Shimmy in nose landing gears may induce high-cycle fatigue in critical structural components and thus poses a safety risk during taxiing, take-off, and landing rollouts. To mitigate shimmy under complex service conditions, this study proposes a passive hybrid suppression concept by integrating a torsional nonlinear energy sink (NES) and an annular granular particle damper (PD) into a single-wheel nose landing gear system. A coupled nonlinear shimmy model involving torsional and lateral bending modes is developed based on the Thota tire force formulation and stretched-string tire deformation dynamics, with geometric effects induced by the rake angle also considered. The torsional NES is realized through a modified roller-spring mechanism, whose nonlinear restoring torque is derived via geometric analysis and cubic Taylor approximation, resulting in near-zero linear stiffness with a positive cubic stiffness component. The annular PD is modeled using a gas-solid two-phase-flowbased equivalent viscous damping approach, and the corresponding torsional damping torque is incorporated into the governing equations. Bifurcation analyses are performed using MATCONT in the (V, Fz)-plane to evaluate the stability boundaries and the oscillation regions of torsional shimmy, lateral bending shimmy, and bistability. The results show that the standalone NES effectively reduces the torsional shimmy region and enlarges the stable domain in the low-load range. In contrast, the standalone PD significantly attenuates vibration amplitudes but enlarges the shimmy region and induces a characteristic "Both" oscillation mode in which torsional and lateral responses coexist. The combined NES-PD configuration simultaneously achieves substantial amplitude reduction and a contraction of the unstable operating region. For a representative low-load case, the maximum torsional amplitude is reduced by about 87% compared with the baseline configuration, while the shimmy speed interval is also decreased. A parametric study is further conducted to evaluate the influence of key NES and PD parameters, including the concave track radius, spring pre-stretch, spring stiffness, roller radius, particle filling ratio, and particle density, on the shimmy suppression performance.
Phononic crystals, owing to their remarkable properties, exhibit broad application prospects. The accurate and efficient calculation of their band structures is fundamental to their design and application. However, existing computational methods still face challenges of high computational cost and resource consumption for complex geometries. This study proposes a novel reduced-order computational method, termed Free-Interface Wave Isogeometric Analysis (FWIGA), to address these challenges. The method integrates the geometric precision of Isogeometric Analysis (IGA) with the model-order reduction capability of free-interface component mode synthesis. Through a two-stage reduction process comprising global modal projection and enforcement of Bloch boundary conditions, it significantly reduces the scale of the problem. Numerical validation on 1D and 2D phononic crystal models demonstrates that the proposed method substantially reduces the degrees of freedom by approximately 98% and the computational time by around 90%, while still maintaining high accuracy. FWIGA offers an efficient and accurate method for band structure analysis of PnCs, supporting their design and optimization.
Segmented hybrid carbon fiber reinforced composite-aluminum variable curvature beams (CFRC-Al VCB) offer a compelling combination of lightweight properties and adaptable geometries, presenting significant potential such as aerospace support structures and parabolic antennas. However, the inherent variable curvature and material heterogeneity result in non-uniform stiffness distributions, which are prone to resonance-induced structural instability, thereby posing a threat to the spacecraft's safety. Consequently, developing a highfidelity dynamic model that accurately characterizes these geometric and material features is essential for the vibration-based optimization of such structures. This study presents a systematic investigation into the semi-analytical modeling, experimental validation, and parametric analysis of CFRC-Al VCB. First, energy expressions for the heterogeneous beam segments in both in-plane and out-of-plane directions were derived based on Timoshenko beam and Classical Lamination Theories (CLT), incorporating curvature functions for geometric correction. A generalized semi-analytical model was then established by employing Chebyshev orthogonal polynomials of the second kind (COPSK) for displacement field representation and a six-degree-of-freedom (6-DOF) artificial spring technique for boundary condition simulation. Subsequently, a hammering test system was developed to validate the proposed model against both experimental data and finite element analysis results from ANSYS. The results demonstrate that the proposed model significantly improves computational efficiency compared to ANSYS while maintaining high numerical accuracy. Finally, the influence of focal length, fiber orientation angles, and cross-sectional dimensions on the vibration characteristics of CFRC-Al VCB was systematically investigated using the validated model. These findings provide critical theoretical insights and design guidelines for the dynamic optimization of such hybrid variable curvature structures.
