Search Results (85)

Vertebral fractures are among the most common skeletal injuries and present significant clinical and biomechanical challenges, particularly in older adults and individuals with low bone density. Accurate prediction of vertebral mechanical response and failure under varying loading conditions is essential for improving understanding of spinal injury mechanisms. This study develops a density-dependent viscoelastic analytical model to predict the stiffness and fracture force of human vertebral specimens subjected to different compression rates. The vertebral body is represented as a composite structure consisting of a cortical shell and a trabecular core. Cortical bone is modeled as a linear elastic material, whereas trabecular bone is described using a Kelvin–Voigt viscoelastic formulation. Density-dependent constitutive relationships are incorporated for the elastic modulus and viscous coefficient of trabecular bone. Unknown material parameters are identified through optimization using the Nelder–Mead algorithm, based on experimental compression data from cadaveric vertebral specimens tested under quasi-static and dynamic loading conditions. The calibrated model reproduced the overall trend of specimen-to-specimen mechanical variation observed experimentally. Predicted stiffness values were in reasonable agreement with measured data. Fracture force predictions showed moderate agreement for dynamically tested specimens (R² = 0.60), which improved to R² = 0.88 after exclusion of one statistically identified outlier. Compared with a purely linear elastic formulation, the proposed viscoelastic model demonstrated modest improvement in stiffness prediction and more substantial improvement in fracture force prediction. These findings indicate that incorporating density-dependent viscoelastic effects improves representation of vertebral mechanical behavior, particularly at higher loading rates. Owing to its simplicity and computational efficiency, the proposed model requires only limited imaging input and may be useful for future biomechanical investigations, rapid screening, and injury risk prediction. Full article

This work is concerned with the numerical treatment of a wave equation with fractional Kelvin–Voigt damping, where the viscoelastic contribution is described by a Caputo derivative in time acting on the elliptic part of the model. Such models are of interest because memory effects produce hereditary damping and reduced regularity near the initial time, which makes both the analysis and the numerical discretization more delicate than in the classical wave equation. We study the problem on a bounded convex domain under homogeneous Dirichlet boundary conditions and derive a solution representation that is suitable for regularity analysis. Based on this representation, we establish stability and smoothing estimates for both homogeneous data and forcing terms, with particular attention to the influence of nonsmooth initial data. For the spatial discretization, we employ a continuous Galerkin finite element method with piecewise linear elements and prove error estimates that are explicit in the regularity of the initial displacement, initial velocity, and source term. We show that the fully discrete approximation inherits the regularity-dependent behavior of the continuous problem and achieves optimal convergence in space together with second-order accuracy in time under appropriate assumptions on the data. Several numerical experiments are presented to illustrate the theoretical findings and to confirm the predicted convergence rates, thereby supporting the effectiveness of the proposed space–time discretization. Full article

Understanding the dynamics of gas bubbles in viscoelastic media is crucial for applications involving stable cavitation under ultrasound, such as drug delivery, materials processing, and biomedical imaging. The Rayleigh-Plesset equation formulated in terms of bubble volume variation, incorporating viscoelastic effects via the linear Kelvin–Voigt model, is extended here to a fourth-order approximation. This formulation allows a more accurate description of nonlinear bubble dynamics at finite acoustic amplitudes. The resulting equation is solved numerically under various acoustic conditions, with particular emphasis on driving frequencies near the bubble’s resonance and differences between Newtonian and viscoelastic media. To identify the physical conditions under which higher-order nonlinearities become necessary, a decision-tree classification analysis is performed. The results show that the proximity to resonance and the excitation amplitude are the primary determinants of higher-order nonlinear effects, while rheological properties act as modulators, with viscosity exerting a stronger influence than elasticity within the explored ranges. This work provides a physically interpretable criterion for selecting the appropriate model order, improving the prediction and control of nonlinear bubble oscillations under ultrasound excitation in viscoelastic media. Full article

