Viscoelastic Structures Research Articles

Wave propagation in poroviscoelastic vertical transversely isotropic media: A sum-of-exponentials approximation for the simulation of fractional Biot-squirt equations

The presence of porous, viscoelastic, and anisotropic structures profoundly influences the propagation of seismic waves. Poroelasticity, based on the Biot-squirt (BISQ) theory, can characterize the impact of fluid flow on seismic waves. However, an improved mechanistic understanding and mathematical representation of seismic wave propagation in porous formations require the accounting of velocity and attenuation anisotropy. We derive the wave equations based on an efficient sum-of-exponentials (SOE) approximation by combining the porous BISQ equations with Kjartansson’s constant- Q dissipative model to describe seismic wave propagation in poroviscoelastic vertical transversely isotropic media. The approximation represents the fractional differential equations as an SOE, enabling a reduction in computational costs and storage compared with the traditional L2 scheme. Numerical examples prove that the extended BISQ model can describe the wave propagation characteristics in poroviscoelastic anisotropic media and effectively captures potentially strong, direction-dependent attenuation phenomena.

Identification of ultrasound characteristics in viscoelastic architectured materials by angular measurements in double through-transmission

Recent advances in additive manufacturing of viscoelastic materials have paved the way towards the design of increasingly complex multi-material structures with heterogeneities from the micro- to the macroscale. However, the measurement of ultrasound characteristics in such viscoelastic structures is a challenging problem, due to the strong attenuation related to both the constituent materials and the architecture. We propose here a methodological framework to identify the phase velocity and attenuation in viscoelastic multi-material quasi-heterogeneous samples. The proposed approach relies on measurements achieved in double through-transmission at various incidence angles, referred as theta-scan. The forward modeling of the wave propagation in such media allows then to identify the ultrasound characteristics based on an inverse approach. Experiments were performed on multi-material samples made of a random pattern of inclusions of a soft elastomer inside a rigid glassy polymer. The effects of the volume fraction of the constituent materials on the ultrasound characteristics was evaluated. This methodology open the path towards ultrasonic measurements in highly attenuating architectures

LONGITUDINAL-RADIAL VIBRATIONS OF A VISCOELASTIC CYLINDRICAL THREE-LAYER STRUCTURE

The paper considers a cylindrical three-layer structure of arbitrary thickness made of viscoelastic material. It consists of two external bearing layers and a middle layer, the materials of which are generally different. The problem of nonstationary longitudinal-radial vibrations of such a structure is formulated. Based on the exact solutions in transformations of the three-dimensional problem of the linear theory of viscoelasticity for a circular cylindrical three-layer body, a mathematical model of its nonstationary longitudinal-radial vibrations is developed. Equations are derived that allow, based on the results of solving the vibration equations, to determine the stress-strain state of a cylindrical structure and its layers in arbitrary sections. The results obtained allow for special cases of transition into cylindrical viscoelastic and elastic two-layer structures, as well as into homogeneous single-layer cylindrical structures and round rods.

A reduced-order finite element formulation for the geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation

A reduced-order finite element formulation for the geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation

Rate-dependent and delayed snap-through behaviors of viscoelastic metamaterials

Snap-through instability can occur after a significant time delay for some viscoelastic structures under certain loading history; the mechanisms of this phenomenon in viscoelastic metamaterials are still unrevealed. This work uses a combined method of experiments, finite element analysis (FEA), and analytical modeling to investigate the rate-dependent and delayed snap-through behavior of viscoelastic metamaterials. The load-displacement responses under different loading-rates and viscoelastic parameters are illustrated with an emphasis on the programable load capacity and stability via FEA. Experimentally, a viscoelastic metamaterial made of silicone rubber is fabricated through 3D printed molds, and demonstrated for delayed snap-through after creeping under a constant force. The sensitivity of the delayed time to the applied force is presented. A phase diagram with respect to the applied force and material viscoelasticity is constructed to demonstrate different snapping behaviors, including near-instantaneous snapping, delayed snapping at finite time, and no snapping. A discrete model that can capture different snapping modes is developed to provide straightforward understanding of the underlying mechanisms. This work can open up potential novel applications of the tunable delayed snap-through behavior of viscoelastic metamaterials.

Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures

The underlying size-dependent mechanism of viscoelastic porous metamaterial structures is still unclear, and the solution to their response using the high-fidelity numerical method is time-consuming, even prohibitive. This paper explores how the size-dependent effect of metamaterial structures emerges from the underlying nonlocal interactions in metamaterial microstructures, and then develops an accurate but efficient homogenization method for analyzing their size-dependent and time-dependent mechanical behaviors of viscoelastic porous metamaterial structures. By accounting for the nonlocal interaction between different representative volume elements and the history-dependent effect, a spatiotemporally nonlocal discrete element model is developed to analyze the mechanical behavior of viscoelastic porous metamaterial structures. With the help of the spatiotemporally nonlocal discrete element model, a spatiotemporally nonlocal homogenization method is proposed to accurately yet efficiently assess the size-dependent mechanical behavior of the porous metamaterial structure. The remarkable potential of the spatiotemporally nonlocal homogenization method is illustrated by simulating the stress relaxation of a viscoelastic porous metamaterial structure under axial strain. Results indicate that the size-dependent phenomenon can be significant, and the spatiotemporally nonlocal homogenization model can efficiently capture the size-dependent relaxation stress evaluated by the high-fidelity finite element model without loss of accuracy.

The Effect of Kinesio Taping on Lumbar Kinematic After Static Lumbar Flexion in Healthy Subjects

Introduction: The application of Kinesio taping (KT) is a rehabilitation technique used to provide muscle and joint support and stability, without limiting the range of motion (ROM). No study evaluated the effects of KT on lumbar flexion relaxation phenomenon and kinematic details after static flexion. This study aims to find out the results of KT on erector spinae (ES) muscle activity, flexion relaxation pattern, and trunk, lumbar, and hip range of motion in healthy subjects during static flexion Materials and Methods: This study used a two-factor within-group design. Twenty-two healthy female students participated in this study. We used surface electromyography (EMG) to assess ES muscle activity and measured kinematic information with data from the camera. Variables related to muscle activity and angles in forward bending movement before and after creep were investigated. The test was performed in two situations with and without the use of KT. Results: KT reduced the time of muscle activity during bending. Also, KT increased trunk, and hip angles at the end of forward flexion. In the lumbar extension phase, the ES muscles were activated later Conclusion: KT can prevent the increase of lumbar spine flexion angle due to the creep effect. It can be used to protect the strained viscoelastic structures and increase the involvement of cutaneous receptors. KT can act as a protector in the dynamic stabilization system of lumbar joints in flexion positions in healthy people.

Dynamic topology optimization of two-phase viscoelastic composite structures considering frequency- and temperature-dependent properties under random excitation

This article proposes an efficient optimum design method of constrained layer damping (CLD) plates characterized by non-proportional damping subjected to random excitation. Considering frequency and temperature dependence, a two-phase viscoelastic composite material composed of stiffness-phase and damping-phase materials is used as the damping layer. The pseudo excitation and hybrid expansion methods are adopted to compute the random responses at the specified frequency intervals as the objective functions. The sensitivity analysis is performed through the adjoint vector method. The similarity index is defined to distinguish the various optimal layouts quantitatively. Several numerical examples clearly demonstrate the robustness and effectiveness of the proposed method, highlighting a remarkable improvement of over 60% in computational efficiency. Furthermore, it is proved that, when subjected to broadband random excitation, the damping materials' temperature- and frequency-dependent properties are critical factors in obtaining accurate vibration responses and desirable optimal layouts. The effects of the layer thicknesses and volume fractions of composite structures on topology optimization are also discussed. The results indicate that both layer thickness and volume fraction can change the mechanical properties of the composite structure and further affect the distribution characteristics of the damping material.

Efficient strategy for topology optimization of stochastic viscoelastic damping structures

In this study, the dynamic topology optimization (TO) of stochastic viscoelastic damping structures (VDSs) is performed for the first time. However, the expensive computation cost seriously hinders the TO process. To address this problem, an efficient strategy is proposed. On the one hand, in the stochastic structural response analysis, a fully adaptive method based on direct probability integral method is presented to determine the number and locations of samples. Meanwhile, to improve the computational efficiency of structural response for each sample, a piecewise model-order reduction method based on Krylov subspace is adopted to generate the orthonormal basis and project the original large-scale system onto a low-order system. On the other hand, to overcome the optimization challenge arising from large number of design variables in the density-based topology method, a material-field series-expansion method is employed to describe the topology layout and significantly reduce the number of design variables. Moreover, the sensitivity of the optimization model is derived by the adjoint method and the method of moving asymptotes (MMA) is used to efficiently update the design variables. Some numerical examples comprehensively demonstrate the effectiveness and efficiency of the proposed strategy. The results indicate that the uncertainty of structural parameters greatly affect both the topology layout of VDS and vibration damping capacity.

