resulting semi-analytical solution is evaluated with a discrete convolution and fast Fourier transform (DC–FFT) formulation combined with a conjugate gradient method (CGM) for the Maugis–Dugdale cohesive conditions. The calculations show that energy increases the central contact pressure through constrained thermal expansion, whereas electric current produces the opposite trend under the prescribed loading convention. Adhesion strength increases the contact radius and shifts the unloading limit point toward a more negative normal load, while film thickness controls the effective compliance by changing the substrate constraint. These results demonstrate that energy, electric current, film thickness, and adhesion strength provide independent parameters for tuning the pressure, deformation, cohesive zone response, and separation stability of thermoelectric thin-film interfaces.
This paper presents a solution for the axisymmetric contact problem of an elastic layer resting on a rigid foundation containing an annular hole, subjected to indentation by a flat rigid punch. The mathematical formulation employs Boussinesq’s stress functions and the Hankel transform technique to reduce the governing equations to a system of coupled dual and triple integral equations involving Bessel functions. To solve this complex system, an analytical method is developed using Bessel function series expansions and the Gegenbauer addition formula, effectively transforming the integral equations into an infinite system of linear algebraic equations. Closed-form expressions are derived for the displacement and stress fields, as well as for the fracture mechanics parameters, including the stress intensity factors at the hole edges and the stress singularity at the punch margin. Numerical results demonstrate that the annular hole creates a stress relief zone that significantly alters the contact stress distribution, particularly in thin layers. The accuracy and validity of the proposed method are confirmed by excellent agreement with finite element method (FEM) simulations and with an analytical solution for a semi-infinite medium.
This study aims to develop a theoretical framework for predicting the dynamic behavior of graphene nanoplatelet-reinforced composite (GPLRC) beams under electrical excitation by incorporating dielectric effect and size-dependent effect through fractional-order nonlocal elasticity theory. The GPLs are distributed through the beam thickness according to three gradient patterns. The effective elastic modulus and dielectric permittivity are evaluated using effective medium theory, while the effective Poisson’s ratio and mass density are determined using the rule of mixtures. Based on Timoshenko beam theory, nonlinear strain–displacement relations, and fractional-order nonlocal elasticity theory, the governing equations are derived through the variational principle and solved by combining the Rayleigh–Ritz and Runge–Kutta methods. The effects of DC voltage, initial axial stress, nonlocal parameter, fractional-order parameter, and GPL mass fraction on the dynamic response are systematically investigated. The results demonstrate that DC voltage increases the electrostatic effect and significantly affects the deformation response of GPLRC beams, particularly for beams with high GPL content. Increasing initial axial stress enhances structural rigidity and suppresses vibration, while higher GPL mass fraction improves stiffness and reduces vibration amplitude. The results provide theoretical insights for the design of nanoscale intelligent composite structures.
We consider the image force (or material force) acting on a screw dislocation in a hexagonal piezoelectric wedge. Using the extended version of the Peach-Koehler formula, explicit expressions for the radial and tangential components of the image force are derived for ten configurations of the piezoelectric wedge: (1) a piezoelectric wedge with two traction-free and charge-free boundaries, (2) a piezoelectric wedge with two fixed and conducting boundaries, (3) a piezoelectric wedge with a traction-free and charge-free boundary and another fixed and conducting boundary, (4) a piezoelectric wedge with a traction-free and charge-free boundary and another traction-free and conducting boundary, (5) a piezoelectric wedge with a fixed and conducting boundary and another fixed and charge-free boundary, (6) a piezoelectric wedge with a traction-free and charge-free boundary and another fixed and charge-free boundary, (7) a piezoelectric wedge with a fixed and conducting boundary and another traction-free and conducting boundary, (8) a piezoelectric wedge with two traction-free and conducting boundaries, (9) a piezoelectric wedge with two fixed and charge-free boundaries, and (10) a piezoelectric wedge with a traction-free and conducting boundary and another fixed and charge-free boundary. The radial image force is independent of the dislocation’s angular position for each configuration, and is also independent of the wedge angle for the third and tenth configurations.
