Search Results (431)

The model is based on the periodic translational symmetry of regular saw-toothed joint surfaces and reveals the time-dependent breaking of this symmetry under hydro-mechanical coupling through the introduction of damage evolution. Traditional creep models typically rely on static constants, which fail to capture the nonlinear, time-dependent degradation of rock under complex conditions. To address this, this paper proposes a novel nonlinear shear creep model for regular saw-toothed joint surfaces under hydro-mechanical coupling. First, a calculation method for effective shear stress is established, accounting for normal stress, asperity height, and water pressure. Next, traditional static parameters are transformed into dynamic variables to accurately model the primary and steady-state creep stages. Finally, a plastic damage element is introduced to simulate the accelerated creep stage, revealing that damage accumulates with time and is exacerbated by higher seepage pressure. By integrating early-stage viscoelastic and late-stage viscoplastic characteristics, this model captures the complete nonlinear shear creep process, providing a robust theoretical basis for long-term stability evaluations. Full article

This work develops an analytical framework for nonlinear fractional partial differential equations that combine Kirchhoff-type terms, double-phase operators, and $\psi$-Hilfer fractional derivatives. This paper investigates two classes of problems involving variable-exponent growth conditions. The first problem analyzes general nonlinear sources and formulates the solution as a fixed point of a nonlinear operator. Precisely, by proving that the functional energy is coercive, hemicontinuous, and strictly monotone, we establish the existence and the uniqueness of weak solutions via monotone operator theory. The second problem incorporates a convection-type nonlinearity, which breaks variational structure and requires the more robust theory of pseudomonotone operators. Under suitable growth and mixed-order assumptions on the nonlinearity, we prove the existence of at least one weak solution. The main tools are grounded in variable-exponent Lebesgue and Musielak–Orlicz–Sobolev spaces, with compact embeddings, modular estimates, and fractional integral identities playing a key role in the proofs. We note that the results contribute to the mathematical modeling of phenomena involving nonlocal elasticity, viscoelastic materials, phase-transition media, and fractional dynamical systems where the stiffness of the medium depends on the total deformation (Kirchhoff effect) and the energy density alternates between distinct growth regimes (double-phase). The $\psi$-Hilfer derivative enhances the scope by enabling models with tunable memory and hereditary effects. Full article

This research utilizes Laser Doppler Vibrometer (LDV) technology to measure pavement deflection velocity under heavy moving loads at the Virginia DOT Accelerated Pavement Testing (VDOT APT) facility. While LDVs are typically integrated into Traffic Speed Deflectometers (TSDs) for measuring deflection velocities, this research employs a standalone, tripod-mounted LDV to capture highly repeatable data under controlled Heavy Vehicle Simulator (HVS) loading. A three-dimensional viscoelastic finite element (3D-FE) model was developed in Abaqus (version 2016) and calibrated using the LDV-measured deflection velocities and site-specific material properties. The model incorporates asphalt viscoelasticity, three-dimensional nonlinear contact stresses, and continuous loading conditions. Results demonstrate very good agreement between the calibrated 3D-FE model and observed responses, with calculated percentage differences of 0.6% and 3.4% for the maximum and minimum deflection velocity peaks, respectively. These findings, along with a 10% ratio between the standard deviation of the error and the measured signal, validate the model’s accuracy and the effectiveness of LDV instrumentation. This stand-alone application of a TSD-type LDV at an APT facility, to directly measure pavement deflection velocity under a moving load to calibrate a 3D-FE model, represents a key innovative aspect and addresses an identified gap in the literature on LDV-based pavement evaluation techniques. It should be noted that the proposed framework is calibrated for a single pavement structure under controlled loading and environmental conditions, and is applicable to the initial, undamaged state of the pavement. Further validation across different material configurations, environmental gradients, and damage stages is required to generalize the approach. Full article