Topology optimization design of frequency- and temperature-dependent viscoelastic shell structures under non-stationary random excitation

Topology optimization design of frequency- and temperature-dependent viscoelastic shell structures under non-stationary random excitation

Rate-dependent energy dissipation of graded viscoelastic structures fabricated by grayscale vat photopolymerization

A major benefit of additive manufacturing technologies is precise control over structural topologies and material properties, which allows to tailor, for instance, energy absorption and dissipation. While vat photopolymerization is generally restricted to a single material, grayscale masked stereolithography (gMSLA) allows to customize material behavior by grading the light intensity within a structure. This study investigates the impact and opportunities of grayscale grading strategies on the rate-dependent mechanical behavior of structures fabricated by gMSLA. Considering the viscoelastic nature of polymers, rate-dependent energy dissipation is explored, introducing a parametric linear viscoelastic constitutive model for varying grayscales. The investigation includes the comprehensive characterization of mechanical properties, numerical finite element simulation, validation through experimental procedures, and exploration of dissipation energy under different strain rates. In this way, a rational function successfully determines the critical strain rate at which the maximum dissipation occurs. Overall, the research offers a comprehensive investigation of the mechanical dissipation behavior of graded 3D printed structures, laying the foundation for further studies and advancements aimed at optimizing these structures for enhanced energy absorption capabilities.

Solutions of Surface-Wave Dispersion and Attenuation in Stratified Viscoelastic Media Using a Spectral-Element Approach

ABSTRACT Efficient and accurate calculation for the dispersion and attenuation of the surface waves in viscoelastic media is numerically challenging because the eigen wavenumbers are located in the complex domain. In this study, we propose a semianalytical spectral-element method (SASEM), which can determine the complex eigen wavenumbers by solving linear eigenvalue problems. By simplifying the structure of the eigenvalue problem, we significantly improve the calculation efficiency. The implementation of the frequency-dependent automatic discretization, semi-infinite element, and mode filter guarantees the correctness and accuracy of the modal solutions. Because no root-searching schemes are required, the root-skipping problem is naturally avoided. The numerical tests show that the SASEM can provide sufficiently accurate solutions with much less computation cost than traditional Muller’s method. Meanwhile, SASEM exhibits high flexibility when applied to media the parameters for which vary continuously with depth. To demonstrate the effectiveness of SASEM for complicated dispersion features, the dispersion curves and eigen wavefields of the viscoelastic media with a low-velocity layer are also analyzed. The results of numerical tests indicate the versatility, efficiency, and accuracy of our method. With further study, the proposed SASEM has the potential to become a promising tool for the investigation and retrieval of viscoelastic subsurface structures.

On the use of multidimensional differential geometry to model covariant behaviors of viscoelastic or hyperelastic structures, illustrated with numerical simulations using spacetime finite element analysis

In the present article, a covariant spacetime formalism is used to model the behavior of viscoelastic and hyperelastic solids, within a thermodynamical framework. The latter aims to ensure the validity of thermodynamics second principle and to derive reversible or irreversible models for thermomechanics. The use of the Lie derivative is of particular interest to achieve such goals. Covariance enables to address finite deformation. Coupled to a covariant finite element analysis, it allows numerical simulations that simultaneously ensure the physical balance of energy and momentum for thermomechanical applications. Different mechanical loadings are considered, bending or uniaxial extension ones, with quasi-static or time exponential or time cyclic evolution. We also provide quantification of the different performances of the numerical simulations, and show the advantages and drawbacks of the spacetime approach.

Exploring induced microstructural changes in magnetically modified crude oils through nonlinear rheology and magnetometry

