Viscoelastic Element Research Articles

Deflection characteristics of semi-rigid base asphalt pavement under traffic speed deflectometer loading

The three-dimensional viscoelastic finite element simulation and on-site validation was combined, so as to study the characteristics of the traffic speed deflection slope curve of the semi-rigid base asphalt pavement. Results show that there is an inert point in the deflection slope curve when only the surface or base structural state changes. With the loading center approaching transverse crack, the ‘three extreme values’ attribute transitions gradually to ‘single extreme value’. For the surface-base penetrating longitudinal crack caused by uneven subgrade settlement, the peak value of deflection slope curve increases significantly as the crack approaches the loading center, reaching an order of magnitude difference, and the attribute transforms from ‘three extreme values’ to ‘single extreme value’. Indicators characterizing the layered structural state were proposed, and the indicator change rules and applicability for the pavement with different surface and base layer thicknesses, under different deflectometer speeds, with or without cracks, were discussed.

Rheological Structure and Stress Triggered Megathrust Slip Constrained From the 2016 Mw 7.8 Kaikōura Crustal Earthquake

AbstractUnderstanding postseismic processes following the 2016 Mw 7.8 Kaikōura earthquake remains challenging due to the time‐dependent afterslip over the complex forearc system including crustal faults and megathrust, and the viscoelastic relaxation of the upper mantle. How the 2016 Mw 7.8 Kaikōura crustal earthquake interacts with the megathrust has yet to be better understood. Here we have derived the first 5‐year postseismic displacements from Global Positioning System (GPS) time series of 75 stations to study postseismic processes through a three‐dimensional viscoelastic finite element model. The optimal steady state viscosities of the crustal shear zone, megathrust shear zone, Australian upper mantle and Pacific upper mantle in the lowest‐misfit model among test models are 1018 Pa s, 4 × 1017 Pa s, 2 × 1019 Pa s and 1020 Pa s, respectively. The stress‐driven afterslip within the first 5 years after the earthquake is up to 80 cm over crustal faults, and up to 70 cm over the megathrust. A Kapiti slow slip sequence is probably promoted with a shorter interval by the 2016 earthquake, and is up to ∼11 cm within the first year after the earthquake. Afterslip over crustal faults and the megathrust are both required to reproduce the first‐order pattern of horizontal GPS observations. Coseismic rupture over the megathrust enhances shallow megathrust afterslip, which better fit the eastward postseismic displacement of sites near the rupture area. The southern end of Hikurangi megathrust may be activated during the 2016 earthquake and undergo continuous aseismic slip after the event.

Viscoelastic modeling based force control framework for enhancing operation safety of soft tissue for orthopedic surgical robots

In robot-assisted laminectomy, precise control of touch force on the spinal cord during the dissection of ossified ligaments is critical to prevent dura mater tearing and ensure surgical safety. However, the complex viscoelastic characteristics of tissue at the lesion site pose a significant challenge for accurately applying touch force. This paper proposes a safe touch force servo framework based on tissue model identification and preoperative optimization of the force controller. First, a soft tissue model is established using elastic and viscoelastic elements, and the transfer function from tissue deformation to touch force is derived. Subsequently, the path and parameters of a safe pre-touch are designed, and force information required for tissue model identification is obtained through the pre-touch experiment. The model order and specific parameter values are then identified using a differential evolution algorithm. Next, force control simulation is conducted based on the identified model, and a specifically designed loss function is introduced to achieve preoperative tuning of the force controller. Finally, step force control experiments on sheep spines validate the effectiveness of the proposed method. This paper provides a safe and available touch motion control framework that can be expandable to impose precise force on various vulnerable soft tissues, with the potential for widespread application.

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Prediction of frequency response of sub-frame bushing and study of high-order fractional derivative viscoelastic model

This paper presents experimental and dynamic modeling research on the rubber bushings of the rear sub-frame. The Particle Swarm Optimization algorithm was utilized to optimize a Backpropagation (BP) neural network, which was separately trained and tested across two frequency ranges: 1–40 Hz and 41–50 Hz, using wideband frequency sweep dynamic stiffness test data. The testing errors at amplitudes of 0.2 mm, 0.3 mm, and 0.5 mm were found to be 1.03%, 3.05%, and 1.96%, respectively. Subsequently, the trained neural network was employed to predict data within the frequency range of 51–70 Hz. To incorporate the predicted data into simulation software, a dynamic model of the rubber bushing was established, encompassing elastic, friction, and viscoelastic elements. Additionally, a novel model, integrating high-order fractional derivatives, was proposed based on the frequency-dependent model for the viscoelastic element. An enhanced Particle Swarm Optimization algorithm was introduced to identify the model's parameters using the predicted data. In comparison to the frequency-dependent model, the new model exhibited lower fitting errors at various amplitudes, with reductions of 3.84%, 3.61%, and 5.49%, respectively. This research establishes a solid foundation for subsequent vehicle dynamic modeling and simulation.