Aiming at the problem that vehicle shimmy deteriorates the driving safety and operational stability of vehicles, the X-shaped nonlinear energy sink (NES) with multiple nonlinear stiffness characteristics is proposed and applied to vehicle steering system for suppressing vehicle shimmy. The dynamic model of vehicle shimmy system coupled with NES is developed. The Hopf bifurcation characteristic of the vehicle shimmy system is analyzed by numerical continuation method, the stable region and limit cycle oscillation (LCO) amplitude of the vehicle shimmy system under different geometric parameters of NES are obtained, together with time history, frequency spectra, and phase portrait to show its shimmy performance, and the modal characteristic of vehicle shimmy system is studied by system feature vector. In addition, the influence of steering system and NES structural configurations on the shimmy performance is discussed in detail, and the adaptive particle swarm optimization (APSO) algorithm is used to determine the optimal structural parameters of the NES. The results show that the NES effectively reduces the unstable region, the maximum LCO amplitude, and the shimmy speed interval. Additionally, the initial arrangement of NES also has an effect on the shimmy performance, and the NES with tri-stable behavior has better shimmy suppression effect. The bifurcation analysis of structural parameters indicates that the shimmy suppression performance can be improved by reasonable selection of steering system and NES structural parameters. Furthermore, the NES optimized by the APSO algorithm has better shimmy suppression performance than the traditional PSO algorithm, which significantly reduces the maximum LCO amplitude and eliminates the unstable region within the investigated parameter ranges. Therefore, the proposed X-shaped NES with multiple nonlinear stiffness characteristic is a novel nonlinear vibration suppression mechanism, which provides guiding significance for vehicle shimmy suppression in engineering application.
This study presented a numerical framework for the vibration response of magneto-electro-elastic (MEE) structures under thermal load, and the edge-based smoothed point interpolation method (ES-PIM) was adopted to integrate the thermal, mechanical, electrical, and magnetic fields for the accurate vibration prediction in coupling fields, which is essential for the design of smart sensors, actuators, energy harvesters, and multifunctional composite systems. By incorporating the gradient smoothing technique into the generalized smoothed Galerkin weak form, the proposed ES-PIM effectively mitigates the overly stiff behavior inherent in conventional finite element method (FEM) and provides a more accurate stiffness than conventional FEM, which enhances numerical accuracy for complex multiphysics problems. The governing equations of thermo-magneto-electro-elastic problem are discretized within this framework to investigate free vibration characteristics, modal behavior, harmonic response, and damping vibration phenomena under thermal environments. Numerical examples validate that the ES-PIM formulation achieves higher accuracy and convergence compared to standard FEM approaches, which confirms its efficacy as a powerful numerical tool for the multiphysics analysis of advanced MEE composite structures.
The present study deals with the effect of an internal heat source in a micropolar thermoelastic plate of finite length with Klein–Gordon NonLocality. The Moore–Gibson–Thompson (MGT) theory of thermoelasticity is employed in the present study. The width of the micropolar thermoelastic plate is taken as 2h with the origin of the coordinate axis at the centre of the plate. The free surfaces of the plate are y = h and y = − h. The equations of motion are solved analytically by normal mode analysis, and the expressions of displacement, stress, couple stress, and temperature field are derived. The effect of nonlocality in time and space is represented graphically for the variables.
This paper investigates the electromechanically driven inflation of pre-stretched rectangular hyperelastic membranes, taking into account dielectric properties of the material. The problem, which is relevant to several emerging engineering applications, is typically addressed numerically due to its mathematical complexity. Here, to accurately capture the inflated configuration of the membrane while retaining a compact formulation, the membrane deformation is represented through suitable kinematic assumptions. Further, a novel variational formulation is developed, based on the stationarity of the potential energy of the system by a Ritz method. To this aim, an incompressible Mooney–Rivlin material model is adopted assuming an ideal dielectric elastomer behavior. The resulting formulation reduces the problem to a small set of nonlinear algebraic equations, enabling efficient prediction of the membrane profile and pressure–deflection response. Notably, for long rectangular membranes, a simplified analytical pressure–deflection expression is also derived, providing direct insight into the role of mechanical pre-stretch, material parameters, geometry, and electrical actuation. The accuracy of the proposed formulation is assessed through comparisons with finite element simulations. Overall, the results offer a practical modeling framework for the analysis and design of rectangular dielectric elastomer membranes in soft actuators, sensors, and related devices.