This paper presents a practical numerical procedure for the study of structures on foundations subjected to soil consolidation settlements, using the Finite Element Method (FEM) coupled with the Boundary Element Method (BEM). A theoretical application is presented for a structure built on saturated soft soil, employing the Kelvin–Voigt and Boltzmann viscoelastic models. The Kelvin–Voigt model is suitable for situations where uniform or negligible initial settlements are assumed before the onset of soil consolidation, whereas the Boltzmann model allows for the consideration of differential movements, including both immediate and time-dependent displacements. This study shows that, although the same viscoelastic parameters are adopted for both models, the differences in internal forces and resulting displacements can be significant due to the distinct relative stiffnesses. The choice of viscoelastic model directly impacts the prediction of structural behavior. The analyses were conducted considering an iterative coupling between the FEM and BEM systems, using an MATLAB R2024a routine developed by the authors. Despite the differences between the models, the results obtained were consistent with the technical literature, reinforcing the applicability of the proposed procedure. 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

Coastal erosion is increasingly influenced by anthropogenic alterations to the sediment cycle and morphological transformations. Traditional shallow water models often neglect the mechanical behavior of the seabed and its rheological response to hydrodynamic forcing, limiting their accuracy in forecasting erosion patterns. To address these limitations, this study extends the classical one-dimensional Saint-Venant (shallow water) model by incorporating effects of viscosity, frictional effects, sediment transport and viscoelasticity. The seabed is treated as a Kelvin–Voigt material, characterized by an elastic modulus and a viscous damping coefficient, to account for both immediate and time-dependent mechanical responses. Using the COMSOL Multiphysics platform, the evolution of the water column and seabed was simulated in six idealized case studies under various conditions, including changes in seabed topography and different frictional and dispersive regimes. The results demonstrate the influence of seabed topography, friction $S_f$, diffusion/dispersion regularization term $E$, and viscoelastic properties on wave seabed interactions and morphodynamic bed evolution (Exner-type). The inclusion of viscoelastic damping contributes to the stabilization of morphological evolution, mitigating abrupt changes in bathymetry and enhancing the physical realism of the simulations. The whole research aims to improve the prediction capabilities of erosion processes and advance the current modeling tools. Full article

The stabilization of rock mass vibrations in underground excavations presents a critical engineering challenge due to the interplay of viscoelastic dynamics, impulsive shocks from blasting or rock bursts, and time-varying delays induced by wave propagation and sensor–actuator networks. In this paper, an integral sliding mode control scheme is developed for a Kelvin–Voigt type hyperbolic system subject to such impulsive effects and time-varying delays. To preserve sliding surface continuity under impulsive disturbances, the impulse information is explicitly incorporated into the design of the integral sliding function. The resulting sliding mode dynamics, which include discrete state jumps, are analyzed using a piecewise Lyapunov functional combined with inequality techniques; sufficient conditions are derived to guarantee asymptotic stability. Moreover, a sliding mode control law is synthesized to ensure that the system trajectories reach and remain on the sliding manifold from the initial time onward, despite parameter uncertainties and external disturbances. Numerical simulations with parameters reflecting realistic mining scenarios verify the effectiveness of the proposed control strategy, demonstrating its potential for practical rock mass vibration stabilization in geotechnical engineering. Full article

Viscoelastic (VE) dampers are widely used for structural response control, but broader engineering adoption is often constrained by temperature- and amplitude-dependent properties and limited full-scale evidence on reliable performance when deformation demands exceed the conventional 300% shear-strain design domain. This study experimentally characterizes a full-scale TRCS-type VE damper (TRCS500T-10) employing a styrene–olefin thermoplastic elastomer, with an emphasis on large-deformation and beyond-design behavior. Four nominally identical specimens were tested in a temperature-controlled chamber using sinusoidal, displacement-controlled loading at target shear strains of 300% (≈30 mm) and 450% (≈45 mm). Effective engineering parameters were obtained from stable hysteresis loops using a Kelvin–Voigt-based reduction, including effective stiffness K_eff, effective damping coefficient C_eff, effective damping ratio ξ_eff, and dissipated energy per cycle W_d. At 300% shear strain, the dampers exhibited stable hysteresis with acceptable specimen-to-specimen variability and only modest changes in K_eff, C_eff, and W_d over an ambient-temperature interval of approximately 20–33 °C, while ξ_eff remained around 0.40–0.42. Beyond-design tests at 450% shear strain maintained stable force–displacement loops with substantial load capacity (peak forces ≈ 435–492 kN) and increased per-cycle energy dissipation (approximately 4.0 × 10⁴ kN·mm). Manufacturer-provided polynomial relations were used to standardize the measured properties to a reference condition and to compile a parameter-estimation table for preliminary engineering application. A monotonic ultimate test on specimen TRC500T-05 indicated an ultimate shear deformation capacity of approximately 850% without interface debonding. Collectively, the results provide full-scale evidence of a widened usable deformation range and a practical, design-oriented parameterization for thermoplastic VE dampers under large deformation demands. Full article