Investigation of Lateral and Longitudinal Deformation of Submarine Nuclear Power Plant Water-Intake Tunnel on Non-Uniform Soft Soil during Earthquake

The safety-grade water-intake immersed tunnel plays a vital role in the nuclear power cooling system, and its seismic safety is crucial. This paper employs the response displacement method and dynamic time-history analysis using the finite element software ANSYS to construct a beam–spring model and a 3D finite element model of a shield tunnel and foundation. It also develops equivalent linear dynamic constitutive and viscoelastic boundary element subprograms. This study focuses on the weak joint sections of immersed tunnels, conducting a seismic performance analysis under extreme safety earthquake conditions (SL-2). The results indicate that the joint stiffness of immersed tunnels and the increase in seismic peak values do not affect the trend of joint opening variation with longitudinal position. The change in joint opening is primarily located where the thickness of the cover layer changes abruptly or where the soil hardness is unevenly distributed. The joint opening is mainly influenced by seismic forces when considering static and dynamic superposition. When the stiffness of the joint GINA water stop exceeds a certain value, the correlation between stiffness change and joint compression–tension variation gradually weakens. This research can provide a reference for the seismic design of similar projects.

Functionally graded bi-material interface for Porcelain Veneered Zirconia dental crowns: A study using viscoelastic finite element analysis

ObjectivesDuring the manufacturing of Porcelain Veneered Zirconia (PVZ) dental crowns, the veneer-core system undergoes high-temperature firing cycles and gets fused together which is then, under a controlled setting, cooled down to room temperature. During this cooling process, the mismatch in thermal properties between zirconia and porcelain leads to the development of transient and residual thermal stresses within the crown. These thermal stresses are inherent to the PVZ dental crown systems and render the crown structure weak, acting as a precursor to veneer chipping, fracture, and delamination. In this study, the introduction of an intermediate functionally graded material (FGM) layer at the bi-material interface is investigated as a potentially viable alternative for providing a smoother transition of properties between zirconia and porcelain in a PVZ crown system. MethodsAnatomically correct 3D crown models were developed for this study, with and without the FGM layer modeled at the bi-material interface. A viscoelastic finite element model was developed and validated for an anatomically correct bilayer PVZ crown system which was then used for predicting residual and transient stresses in the bilayer PVZ crown. Subsequently, the viscoelastic finite element model was further extended for the analysis of graded sublayers within the FGM layer, and this extended model was used for predicting the residual and transient stresses in the functionally graded PVZ crown, with an FGM layer at the bi-material interface. ResultsThe study showed that the introduction of an FGM layer at the bi-material interface has the potential to reduce the effects from transient and residual stresses within the PVZ crown system relative to a bilayer PVZ crown structure. Furthermore, the study revealed that the FGM layer causes stress redistribution to alleviate the stress concentration at the interfacial surface between porcelain and zirconia which can potentially enhance the durability of the PVZ crowns towards interfacial debonding or fracture. SignificanceThus, the use of an FGM layer at the bi-material interface shows a good prospect for enhancing the longevity of the PVZ dental crown restorations by alleviating the abrupt thermal property difference and relaxing thermal stresses.

Comprehensive sensitivity analysis of repeated eigenvalues and eigenvectors for structures with viscoelastic elements

The paper discusses systems with viscoelastic elements that exhibit repeated eigenvalues in the eigenvalue problem. The mechanical behavior of viscoelastic elements can be described using classical rheological models as well as models that involve fractional derivatives. Formulas have been derived to calculate first- and second-order sensitivities of repeated eigenvalues and their corresponding eigenvectors. A specific case was also examined, where the first derivatives of eigenvalues are repeated. Calculating derivatives of eigenvectors associated with repeated eigenvalues is complex because they are not unique. To compute their derivatives, it is necessary to identify appropriate adjacent eigenvectors to ensure stable control of eigenvector changes. The derivatives of eigenvectors are obtained by dividing them into particular and homogeneous solutions. Additionally, in the paper, a special factor in the coefficient matrix has been introduced to reduce its condition number. The provided examples validate the correctness of the derived formulas and offer a more detailed analysis of structural behavior for structures with viscoelastic elements when altering a single design parameter or simultaneously changing multiple parameters.