Hydrogels, particularly those based on polymer networks, exhibit complex mechanical behaviors arising from the interplay between network architecture, molecular interactions, and external stimuli. In particular, their viscoelasticity, energy dissipation, and nonlinear mechanical responses arise from the dynamic nature of crosslinking and multiscale relaxation processes. This review provides a comprehensive overview of hydrogel mechanics from a multiscale perspective, covering viscoelastic behavior, relaxation dynamics, energy dissipation mechanisms, nonlinear deformation, and fracture properties. We summarize recent advances in experimental characterization, including bulk rheology and single-molecule force spectroscopy, and discuss how molecular-level interactions, bond kinetics and mechanochemical processes contribute to macroscopic mechanical performance. In addition, theoretical models and constitutive frameworks describing transient and dynamic polymer networks are critically evaluated to bridge microscopic dynamics with bulk responses. Emerging strategies that integrate dynamic bonding and force-responsive elements are also discussed in the context of tailoring mechanical adaptability and functionality. Finally, we outline current challenges and future directions toward the rational design of hydrogels with tunable viscoelasticity, enhanced mechanical robustness, and programmable mechanical functions. Full article

During service in engineering fields, the performance of carbon black (CB)/silica-filled rubber suffers degradation because of the influence of aging. In the process of reproducing the mechanical behavior of CB/silica-filled rubber, many constitutive models have been proposed. However, the model selection strategy taking the aging effect into consideration is still unclear, especially the classical model selection strategy. In this work, the effects of thermo-oxidative and ultraviolet aging on the nonlinear viscoelasticity of CB/silica -filled rubber were investigated using dynamic mechanical analysis tests. It was found that aging conditions had a great effect on the nonlinear viscoelasticity of CB/silica -filled rubber. Meanwhile, the degradation mechanisms were discussed on the basis of the existing works. To accurately reproduce the nonlinear viscoelasticity degradation, classical models, such as the Kraus model and Maier–Göritz model, were used to describe the experimental data. In the reproducing process, fitting correlation coefficients and root mean square error were used to verify the reliability of classical models. Comparingsimulation results and experimental ones, it was found that the Maier–Göritz model was more reliable under all aging conditions. This work will contribute to a model selection strategy and a deeper understanding of the degradation mechanism. Full article

Long-distance belt conveyors exhibit significant nonlinear dynamic characteristics due to factors such as the viscoelasticity of the conveyor belt, startup curves, and material loading, which lead to substantial variations in component loads and belt tension. This complexity poses challenges for dynamic analysis and the study of dynamic properties. Based on the Kelvin–Voigt viscoelastic constitutive relation, this paper establishes a discrete model of the conveyor belt and further develops a nonlinear dynamic model for long-distance belt conveyors. The model is numerically solved using the fourth-order Runge–Kutta method. On this basis, the influence of key parameters—such as integration step size, startup curve, operating time, and belt speed—on the dynamic behavior of the belt conveyor is investigated. The results indicate that increasing the counterweight mass effectively suppresses oscillation in the tensioning device and enhances system stability. Prolonging the startup duration and optimizing belt speed also mitigate load impacts. Compared with conventional methods, a composite transitional startup strategy is proposed, which significantly reduces transient tension peaks in the conveyor belt. This study provides a theoretical basis for optimizing control strategies and structural design of long-distance belt conveyors, thereby improving operational safety and reliability. Full article