This study conducts the first systematic investigation into the nonlinear vibration characteristics of hard-coating thin-walled cylindrical shell with stick-slip bolted connections under thermomechanical coupling conditions. To achieve a more precise characterization of the stick-slip contact behaviour of bolted connections in thermal environments, a novel coupled stick-slip model incorporating the effects of temperature, bolt quantity, and initial preload on the evolution of actual bolt preload is presented. On this basis, a semi-analytical model for the nonlinear thermomechanical coupling vibration of hard-coating cylindrical shells with stick-slip characteristic bolted connections is established by means of the Rayleigh-Ritz method. Furthermore, a dedicated vibration testing system is designed and developed to provide direct experimental validation for the accuracy and reliability of the proposed model. The governing dynamic equations are derived by integrating the Sanders shell theory and von Karman geometric nonlinearity, and an extended Newton-Raphson iterative algorithm is developed to simultaneously solve the nonlinear terms and identify the stick-slip contact states of bolts. A systematic and rigorous comparison is performed among the semi-analytical results and experimental data. Finally, the nonlinear vibration mechanisms are comprehensively elucidated from the perspectives of equivalent stiffness and equivalent damping, and the influence laws of temperature, coating parameters, and excitation levels on the nonlinear vibration behaviour are explored. This work provide critical insights for the design of vibration reduction of relevant cylindrical shell components.
This study proposes a novel sandwich beam structure designed for superior low-frequency broadband flexural wave control. The proposed structure synergistically integrates discontinuous sandwich cores with Acoustic Black Holes (ABHs) embedded in the face sheets, demonstrating performance that outperforms conventional designs. To elucidate the coupling mechanisms between the periodic effects of discontinuous cores and ABH effects, two distinct configurations are systematically investigated: the C-ABH and NC-ABH sandwich beams. The sandwich beam with ABHs embedded in the beam segments coupled with the core is designated as C-ABH sandwich beam, while that with ABHs embedded in the segments non-coupled from the core is termed NC-ABH sandwich beam. A wave vector method is employed to establish flexural wave propagation models for both beam configurations, alongside a transmission coefficient model characterizing flexural wave attenuation. Using these models, the influence of four key factors is investigated on the flexural wave attenuation performance of the sandwich beams. Research results show that the proposed NC-ABH sandwich beam delivers superior flexural wave attenuation performance; the attenuation performance is markedly enhanced by embedding ABHs in the face sheet with higher flexural rigidity and by increasing the flexural rigidity asymmetry between the upper and lower face sheets; reducing the ABH minimum thickness and increasing its length and quantity further widen the bandgaps and shift them toward lower frequencies. These findings indicate that the proposed NC-ABH sandwich beam offers an effective strategy for achieving strong flexural wave attenuation in low-frequency broadband applications.
The Prager-Synge relationship known as the hyper-circle relation, has been widely used for static and elliptic partial differential equations. There are two scientific domains in which this relation appeared to be very useful. One is the error analysis in a finite element approximation and the other one is the reduced modeling for instance in the justification of shell and plate models in structural mechanics. The strategy consists in building a couple of terms which are separately kinematically and statically admissible. But they do not necessarily satisfies the constitutive relationship. In this paper we extend this theory to parabolic and hyperbolic models. Very simple examples for dimension reduction are given. But the theory can also be applied to more complex models like plates and shells in dynamics. A basic point is that the error is exact in a particular norm which is the most physically meaningful one. This norm is the sum of the primal and a dual energy which are not equal as far as the constitutive relationship for the dual model is not the physical one.
Ultrasonic inspection is a promising non-destructive approach for evaluating the internal state of lithium-ion batteries, but its application to pouch cells is strongly limited by wave reflection and scattering caused by densely stacked multi-layer structures. In this work, we propose an elastic complementary meta-layer (CML) that enables ultrasonic penetration through battery pouch cells by compensating the wave response of the battery. The penetration condition is formulated within a transfer matrix framework in terms of impedance matching and phase compensation. To satisfy these conditions, a novel meta-atom with independently tunable effective mass and stiffness is employed, enabling precise control of dynamic properties through geometric design. Theoretical analysis and numerical simulations show that the proposed CML restores near-complete ultrasonic transmission through both single and multiple stacked pouch cells, despite severe impedance mismatch and accumulated phase delay in the bare battery structures. This study presents a general wave-based strategy for penetrating complex multi-layer barriers and provides a new route for ultrasonic inspection of battery systems that are difficult to access using conventional methods.