Viscoelastic finite element analysis of roll transfer process with rate-dependent adhesion behavior and multi-element cohesive interaction

Viscoelastic finite element analysis of roll transfer process with rate-dependent adhesion behavior and multi-element cohesive interaction

Research on damage behavior of silicone rubber under dynamic impact

Viscoelastic rubber materials are widely used in various vibration reduction structures of military and construction machinery. The complex driving and working conditions make the mechanical structure suffer severe impact, which leading to the damage or lose efficacy of the important viscoelastic elements. In order to reveal the dynamic mechanical properties of silicone rubber after impact, the Uniaxial compression tests of silicone rubber under different high strain rates were carried out with the separated Hopkinson pressure bar (SHPB) dynamic impact experiment, and the original Zhu-Wang-Tang (ZWT) constitutive model was modified by combining logarithmic law and power function law. The dynamic impact simulation model of silicone rubber was established using the modified ZWT-rate-dependent constitutive model, and the dynamic impact damage behavior of silicone rubber was studied under the condition of high strain rate, and the microscopic damage analysis was carried out on the experimental silicone rubber samples by scanning electron microscopy (SEM). The results show that the silicone rubber has obvious strain rate effect and strong deformation resistance at high strain rate. The modified ZWT-rate-dependent constitutive model can be used to obtain the constitutive expression of unified parameters, which can better describe the dynamic mechanical properties of silicone rubber at high strain rates. After dynamic impact compression, a damage line zone appears in the silicone rubber sample. There is a certain rule between the position of the line zone and the loading strain rate and the friction coefficient of the end face, and the silicone rubber is significantly affected by the friction effect of the end face.

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

Numerical simulation of fault activity in the Qilian tectonic belt and dynamic background of Menyuan earthquake series

Some faults in the Qilian tectonic belt are seismogenic areas for strong earthquakes, including the western section of the Lenglongling fault, which frequently occures moderate-strong Menyuan earthquakes. In this study, using GPS velocity data of 1991–2015 as the boundary constraints, a three-dimensional viscoelastic finite element dynamic model is constructed by comprehensively considering the regional dynamic environment, crust-mantle transverse-longitudinal inhomogeneity, and spatial spreading of a complex fault system. The objective is to investigate the long-period characteristics of fault movement and stress change in the Qilian tectonic belt caused by tectonic loading, and to discuss the seismogenic conditions of the Menyuan earthquakes. The results show that the annual change of long-period movement and stress of the major faults in the Qilian Mountain tectonic zone are characterized by significant segmentation. Due to its unique geometric bend morphology, the western section of Lenglongling fault has a low movement rate, significant slip deficit and high shear stress accumulation, which are conducive to the gestation and occurrence of earthquakes. Furthermore, the seismogenic area of the Menyuan earthquake series is jointly subjected to NE-SW compressive and NW-SE tensile stress fields, and the maximum shear stress and elastic strain energy accumulate faster than in the surrounding areas. Overall, the western section of the Lenglongling fault has a strong dynamic background and favorable conditions for the frequent occurrence of the Menyuan earthquake series.

Viscoelastic Analysis of Asphalt Concrete with a Digitally Reconstructed Microstructure.

In the finite element analysis of asphalt concrete (AC), it is nowadays common to incorporate the information from the underlying scales to study the overall response of this material. Heterogeneity observed at the asphalt mixture scale is analyzed in this paper. Reliable finite element analysis (FEA) of asphalt concrete comprises a set of complex issues. The two main aspects of the asphalt concrete FEA discussed in this study are: (1) digital reconstruction of the asphalt pavement microstructure using processing of the high-quality images; and (2) FEA of the asphalt concrete idealized samples accounting for the viscoelastic material model. Reconstruction of the asphalt concrete microstructure is performed using a sequence of image processing operations (binarization, removing holes, filtering, segmentation and boundaries detection). Geometry of the inclusions (aggregate) are additionally simplified in a controlled mode to reduce the numerical cost of the analysis. As is demonstrated in the study, the introduced geometry simplifications are justified. Computational cost reduction exceeds of several orders of magnitude additional modeling error occurring due to the applied simplification technique. Viscoelastic finite element analysis of the AC identified microstructure is performed using the Burgers material model. The analysis algorithm is briefly described with a particular focus on the computational efficiency aspects. In order to illustrate the proposed approach, a set of 2D problems is solved. Numerical results confirm both the effectiveness of the self-developed code and the applicability of the Burgers model to the analyzed class of AC analysis problems. Further research directions are also described to highlight the potential benefits of the developed approach to numerical modeling of asphalt concrete.