An integrated numerical method is proposed for analyzing the nonlinear seismic response of near-fault building clusters, comprising three algorithms: (1) a structural investigated lump algorithm for elastoplastic dynamic response of structure; (2) a connecting investigated lump algorithm for bidirectional wave propagation between the site and elastoplastic building clusters; (3) a geomedia investigated lump algorithm for seismic wave propagation with an improved viscoelastic constitutive model, which allows independent definition of P/S-wave quality factors to characterize geomedia attenuation. Validated for its capability in simulating site-city dynamic interaction problems via a shaking table test, the method is applied to study the seismic response of near-fault building clusters in Xichang City under a hypothetical M_w6.8 earthquake. It is shown that irrespective of whether shallow geological structures are considered, clusters (c2–c4) situated in rupture-forward surface area within ~1.5 km of the fault trace entered the elastoplastic stage, while others (c1, c5) remained elastic. Shallow geological structures may reverse locally hanging-wall/footwall effects of both near-fault structural seismic response and ground motion. A notable seismic-response characteristic of near-fault structures undergoing the elastoplastic stage is that the permanent structural motion displacement (PSMD) at the slab of a specific floor incorporates not only the non-zero permanent ground motion displacement (PGMD) but also the non-zero final structural residual displacement (FSRD) relative to the supporting ground. The developed method could provide support for seismic damage assessment, site selection, and structural optimization design of near-fault building clusters. Full article

Background/Objectives: The uprighting of mesially tipped mandibular second molars following first molar loss is a complex surgical and orthodontic challenge. Conventional methods often result in reciprocal anchorage loss. Mini-implants (MIs) have emerged as essential temporary anchorage devices (TADs) that provide absolute anchorage and enable more predictable tooth movements. Methods: Numerical simulations were performed to evaluate the forces required for mandibular second molar uprighting under two conditions: first, only with the second molar present, and second, with both the second and the third molars present. Although the periodontal ligament exhibits nonlinear and viscoelastic behavior in vivo, a linear elastic approximation was adopted to allow for a reliable evaluation of comparative stress distribution and initial displacement patterns within the scope of this exploratory biomechanical study. Stress distribution in the roots, periodontal ligament, and alveolar bone was assessed for each scenario. Two three-dimensional (3D) models of the left mandibular segment were created from scans of a human mandible and its teeth. The first model included the canine, the first and second premolars, and the second molar. A second model additionally incorporated the third molar. A retromolar MI was placed in both models. Molar uprighting was simulated using a spring connecting the implant to a button bonded on the mesial surface of the second molar. A force of 200 g was applied because in clinical orthodontic practice, forces that exceed approximately 2 N may cause pain or undesirable tooth mobility. Displacements along the X, Y, and Z axes, as well as regions of peak stress, were analyzed. Results: Model 1 showed maximum displacements at the furcation/mid-root, distal root apex, and distal crown, with von Mises stresses of 0.470 to 0.371 MPa. In Model 2, peak displacements occurred at the mesial root and crown, with stresses of 0.185 and 0.149 MPa, respectively. The magnitude of displacements was in the order of 10⁻⁵ mm. Such values represent initial mechanical responses rather than clinically observable tooth movements. However, the differences between models (e.g., the stress reduction) are expected to be clinically meaningful. Conclusions: Since clinical measurements regarding the stress distribution on teeth and surrounding tissues during orthodontic molar uprighting movements are impossible to perform, the finite element method (FEM) can offer insight into these aspects. The presence of the third molar significantly modulates the biomechanics of second molar uprighting via retromolar MIs. When the third molar is present, the second molar exhibits a reduced tendency for deformation during distalization, although this leads to a slower displacement. This FEM provides biomechanical insights but does not support direct clinical decision-making. The present findings should be viewed as theoretical biomechanical tendencies that require confirmation through clinical, experimental, and longitudinal studies before translation into clinical practice. Full article

This paper proposes a machine-learning-assisted framework for modal sensitivity analysis of systems with viscoelastic damping elements, including both classical and fractional rheological models. Surrogate models are trained to approximate natural frequencies over a prescribed parameter space using two sampling strategies (Grid and Latin Hypercube) and two regression approaches: multi-layer perceptron (MLP) and Gaussian process regression (GPR). Sensitivities are obtained from the surrogates by finite differences and complemented by model-interpretability measures, namely permutation feature importance (PFI) and Shapley Additive Explanations (SHAP). The surrogate-based results are compared with analytically obtained sensitivities. Local first- and second-order sensitivities of natural frequencies are derived analytically using the direct differentiation method (DDM) for a nonlinear eigenvalue problem formulated in the Laplace domain and further transformed into dimensionless sensitivity measures. The methodology is demonstrated for a single-degree-of-freedom oscillator with classical and fractional Kelvin damper models and a two-story frame equipped with a fractional Kelvin damper. The results show very good agreement between analytical and surrogate-based sensitivities. Feature-importance rankings obtained by PFI and SHAP are consistent with the dimensionless sensitivities and capture changes in parameter influence under varying damping levels. Dispersion studies indicate only minor ranking variations. Full article