In this work, we develop an analytical framework for pre-stressed bistable low arches with pinned-pinned boundary conditions that explicitly relates the pre-stressed initial profile and the toggled stable profile. The key novelty of the present work lies in establishing a direct profile-based relation between the two stable states of a pre-stressed pinned-pinned low arch and in deriving from this relation explicit equations for both analysis and design. Both stable profiles are expressed in terms of pinned-pinned beam mode shapes, and a bistability condition is derived from the total potential energy. It is further shown that bistability in prestressed arches requires nonzero fundamental mode weights in both stable states. Fundamental equations are then derived for the analysis and design of pre-stressed bistable arches, including a general relation between the initial and toggled mode coefficients, a single-variable nonlinear equation for determining the toggled profile from a given pre-stressed initial profile, and a closed-form equation for obtaining the required initial profile for a prescribed toggled shape. Several corollaries are also established and proved on mode preservation, symmetry, sign changes, relative modal magnitudes, approximate equality of higher-mode weights, and lower bounds on the fundamental mode contribution, which provide design guidelines and assist in selecting suitable inputs for the optimization of bistable arches. Examples of analysis and design of pre-stressed bistable arches with different arch profiles are presented. The results are compared with physical experiments of 3D-printed prototypes and finite element analysis, confirming the credibility and usefulness of our formulations.
Track nonlinear energy sink (TNES) cells provide a promising passive approach for broadband vibration mitigation. However, their mechanical characteristics and vibration control performance under inclined installation remain insufficiently understood. This study investigates the influence of beam inclination angle on the stiffness and damping properties of TNES cells and their effectiveness in multimode vibration reduction of an inclined beam. A mechanical model of an inclined beam coupled with a concentrated exciter mass and TNES cells is established to analyze the steady-state response of the system. Meanwhile, the nonlinear stiffness and damping characteristics of TNES cells at different inclination angles are identified experimentally. The results show that distributed TNES cells can provide effective vibration mitigation over a wide range of inclination angles. The identified parameters further indicate that the inclination angle significantly affects the equivalent linear stiffness and damping of the TNES cells. In addition, the experimental results agree reasonably well with the theoretical predictions in terms of the overall response trends, although larger discrepancies are observed for higher-order modes. This study provides theoretical and experimental support for the design and application of TNES cells in inclined beam structures.
The inherent conflict between low mass and high sound insulation presents a critical bottleneck in the development of advanced honeycomb structures for engineering applications. To address this, a broadband yet highsound-insulation honeycomb acoustic metastructure is proposed by synergistically coupling membrane antiresonance with Helmholtz resonance for the first time. A theoretical model is developed based on the spaceharmonic expansion method to predict its sound transmission loss, and is validated against both finite element simulations and impedance tube measurements. The results demonstrate that the proposed metastructure achieves superior broadband insulation, with its STL significantly exceeding the mass law prediction over multiple frequency bands. Specifically, the synergistic enhancement mechanism is verified by evaluating the cross-sectional energy flux. Furthermore, the theoretical bound of the synergistic enhancement is determined analytically. Moreover, parametric studies are conducted to confirm the tunability and the robustness of the proposed design method. Finally, given in practical engineering applications, the proposed metastructure is applied to a soundproof enclosure. Compared with the traditional honeycomb enclosure, the radiated sound pressure level of the soundproof enclosure has been reduced by 45.5 dB at the single line spectrum, and the Aweighted sound pressure level in the external environment within 500 Hz-2000 Hz has been reduced by 4.1 dB. This work provides new physical insights into coupled acoustic metamaterials and offers a viable pathway toward multifunctional structural-acoustic integration.
The dry friction energy dissipation mechanism is widely employed to design passive vibration reduction dampers in industrial equipment. This paper presents a novel architected material that utilizes friction hysteresis for energy dissipation while possessing a self-recovering capability. The design features an M-shaped strut integrated within a re-entrant honeycomb frame. Under compression, the M-shaped strut contacts the frame base and slides, engaging the friction hysteresis mechanism to dissipate energy. Crucially, upon unloading, the elastic strain energy stored in the deformed structure enables it to self-recover entirely to its original configuration without external intervention. We validated this concept through loading-unloading tests on 3D-printed samples and finite element simulations that elucidate the structural deformation and contact evolution. Moreover, a theoretical model was established to accurately reproduce the force-displacement response of the metamaterial unit cell, enabling a parametric study. The results confirmed that the energy dissipation performance can be effectively tuned by parameters such as the friction coefficient, rib width, and strut inclination angle. This work pioneers a pathway for developing high-performance, self-recovering metamaterials based on tailored friction hysteresis.