We calculate the mechanical response $r\left(x,t\right)$ of an initially quiescent semi-infinite homogeneous medium to a pulse applied at the origin, and this is achieved within the framework of the Kelvin–Voigt model. Although this problem has been extensively studied in the literature because of its wide range of applications—particularly in seismology—here, we present a solution in a novel integral form. This integral solution avoids the numerical computation of the solution in terms of the inverse Laplace transform; that is, numerical integration in the complex plane. In particular, we derive integral form expressions for both delta-pulse and step-pulse excitations which are simpler and more computationally efficient than those previously reported in the literature. Furthermore, the obtained expressions allow us to obtain simple asymptotic formulas for $r\left(x,t\right)$ as $x,t\to 0,\infty$ for both step- and delta-type pulses. Full article

The numerical analysis of dissipative energy in dynamic problems involving impact and contact phenomena relies on the physical principles of classical thermodynamics and on the constitutive equations of the material, supplemented by some additional considerations of potential contact interfaces. From the mathematical perspective, we come to a weak form of partial differential equation(s) of evolution with initial, boundary, and interface conditions, whose numerical analysis is required using the method of discretisation in time and typically the finite element technique. Dissipative energy is an important metric for quantifying the portion of mechanical work that is permanently converted to plastic work and thermal energy, among other applications. Crucially, the localised accumulation of this energy, often expressed as the plastic work density, is the primary physical parameter driving microstructural changes, damage initiation, and crack propagation under intense loading. This paper demonstrates how the dissipative energy resulting from material nonlinearities can be evaluated in dynamic problems involving the impact of one body on another and provides a quantitative comparison of numerically calculated dissipated energy using three types of nonlinear constitutive material models, namely the plastic material model with Rankine–Hill criterion, the Mazars damage model, and the Kelvin–Voigt viscoelastic model. Full article

Structural adhesives in aeronautical applications are routinely exposed to complex loading histories that generate time-dependent deformation, making accurate prediction of their viscoelastic response essential for reliable assessment of joint integrity. This work presents an integrated experimental and modeling study of the aerospace-grade epoxy adhesive 3M Scotch-Weld EC-2216 using multi-step creep and stress-relaxation tests performed at room temperature and controlled loading rates, combined with fractional viscoelastic modeling. Unlike traditional single-step characterizations, the multi-step protocol employed here captures the cumulative loading effects and fading-memory dynamics that govern the adhesive’s mechanical response. The experimental data were analyzed using fractional Maxwell, Voigt–Kelvin, and Zener formulations. Statistical evaluation based on the Bayesian Information Criterion (BIC) consistently identified the Fractional Zener Model (FZM) as the most robust representation of the stress-relaxation behavior, effectively capturing both the unrelaxed and relaxed modulus. The results demonstrate that EC-2216 exhibits hierarchical relaxation mechanisms and history-dependent viscoelasticity that cannot be accurately described by classical integer-order models. Overall, the study validates the use of fractional operators to represent the broad and hierarchical relaxation spectra typical of toughened aerospace epoxies and provides a rigorous framework for durability assessment and predictive modeling of adhesively bonded structures. Full article