Adsorptive phenomena involving dispersed iron oxide superparamagnetic nanoparticles and asphaltenes in crude oil have been profiled as promising technological alternatives, particularly since these interactions can induce significant structural changes within the oil matrices, effectively inhibiting the formation of complex long-range viscoelastic structures. Furthermore, the effect of adsorbed asphaltenes on magnetic dipolar interactions among particles has been proven, showing the formation of multiple asphaltene layers that stimulate a steric repulsive barrier. Despite the discussed hindering phenomena, this research demonstrated the effectiveness of the sequence of physical processes framework to provide intra-cycle structure-rheological interpretations in large amplitude oscillatory shear of a ferrofluid-modified heavy oil, upon the application of an external magnetic field. The analysis proved that disordered nanoparticle/asphaltene aggregates are highly extended and naturally formed in the absence of magnetic forces. In contrast, in the presence of a perpendicular field applied by a controlled rate magneto-rheometer, the formation of interacting structural aggregates of several hundred nanometers was observed, analogous to magnetorheological fluids. These results were validated by adjusting a phenomenological model that effectively represented the intricate processes involved in the formation and reorientation of aggregates, based on the experimental data acquired from zero-field-cooled and field-cooled magnetization curves. This revealed a distinct blocking temperature distribution at around 274 K, which was linked to Brownian relaxation phenomena exhibited by nanoparticle aggregates. In this regard, this research provided a precise extended description of the effect of magnetic fields on the microstructural organization of complex fluids using nonlinear rheology and magnetometry.

Determination of Dynamic Characteristics of Lattice Structure Using Dynamic Mode Decomposition

Abstract In this work, dynamic mode decomposition (DMD) was applied as an algorithm for determining the natural frequency and damping ratio of viscoelastic lattice structures. The algorithm has been developed based on the Hankel alternative view of Koopman (HAVOK) and DMD . In general, the Hankel matrix is based on time-delay embedding, which is meant for the hidden variable in a time-series data. Vibration properties of a system could be then estimated from the eigenvalues of the approximated Koopman operator. Results of the proposed algorithm were firstly validated with those of the traditional discrete Fourier transform (DFT) approach and half-power bandwidth (HPBW) by using an analytical dataset of multi-modal spring-mass-damper system. Afterward, the algorithm was further used to analyze dynamic responses of viscoelastic lattice structures, in which data from both experimental and numerical finite element (FE) model were considered. It was found that the DMD-based algorithm could accurately estimate the natural frequencies and damping ratios of the examined structures. In particular, it is beneficial to any dataset with limited amounts of data, whereby experiments or data gathering processes are expensive.

Nonlinear vibrations of fractional viscoelastic PET membranes subjected to tangential follower force

Nonlinear forced vibrations of simply supported viscoelastic Polyethylene Terephthalate (PET) membranes subjected to a harmonic excitation and tangential follower force are investigated in this paper. The consideration of vibration systems under follower force requires special attention to the modeling of non-conservative force and its influence on nonlinear analysis. Herein, a fractional Kelvin-Voigt Hamilton-based framework accounting for the viscoelastic PET membrane is developed. Based on the Hamilton principle for the non-conservative system, the mathematical modeling of viscoelastic PET membrane taking into account non-conservative force and geometric nonlinearity is formulated, and the derived equations are discretized via the Galerkin schemes. A technique of multiple scales is employed to numerically acquire the frequency–response curves with different system configurations. Numerical investigations are conducted to analyze the effects of tangential follower force, viscous coefficient, as well as fractional order on the dynamic stability of the considered structure. Further ramifications of the present study point to the paramount importance of tangential follower force and an accurate viscoelasticity model on the dynamic behaviors of the viscoelastic structures.

Prediction on wind‐induced responses for tall buildings considering frequency dependency of viscoelastic damped structures

SummaryTime history analysis is sometimes used in an estimation of the wind‐induced response of a tall building. However, time history analysis for the wind‐induced behavior by the ensemble‐averaging wind force costs much computation time. This paper provides a reliable prediction method for the wind‐induced response of the viscoelastic (VE)‐damped system considering its frequency dependency coupling with frame damping effect with frequency spectral method. VE damper used in high‐rise buildings can dissipate energy from excessive vibration induced by seismic or wind excitation. Fractional derivative (FD) model of VE dampers can express VE frequency dependency clearly, but it is computationally complicated. The herein proposed prediction method is based on frequency spectral method and evaluated wind‐induced responses of the single degree of freedom (SDOF) VE‐damped system with a FD VE damper subjected to the respective 1st modal along‐ and across‐wind force. The maximum error of wind‐induced responses of the VE‐damped system, such as the root mean square value of responses, the total input energy, and the total energy dissipation, is within . In summary, the proposed method had high accuracy in the prediction of wind‐induced responses of the VE‐damped system considering its frequency dependency with the coupling effect of frame damping.