The accurate quantification of cumulative relative motion at contacting interfaces is critical for predicting fretting fatigue, wear, and loosening in engineering systems. Yet standard approaches within commercial finite element software suffer from two independent structural deficiencies: algebraic cancellation, where reciprocating slip increments cancel in the signed accumulation; and separation-reset, where contact loss erases the accumulated motion history. Neither error can be reduced by mesh refinement or convergence control; both are embedded in the contact variable definition itself. This paper presents a post-processing framework that addresses these limitations. Two methods are proposed, a Solver-Coupled Method (SCM) and a novel Solver-Decoupled Kinematic Framework (SDKF), whose kinematic predictions mutually validate each other. Both accurately accumulate the true scalar motion path with normal-tangential decomposition; the SDKF additionally provides stability of normal-vector determination against mesh irregularities through integrated Principal Component Analysis (PCA)-based local coordinate algorithms. By decoupling kinematic analysis from geometric evolution, the SDKF transforms parametric studies of contact clearance, a physically meaningful but traditionally fixed parameter, into routine post-processing tasks, achieving two to three orders of magnitude speed-up over re-simulation. Validated on a contact benchmark with discontinuous non-proportional loading, the framework reveals that standard endpoint calculations underestimate cumulative motion by approximately 50% under a single reciprocating load cycle. The resultant-based endpoint metric conflates normal and tangential components, rendering comparison against established motion thresholds physically ambiguous even under monotonic loading. Under this benchmark, solver-reported contact slip requires path correction before use as kinematic input for wear or fretting predictions.
This paper investigates the subcritical crack growth behavior of penny-shaped fatigue cracks in a high-temperature superconducting cylinder subjected to the axial periodic motion of a coaxial permanent magnet. The governing equations of the magnetic field in the computational region are formulated using the H-formulation, with boundary conditions accounting for the coupled effects of the permanent magnet and the superconductor. A nonlinear finite element method is adopted to compute the electromagnetic field distribution. To capture the influence of the penny-shaped crack on the electromagnetic field in the superconductor, a crack influence region is incorporated into the numerical model. Under axial periodic motion of the permanent magnet, both the electromagnetic field and the associated body forces within the superconductor exhibit pronounced time-dependent variations. Based on damage accumulation theory, the subcritical crack growth driven by time-varying electromagnetic forces is analyzed. Numerical simulations are conducted to systematically examine the effects of the geometric parameters of the permanent magnet, the crack axial position within the superconductor, the motion trajectory and velocity of the permanent magnet, and the mechanical constraint conditions of the superconducting cylinder on the subcritical crack growth behavior. The numerical results indicate that: (1) when the radius of the permanent magnet cylinder approaches that of the superconducting cylinder, the subcritical growth rate of the fatigue crack within the superconductor increases significantly; (2) there exists a most unfavorable initial distance between the permanent magnet and the superconductor, from which periodic motion of the magnet leads to the fastest crack growth; and (3) the mechanical constraints of the superconducting cylinder play a significant role, with fixed upper and lower surfaces effectively suppressing crack growth and enhancing structural safety. This study provides theoretical and numerical guidance for the fatigue fracture oriented design and safety assessment of permanent magnet-superconductor levitation systems operating under dynamic service conditions.
Extracting model parameters from experiments mimicking earthquake loading conditions is of interest to better design civil engineering structures. In the present case, the challenge is to identify the complex response of a notched section of a structure described as a beam assembly, using a complete 3D description that requires a 6 & times; 6 stiffness matrix for the simple case of an elastic behavior, while here one addresses the presence of a notch or crack which opens or closes along the loading. A shaking table with an earthquake-like motion in one dimension was used to load the structure. The full 3D kinematics of the structure was measured using a pair of high-speed cameras and stereocorrelation. The displacement field allows the discontinuity of the generalized displacements at the notch root to be characterized. The deduced acceleration field gives access to the generalized forces in the structure, and, in particular, at the notch cross section. Relating generalized forces to generalized displacements discontinuity is the objective of the present study. A POD analysis of either the loading (generalized forces) or response (generalized displacements) gives a natural access of the complexity of loading experienced by the structure. Additionally, the POD analysis provides a direct access to the identification of the local elastic response (independently for the open and closed notch configuration). Identification finally appears as a mere projection of the force signal onto the temporal basis of the displacement or reciprocally. Because of the inertial loading of the structure, a full 3D characterization of the kinematics as enabled by stereocorrelation offers a very simple framework, which is the focus of the present paper, for the identification of elastic properties.