This paper proposes a novel arbitrary Lagrangian–Eulerian (ALE) frictional beam formulation for the quasi-static simulation of cable-actuated systems. While classical Lagrangian finite element formulations are often inefficient for modeling cables moving through contact patches due to the requirement for global mesh refinement, the proposed ALE formalism describes both the spatial motion of the nodes and the material flow through the mesh. The formulation is based on a geometrically exact beam model defined on the special Euclidean group SE(3). To rigorously capture stick–slip transitions and strictly enforce Coulomb’s law without the need for numerical regularization or ad hoc penalty parameters, the friction law is introduced using a nonsmooth augmented Lagrangian framework. The contact model is developed for systems where the location of the contact patch is known a priori, such as cable-pulley systems, cables moving through linear guiding elements, and cables sliding inside sleeves or through eyelets. In all these cases, the cable interacts with a guiding element attached to a support by a kinematic joint with at most one degree of freedom. Numerical results are presented for several quasi-static test cases, including a cable on a conveyor belt, a driving-driven pulley system, and a beam sliding in a sleeve. These results illustrate the capability of the formulation to capture stick–slip transitions in the contact zones, Eshelby configurational forces and hysteresis loops arising under cyclic loading.
To realize effective regulation of semiconductor carrier transport via enhanced flexoelectric effect, this paper designs a core–shell composite rod composed of functionally graded flexoelectric shell and semiconductor core. The nonlocal theory is incorporated to describe the size-dependent multi-field coupling characteristics of the composite system. Based on the flexoelectric theory and nonlinear semiconductor drift–diffusion theory, a one-dimensional coupling model is established, and the corresponding boundary value problem is numerically solved through using the weak-form finite element method. By comparing electrical behaviors from linear and nonlinear drift–diffusion frameworks, key factors governing nonlinear electro-carrier coupling are systematically investigated. Numerical results indicate that larger gradient parameter aggravates axial material inhomogeneity and amplifies nonlinear electrical responses. The increasing semiconductor core proportion weakens the flexoelectric coupling effect and consequently suppresses the nonlinear electro-carrier interaction. Besides, nonlocal parameter and material characteristic length dominate field variation merely around the loading site, and large values of these two parameters lead to opposite nonlinear evolution of perturbation carriers on tension and compression sides. A higher flexoelectric coefficient strengthens flexoelectric polarization and triggers prominent nonlinearity of electric potential and carrier density, and high external load further highlights nonlinear coupling which mainly alters carrier spatial distribution. This research could be a reliable guide for designing structures for flexoelectric-field-controlled carrier manipulation in semiconductor devices.
This study established a biomechanical analysis framework for cervical spondylosis evaluation by integrating reverse engineering, representative volume element (RVE) homogenization, and finite element analysis. First, clinical imaging data of the cervical spine segments were obtained through continuous cross-sectional scanning. Based on anatomical threshold segmentation, reverse engineering techniques were introduced to optimize the geometric model parameters, thereby constructing a geometric model with patient-specific anatomical characteristics. Second, the equivalent material parameters of bone tissue were determined using the RVE homogenization method, and a thermo-mechanically coupled finite element model incorporating stress transmission, ligament constraint characteristics, and human body temperature was developed and validated. Finally, a biomechanical model including vertebrae, intervertebral discs, and ligamentous structures was established to investigate the mechanical response characteristics of cervical spine segments under different loading conditions. On this basis, a biomechanical analysis method for cervical spondylosis based on the mechanical response of the intervertebral disc was proposed. By combining the visualized biomechanical characteristics of the intervertebral disc with the patient’s primary complaints, the proposed model can provide clinically relevant insights and more targeted support for treatment planning in cervical spondylosis.
The problem of detection of multiple transverse cracks in the Euler–Bernoulli and Timoshenko–Ehrenfest beam by means of the natural frequencies is considered. The cracks are simulated by massless rotational springs. It is assumed that the cracks are small. It is proved that in case of simply supported beam, location of n cracks can be identified by means of 2n natural frequencies with an accuracy of symmetrical arrangement. A similar result is obtained by means of a single natural frequency of a simply supported beam and 2n natural frequencies corresponding to Rayleigh conditions at the ends of the beam. Using 2n natural frequencies corresponding to simply supported beam and 2n + 1 natural frequencies corresponding to Rayleigh-free support boundary conditions n cracks can be identified uniquely. Numerical examples are considered.