A numerical scheme utilizing shifted Bernstein polynomials is developed to address the variable fractional-order governing equation in viscoelastic fluid-conveying pipes. The pipe’s mechanical response is characterized through a variable fractional-order Kelvin–Voigt (FKV) model, which effectively captures the time-dependent and memory properties of viscoelastic materials. By coupling the FKV constitutive model with the motion equation, the governing equation for a viscoelastic pipe is obtained. The deformation field is approximated using shifted Bernstein trial functions, leading to the construction of a derivative matrix with a variable fractional order. The obtained governing relation is expressed in matrix form, and after discretization, an algebraic system is formulated that is solvable in the time domain to evaluate the pipe displacement. Moreover, a convergence investigation is carried out to examine the reliability and effectiveness of the proposed framework. Computational results demonstrate that the introduced method delivers outstanding precision and performance, while the viscoelastic pipe’s response under different scenarios—including applied loads and fluid flow rates—is comprehensively investigated. Full article

This paper presents a novel algorithm for the dynamic analysis of fractional-order viscoelastic spinning disks in the time domain. The novelty mainly lies in the use of the shifted Legendre polynomial algorithm for the direct time-domain numerical analysis of displacement in two directions for a three-dimensional viscoelastic rotating disk, tackling a more complex and strongly coupled problem than those addressed in previous studies. By using the fractional-order Kelvin–Voigt model to describe the viscoelastic properties of the disk, a system of governing equations with three independent variables is established. For the two ternary unknown functions in the equations, a fractional-order differential operator matrix based on Shifted Legendre polynomials is derived, transforming the original equations into two sets of algebraic equations that are easier to solve. This paper presents an in-depth analysis of the convergence of the Legendre polynomial algorithm, complemented by an investigation of its error characteristics using numerical examples, thereby verifying the method’s accuracy and feasibility. This study can be applied to the dynamic analysis of viscoelastic rotating structures under body force density. The findings provide theoretical support for the optimization and safety assessment of load-bearing rotating components in engineering. And the algorithm demonstrates high accuracy and applicability in handling fractional-order equations in science and engineering. Full article

In this study, numerical simulations were performed, and leaks in viscoelastic pipelines were detected. Based on the transient flow equations derived from the continuity and momentum equations, the Kelvin–Voigt model was used to describe the viscoelastic constitutive relationship and derive the strain equation, further establishing a one-dimensional transient flow model for viscoelastic pipelines. A frequency-domain analysis of the transient flow was performed by deriving the Fourier transform and transfer matrix. An inverse problem analysis method for transient flow leak detection was proposed to identify the leak location and rate by minimizing the objective function. To verify the effectiveness of the proposed model, an experimental platform was built, and the pressure head frequency-domain data under working conditions of no leak, experimental leak, and simulated leak were compared. The results showed that the experimental data were consistent with the simulated data under leakage conditions, thus proving that the model was accurate and reliable. Under leak-free conditions, the frequency-domain characteristics of transient pressure waves exhibit significant symmetrical features, whereas when a leak exists in the pipeline, the leak point acts as a localized non-uniform disturbance source, disrupting the symmetry of the frequency-domain characteristics. Moreover, the leak point can be determined by the difference in the peak heights between the no-leak and leak conditions, and the leak parameters can be accurately identified using the inverse problem method. Full article

We present a novel formulation of the Rayleigh–Plesset equation to describe stable gas bubble dynamics in viscoelastic media, using bubble volume variation, rather than radius, as the primary variable of the resulting nonlinear ordinary differential equation. This formulation incorporates the linear Kelvin–Voigt model as the constitutive relation for the surrounding fluid, capturing both viscous and elastic contributions, to track the oscillations of a gas bubble subjected to an ultrasonic field over time. The proposed model is solved numerically, subjected to a convergence analysis, and validated by comparisons with theoretical and experimental results from the literature. We systematically investigate the nonlinear oscillations of a single spherical gas bubble in various viscoelastic environments, each modeled with varying levels of rheological complexity. The influence of medium properties, specifically shear elasticity and viscosity, is examined in detail across both linear and nonlinear regimes. This work improves our understanding of stable cavitation dynamics by emphasizing key differences from Newtonian fluid behavior, resonance frequency, phase shifts, and oscillation damping. Elasticity has a pronounced effect in low-viscosity media, whereas viscosity emerges as the dominant factor modulating the amplitude of oscillations in both the linear and nonlinear regimes. The model equation developed here provides a robust tool for analyzing how viscoelastic properties affect bubble dynamics, contributing to improved the prediction and control of stable cavitation phenomena in complex media. Full article