This paper studies analytically/numerically the dynamic response of a rigid wall retaining a cross-anisotropic partially saturated poroelastic soil to seismic forces, assuming plane strain conditions. The soil is treated as a three-phase medium, consisting of a linear cross-anisotropic elastic porous skeleton, with fluid and air phases flowing through the pores interactively, thereby providing a more general and realistic model than a saturated or a fully dry poroelastic model. The problem is first solved for the case of two rigid walls retaining the soil, and the solution for the single wall case is obtained by taking a sufficiently large separation distance between the two walls. The system of the governing partial differential equations of motion is considered in the frequency domain, assuming a time harmonic seismic excitation, and is reduced algebraically to a system with only four unknowns (two solid displacements and two pressures for fluid and air). Expansion of the unknown displacements and pressures in sine and cosine Fourier series along the horizontal direction reduces the system of the four partial differential equations to a system of four ordinary differential equations in the vertical direction, which can be solved in closed form. The obtained frequency-domain solution is used to recover the corresponding solutions for the special cases of elastic and saturated poroelastic soils reported in the literature, for verification purposes. Parametric studies are conducted to assess the effect of various parameters, such as the degree of saturation and the excitation frequency on the base shear force and the base bending moment. The results show that the degree of saturation significantly affects the dynamic response of the system. Finally, the response of the wall-soil system to a transient seismic excitation (real recorded ground motion) is obtained numerically through Fourier transform inversion.
To enhance the device's adaptability in variable environments and improve its efficiency in harvesting low-frequency vibrations, this paper proposes a novel low-frequency vibration energy harvesting system based on a flute-shaped slider structure (LFV-FSD). The flute hole can adjust the pitch of the flute. The flute-shaped slider can adjust the distribution of beam stiffness, thereby regulating the beam's vibration frequency. In response to variable external conditions, the sliding mass block on the cantilever beam with holes can automatically adjust its position to match the frequency of external excitation, inducing resonance within the apparatus and thereby enhancing the system's energy harvesting efficiency. A dynamic model was established using Lagrange's principle, and a 3D model of the LFV-FSD apparatus was constructed. In this paper, the explicit Euler method and the Runge-Kutta method are respectively adopted to plot the root-mean-square diagram of induced voltage and the basin of attraction diagram. Numerical simulations analyzed the disparity in energy harvesting performance between the LFV-FSD device and conventional piezoelectric energy harvesting device. The maximum induced voltage generated by the LFV-FSD harvester approached five times that of the traditional device. By integrating bifurcation diagrams with Lyapunov exponents, the evolutionary pattern of a system transitioning from periodic motion to chaos is elucidated, and the impact of chaotic states upon the system's energy harvesting efficiency is assessed. Finally, by analyzing the system's basin of attraction and its phase portraits, initial conditions are linked to high-energy states to boost the overall energy harvesting performance via high-energy trajectories. When the dimensionless frequency Omega 0 = 0.25, the dimensionless natural frequency ratio zeta = 0.75, and the mass ratio theta = 1.00, four coexisting attractors exist in the system, and the voltage value on the high-energy orbit is approximately four times that on the low-energy orbit.
Textile dyeing vessels operate under sustained high temperature and pressure, generating steep thermal gradients and pressure-driven deformation. These coupled effects produce severe thermo-mechanical stresses. Metal-ceramic functionally graded materials (FGMs) are therefore employed, as they combine thermal resistance, mechanical integrity, and non-corrosive behavior. However, most existing analyses neglect two features that are crucial under realistic service conditions: temperature-dependent material behavior and manufacturing-induced porosity. To address this problem, we develop a novel fully analytical layer-wise power-law thermo-inhomogeneity (LWPTI) framework for coupled thermoelastic analysis of porous, temperature-dependent FGM cylindrical vessels. The graded wall is discretized into inhomogeneous sublayers, where radial property variation is described by layer-wise thermo-power-law functions. Closed-form thermoelastic fields are obtained by enforcing interfacial continuity and boundary conditions. The framework is validated with finite-element and literature solutions, demonstrating rapid convergence and high accuracy. Application to a textile dyeing vessel shows that temperature dependence affects stress far more strongly than temperature prediction itself, so neglecting it can markedly underestimate structural demand. A lower gradation index and higher porosity increase thermal resistance, while controlled porosity redistributes hoop stress away from the outer surface. These results establish LWPTI as an efficient analytical tool for the design of high-temperature FGM vessels.