Retrofitting the Heart: Explaining the Enigmatic Septal Thickening in Hypertrophic Cardiomyopathy.

Hypertrophic cardiomyopathy is the most common genetic cardiac disease and is characterized by left ventricular hypertrophy. Although this hypertrophy often associates with sarcomeric gene mutations, nongenetic factors also contribute to the disease, leading to diastolic dysfunction. Notably, this dysfunction manifests before hypertrophy and is linked to hypercontractility, as well as nonuniform contraction and relaxation (myofibril asynchrony) of the myocardium. Although the distribution of hypertrophy in hypertrophic cardiomyopathy can vary both between and within individuals, in most cases, it is primarily confined to the interventricular septum. The reasons for septal thickening remain largely unknown. In this article, we propose that alterations in muscle fiber geometry, present from birth, dictate the septal shape. When combined with hypercontractility and exacerbated by left ventricular outflow tract obstruction, these factors predispose the septum to an isometric type of contraction during systole, consequently constraining its mobility. This contraction, or more accurately, this focal increase in biomechanical stress, prompts the septum to adapt and undergo remodeling. Drawing a parallel, this is reminiscent of how earthquake-resistant buildings are retrofitted with vibration dampers to absorb the majority of the shock motion and load. Similarly, the heart adapts by synthesizing viscoelastic elements such as microtubules, titin, desmin, collagen, and intercalated disc components. This pronounced remodeling in the cytoskeletal structure leads to noticeable septal hypertrophy. This structural adaptation acts as a protective measure against damage by attenuating myofibril shortening while reducing cavity tension according to Laplace Law. By examining these events, we provide a coherent explanation for the septum's predisposition toward hypertrophy.

A mathematical model of the gravitational potential of the planet taking into account tidal deformations

Objectives. This paper investigates the gravitational potential of a viscoelastic planet moving in the gravitational field of a massive attracting center (star), a satellite and one or more other planets moving in Keplerian elliptical orbits relative to the attracting center. Celestial bodies other than a viscoelastic planet are modeled by material points. Within the framework of the linear model of the theory of viscoelasticity, the problem of finding the vector of elastic displacement has been resolved. Traditionally, a solid body model is used to determine the Earth’s gravitational field, while tidal deformations are taken into account in the form of small corrections to the coefficients of the geopotential model. In this work, the viscoelastic ball model is used to take into account tidal effects. The relevance of the research topic is associated with high-precision forecasting of the movement of artificial satellites of the Earth, high-precision measurement of the Earth’s gravitational field.Methods. In this study the asymptotic and analytical methods developed by V.G. Vilke are used for mechanical systems containing viscoelastic elements of high rigidity, as well as methods of classical mechanics, mathematical analysis. The graphs were plotted using the Octave mathematical package.Results. After resolving the quasi-static problem of elasticity theory by calculating triple integrals over a spherical area, a formula for the gravitational potential of a deformable planet was obtained. In addition, the gravitational potential of the Earth was also calculated taking into account solid-state tidal effects from the Moon, Sun, and Venus at an external point. Graphs were constructed to show the dependence of the Earth’s gravitational potential on time.Conclusions. The theoretical and numerical results established herein show that the main contribution to the gravitational potential of the Earth is made by the Moon and the Sun. The influence of other planets in the solar system is small. The value of the gravitational potential at the outer point of the Earth, taking into account tidal effects, depends both on the position of the point in the moving coordinate system and on the relative position of celestial bodies.

Integrated Investigation on Heterogeneous Lower Crust Rheology in Kyushu and Afterslip Behavior Following the 2016 Mw7.1 Kumamoto Earthquake

AbstractThe viscoelastic lower crust beneath Kyushu Island, influenced by the volcanic arc, interplays with active crustal faults in this region and helps to shape local tectonics. In this study, we employed a three‐dimensional viscoelastic finite element model to gain insights into the lithospheric rheology and crustal faulting kinematics, through modeling the postseismic deformation processes of the 2016 Mw 7.1 Kumamoto earthquake. Our model reveals a viscosity of 2 × 1020 Pa s for the lower crust and 2 × 1019 Pa s for the upper mantle. A reduced lower crust viscosity of 2 × 1019 Pa s in the volcanic arc area is required for better reproducing the Global Positioning System data. The stress‐driven afterslip decays rapidly over time and is up to 0.3 m within 5 years after the earthquake. We propose additional normal‐component afterslip to better explain the complex postseismic deformation in the near field, which may be due to the interaction between the fault and volcano Aso.