Background and objectives: Articular cartilage provides low-friction articulation across joint surfaces, distributes loads, and absorbs stress, all of which are crucial mechanical functions of joints. Changes in the mechanical characteristics of cartilage are among the first signs of degenerative joint disease, and they are especially important for athletes who are subjected to high-impact, high-magnitude loading on a regular basis. The objective of this study was to: (i) compare the mechanical characteristics of tibiofemoral cartilage in healthy and osteoarthritic conditions across medial and lateral anatomical compartments; and (ii) use nonlinear phenomenological viscoelastic modeling in conjunction with unconfined compression testing to characterize compartment-specific viscoelastic behavior. Materials and Methods: Forty-six human tibiofemoral cartilage samples were collected during knee surgeries and classified as healthy (n = 17) or osteoarthritic (n = 29) and as medial (n = 26) or lateral (n = 20). Quasi-static unconfined compression tests were performed at 1 mm/min to obtain stress–strain responses, Young’s modulus, maximum compressive stress, and energy absorption. Viscoelastic behavior was analyzed using a nonlinear phenomenological viscoelastic model. Appropriate parametric or non-parametric statistical tests and effect size measures were applied. Results: Osteoarthritic cartilage’s stiffness and energy absorption were significantly higher than those of healthy tissue (p < 0.05). Medial cartilage exhibited significantly greater stiffness and stress than lateral cartilage (p < 0.001). The nonlinear phenomenological viscoelastic model provided an excellent fit (R² > 0.999). Conclusions: The mechanical profile of osteoarthritic tibiofemoral cartilage is characterized by pathological mechanical remodeling and increased stiffness. Greater mechanical susceptibility in the medial compartment supports the significance of cartilage biomechanical properties as sensitive indicators of early degeneration and osteoarthritis risk in athletic populations. Full article

The paper proposes a new mathematical framework in explaining the effect of periodic electric fields on the nonlinear interfacial instability emerging between two Walters’ B/Rivlin–Ericksen of non-Newtonian fluids. The suggested approach is designed to increase the prediction and control of electrically induced instability phenomena observed in advanced Electrohydrodynamics. Accordingly, under the impact of periodic EFs, the instability properties between the two superposed, electrically conducting viscoelastic fluids passing through a porous medium are examined. Furthermore, the fluids differ in their densities, electrical conductivities, permeabilities, and viscoelastic characteristics, surface tension and are supposed to performance at the disturbed interface. To decrease the mathematical complexity, viscous potential theory is adopted. By combining the pertinent nonlinear boundary conditions with the governing linearized equations of motion, more simplifications are made. The methodology leads to a nonlinear Mathieu oscillator characterizing the interfacial displacement. Within the scope of the non-perturbative approach, the resulting nonlinear ordinary differential equation is converted into an equivalent linear representation. A non-dimensional analysis yields a set of typical dimensionless parameters, significantly reducing the number of governing variables and facilitating physical interpretation. The stability criteria are numerically studied under complex conditions, indicating that the fundamental stability mechanism stays unchanged for both real and imaginary coefficients of the nonlinear characteristic equation regulating the interfacial motion. Full article