This study proposes a novel analytical framework for shear-horizontal (SH) wave propagation in a piezoelectric semiconductor (PSC) thin film deposited on a magneto-electro-elastic (MEE) substrate through an electrically tunable, coupled electromechanical spring interface. The central novelty lies in formulating and employing new interface conditions that simultaneously incorporate mechanical, electrical, and electromechanical behavior. These generalized spring relations effectively represent displacement jumps, potential discontinuities, and cross-field coupling at the interface. This framework enables the interface to be externally controlled, offering a new mechanism for tunable imperfect bonding. Using a rigorous mathematical formulation based on the governing field equations and interface continuity conditions, dispersion relations are found. For numerical analysis, three MEE composite configurations are considered. The obtained results are validated numerically with the previously established results. The effect of PSC film thickness and the impact of externally applied horizontal electric biasing are also evaluated numerically to assess their roles in dispersion tuning. The study also includes special cases and contour plots to represent the effects of parameters on the propagation behavior of the SH wave. This architecture could be used to make reconfigurable surface acoustic wave (SAW) devices, adaptive sensors, micro-nano resonators, and tunable filters, where it is very important to have exact control over where the acoustic energy goes and how it moves.
Soft active polymers respond strongly to external fields due to their molecular architecture and material characteristics. Among these, dielectric elastomers-a widely used class of soft active polymers exhibit large electro-mechanical deformation when electrically stimulated. When a pre-stretched dielectric elastomer membrane is bonded to a compliant frame, the assembly naturally relaxes into a dielectric elastomer minimum energy structure (DEMES). In the present study, the dynamic response of such DEMES actuators is analyzed by incorporating the coupled effects of membrane pre-stretch, material anisotropy, and ambient temperature. A Zener rheological model, consisting of a Maxwell element in parallel with a spring, is used to represent the visco-hyperelastic behavior, and an analytical neo-Hookean material-based formulation is developed. A computationally efficient governing model is derived using the non-conservative Euler-Lagrange equation based on the principle of least action. The proposed framework is applied to examine equilibrium configurations, transient response, DC and AC actuation characteristics, periodicity (using Poincar & eacute; and phase-portrait analysis), and resonant behavior. The results show that membrane pre-stretch, anisotropy, and temperature significantly influence the oscillation amplitude, permanent deformation, dynamic stability, and resonant frequency. The temperature-dependent behavior of isotropic membranes leads to supercritical pitchfork bifurcation but anisotropic systems show faster convergence and larger deformations under identical conditions. The proposed analytical model offers essential design directions which enable engineers to optimize DEMES-based soft robotic actuators for operation across different environmental settings.
Piezoresistive materials, including metals, semiconductors, and conductive composites, have been widely used in structural health monitoring (SHM) because their electrical response is sensitive to mechanical deformation and damage. To describe this coupled behaviour, this study proposes a generalized elasto-plastic-damage model integrated with a piezoresistive formulation, enabling the simultaneous prediction of mechanical response and resistivity evolution under different loading conditions. Although piezoresistive simulations are often conducted in commercial multiphysics finite-element software, their capability for strongly nonlinear behaviour, such as plasticity and progressive damage, remains limited. By contrast, ABAQUS provides robust tools for nonlinear mechanical analysis but lacks a built-in electromechanical framework for piezoresistive modelling. To address this gap, a practical one-way coupled implementation strategy is developed in ABAQUS through the combined use of UMAT and UMATHT subroutines. The proposed framework is validated against experimental results for carbon black-filled cement composites (CBCC) and brittle carbon nanotube (CNT) composites. The simulations show good agreement with the measured mechanical and electrical responses, including the stress-strain behaviour and the evolution of fractional resistance change, for both plastic damage-coupled and brittle material systems. These results demonstrate that the proposed approach can effectively capture nonlinear damage-dependent piezoresistive behaviour in a general-purpose finite-element platform, providing a practical tool for the analysis and design of piezoresistive materials for SHM applications.