An isochronous stress ratio logarithmic strain curve based clay creep model considering the effects of hardening and damage

Creep is one of the typical mechanical properties of clay, and studying the creep mechanical properties of clay is of great significance to construction projects in clay sites. This study conducted creep tests on Chengdu clay and found that the soil mass underwent elastic deformation, decay creep deformation, steady-state creep deformation, and accelerated creep deformation. The isochronous stress ratio-logarithmic strain curves and their mathematical models were proposed to thoroughly analyze clay creep mechanical properties. Creep automatic feature points, such as linear elastic extreme point, initial yield point, long-term strength point, and plastic point, were identified on the curve. Considering the hardening and damage effects during creep loading, linear elastic and viscoelastic elements considering the time-dependent damage, a viscoplastic element considering the load hardening effect, and viscoplastic and plastic elements considering the load damage effect were established based on the element model and the Riemann–Liouville fractional derivative. Based on the mechanical properties of the whole clay creep process, the creep mechanical feature points, and the established element model, a clay creep model was proposed considering the hardening and damage effects. The rationality and regularity of the creep model were verified using the creep test data. This research accurately revealed the creep mechanical properties of clay and facilitated soil deformation prediction, thus providing technical guidance and references for construction projects in clay sites.

Atomic force microscopy, deformation-recovery and numerical study of wheat dough

Experimental and numerical modelling work related to microstructure and deformation of starch, gluten and wheat dough was presented. Atomic force microscopy analyses through force spectroscopy on starch samples showed elastic behaviour of both dried and reconstituted wet starch granules, where wet starch was shown to be more cohesive than dried starch. Deformation-recovery test over time under compression mode showed almost complete recovery to original sample height of gluten, whereas only a slight recovery was observed for dough. Finite element modelling was then commenced to simulate gluten deformation-recovery and starch-gluten dough deformation. The gluten geometry used for the starch-gluten dough model was obtained from cryo-SEM image from the previous work before the starch geometry was then included. The interface between the starch and gluten model was defined using viscoelastic cohesive zone elements. The modelling results suggested significant influence of gluten cellular structure towards starch-gluten dough integrity. In addition, the results from the current work further supported the previous report of the starch-gluten interfacial behaviour using viscoelastic cohesive zone model.

Eric Ungar and vibration damping

This presentation honors Eric Ungar’s contributions to vibration damping. The classic paper titled “Loss Factors of Viscoelastic Systems in Terms of Energy Concepts,” which he co-authored with Edward Kerwin in 1962, takes center stage. Two significant contributions of the paper deserve detailed discussion. The first is the time dependence of total energy for viscoelastic systems with added mass, which results in ambiguous loss factor definitions off resonance. The second and most important contribution is an equation for the loss factor of a network of ideal viscoelastic springs. This equation reveals that the system loss factor is a weighted average of the loss factors of the viscoelastic springs, where the weights are the total energies in the viscoelastic springs. Next, the value of this work is illustrated by some recent work inspired by the 1962 paper. This recent work, which was published 60 years after the 1962 paper, involves the calculation of loss factors from finite element models of complex structures with viscoelastic elements. The presentation concludes with recollections that celebrate Eric Ungar’s talent in educating and inspiring generations of engineers and researchers. [Work supported by ONR under Grant N00014-22-1-2785.]

The impact of non-monotonic relaxation on numerical accuracy and stability of viscoelastic finite elements

Analysis of sound and vibration in linear viscoelastic materials is based on a relaxation function that is the time-dependent stress resulting from a unit step in strain. It is well established that relaxation functions decrease monotonically in time. The most common constitutive relaxation functions, such as the Kelvin–Voigt or General Maxwell Model, produce curves that must be monotonic. However, recently, the authors have produced a methodology that allows the use of discrete data for the time-dependent relaxation function. One result of this approach is the possibility of non-monotonic relaxation function input. This non-monotonic data may be the result of test and measurement errors. Alternatively, this non-monotonicity may be an actual anomalous physical result, such as in rock salt (He et al. 2019). The authors use validated viscoelastic finite element models in the time domain to determine the instability caused by such non-monotonic datasets. The study uses randomized non-monotonic datasets that maintain the fundamental material trend to find unstable or inaccurate results. A mathematical review highlights the conditions causing numerical instability in modern stepwise time integration solvers. The results provide clarity for viscoelastic analysts considering low-precision viscoelastic measurements or unusual physical properties. [Work supported by ONR under Grant N00014-22-1-2785.]