Flexible resistive bend sensors are essential for monitoring human movement in smart rehabilitation and soft robotics. However, widespread adoption is currently hindered by a trade-off between the high cost of metal-film technologies and the performance degradation (significant hysteresis and non-linearity) of low-cost carbon/polymer composites. This study presents a geometrically customizable bending sensor fabricated from conductive thermoplastic polyurethane (TPU) using Fused Deposition Modeling (FDM) technology as an accessible alternative to commercial sensors. By parametrically optimizing physical dimensions—including trace width, layer thickness, and pattern geometry—the sensors were tailored to achieve target resistance values within a target window of 20–50 kΩ (achieved: ~44 kΩ nominal) for specific finger-joint applications. Electromechanical characterization revealed a negative gauge factor (GF), where resistance decreases upon bending or elongation due to conductive pathway formation and densification within the polymer matrix. This behavior cannot affect sensor operation, and required bend-resistance responses were acquired using geometrical optimization. To compensate for inherent viscoelastic-induced hysteresis and non-linear behavior, a third-degree polynomial modeling approach was implemented. This modeling approach yielded a coefficient of determination (R²) of approximately 0.90. Compared to standard commercial sensors, the proposed FDM-printed design successfully overcomes geometric limitations while offering a cost-effective, high-performance solution for tailor-made wearable technologies and smart rehabilitation gloves. Full article

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps ($O\left(N_t^2\right)$), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to $O\left(N_t\right)$, yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems. Full article

This study investigated the linear and nonlinear viscoelastic properties of cherry Jell-O^® samples through oscillatory shear methods including small-amplitude (SAOS), medium-amplitude (MAOS), and large-amplitude (LAOS) experiments. Cherry Jell-O^® showed solid-like gel behavior (tanδ < 1) up to γ₀:160%. The sample transitioned into nonlinear behavior above γ_cri: 16% and was classified as type III (weak strain overshoot). Chebyshev coefficients revealed that the samples exhibited strain-stiffening (e₃/e₁ > 0) and shear-thickening (v₃/v₁ > 0) intracycle behavior in the nonlinear region. Both elastic and viscous Lissajous–Bowditch curves showed distortions from elliptical trajectories in the nonlinear region. FTIR spectra showed LAOS deformation-induced structural changes, particularly in the Amide I and Amide II regions. Tanδ decreased below 1 upon the removal of the LAOS deformation. These findings showed that although LAOS deformation induced molecular changes in the cherry Jell-O^® samples, their elasticity was largely preserved by a strong, resilient network. Full article

Accurate prediction of surface rupture induced by seismogenic fault displacement is essential for the seismic safety assessment of major engineering projects. Most existing numerical simulations adopt quasi-static approaches, in which the effect of fault displacement is simplified as static loading. As a result, these methods cannot represent the dynamic characteristics of the fault rupture process, such as stress-wave propagation, soil inertial effects, and the influence of dynamic loading paths on rupture extension in soil layers. To address this issue, a full-process simulation method is established for simulating rupture of overlying soil subjected to dynamic fault displacement: Firstly, a non-uniform dynamic fault displacement loading is formulated for the two sides of the fault based on viscoelastic artificial boundaries, allowing the differential motion of the bedrock on both sides of the fault to be represented. Secondly, an improved dynamic skeleton curve constitutive model of soil is developed by introducing a minimum modulus constraint, providing an improved description of soil nonlinear dynamic behavior from small-strain hysteresis to large-strain shear failure. The reliability of the proposed method is verified through element-level tests and horizontal-site response simulation. As a benchmark, its ability to reproduce key rupture characteristics under quasi-static conditions is also assessed by comparison with classical quasi-static rupture studies. The method is then applied to simulate rupture extension and deformation response of overlying soil under strike-slip fault displacement. The results show that, compared to quasi-static analysis, dynamic fault displacement produces similar cumulative slip for surface rupture initiation and full connection, but induces transient amplification of peak surface displacement and a wider deformation zone with gentler displacement gradients. These findings demonstrate the necessity of considering dynamic fault dislocation of bedrock–overlying soil interaction in seismic assessments of engineering projects crossing active faults. Full article