Holocene southwest Greenland ice sheet behavior constrained by sea-level modeling

The melting of the Greenland ice sheet (GrIS) is a major contributor to past and future global sea-level rise. Understanding the response of the GrIS to times in the past when temperatures were as warm or warmer than today offers insights into its current and future response to climate change. In the southwest sector, the GrIS retreated inland beyond its current margin during the (at least regionally) warmer-than-present mid-Holocene, before it readvanced to the historical maximum position during the Little Ice Age. This was then followed by a slight retreat to its current position. To investigate the timing and magnitude of southwest GrIS retreat and readvance in response to Holocene warmth, we model the response of the solid Earth and local relative sea level (RSL) to past ice sheet change. We test a suite of eleven ice sheet scenarios that are based on ICE-6G_C but are modified in the timing and magnitude of ice retreat and readvance and pair them with four different viscoelastic Earth structures. We compare model predictions to observations of paleo sea level, present-day sea-level change, and present-day vertical land motion (VLM) around Nuuk, Greenland. We find that the modeled timing and magnitude of the Holocene retreat and readvance have a significant impact on modern sea-level change and VLM in Nuuk. Models that assume a readvance approaching the southwest GrIS’ historical maximum between 2 and 1 ka are most consistent with observations. The RSL response, however, is less sensitive to the timing of the minimum GrIS extent. Nonetheless, better data-model fits are generally obtained when the minimum ice sheet extent is reached between 5 and 3 ka, within the tested range of 6-3 ka. Comparing this timing to local and regional records of temperature and ice-sheet change suggest that the evolution of the southwestern GrIS presented here was in-phase with the likely evolution of southwestern GrIS mass balance through the Holocene. Our results have implications for future ice sheet modeling studies targeting southwestern Greenland by providing additional constraints and strengthening existing ones. Moreover, this work provides a deeper understanding of the interactions between the climate and the cryosphere and thus of future ice sheet change.

Unsupervised graph anomaly detection with discriminative embedding similarity for viscoelastic sandwich cylindrical structures

In the detection of slipping anomalies in viscoelastic sandwich cylindrical structures (VSCS), conventional methods may encounter challenges due to the extremely rare and weak nature of slipping signals. This study focuses on normal signals and introduces unsupervised graph representation learning (UGRL) with discriminative embedding similarity for VSCS's detection. UGRL involves data preprocessing, model embedding, and matrix reconstructing. Association graphs are constructed based on sample similarities for yielding adjacency and attribute matrices. Subsequently, the matrices undergo embedding and reconstruction via various network modules to enhance graph data characterization. Detection indicators are derived by calculating embedding similarities and reconstruction errors, and thresholds are constructed using these indicators to enable efficient anomaly detection. The experiments in VSCS slipping dataset effectively indicate the superiority of the proposed method.

Ceragenin-mediated disruption of Pseudomonas aeruginosa biofilms.

Microbial biofilms, as a hallmark of cystic fibrosis (CF) lung disease and other chronic infections, remain a desirable target for antimicrobial therapy. These biopolymer-based viscoelastic structures protect pathogenic organisms from immune responses and antibiotics. Consequently, treatments directed at disrupting biofilms represent a promising strategy for combating biofilm-associated infections. In CF patients, the viscoelasticity of biofilms is determined mainly by their polymicrobial nature and species-specific traits, such as Pseudomonas aeruginosa filamentous (Pf) bacteriophages. Therefore, we examined the impact of microbicidal ceragenins (CSAs) supported by mucolytic agents-DNase I and poly-aspartic acid (pASP), on the viability and viscoelasticity of mono- and bispecies biofilms formed by Pf-positive and Pf-negative P. aeruginosa strains co-cultured with Staphylococcus aureus or Candida albicans. The in vitro antimicrobial activity of ceragenins against P. aeruginosa in mono- and dual-species cultures was assessed by determining minimum inhibitory concentration (MIC) and minimum bactericidal/fungicidal concentration (MBC/MFC). Inhibition of P. aeruginosa mono- and dual-species biofilms formation by ceragenins alone and in combination with DNase I or poly-aspartic acid (pASP) was estimated by the crystal violet assay. Additionally, the viability of the biofilms was measured by colony-forming unit (CFU) counting. Finally, the biofilms' viscoelastic properties characterized by shear storage (G') and loss moduli (G"), were analyzed with a rotational rheometer. Our results demonstrated that ceragenin CSA-13 inhibits biofilm formation and increases its fluidity regardless of the Pf-profile and species composition; however, the Pf-positive biofilms are characterized by elevated viscosity and elasticity parameters. Due to its microbicidal and viscoelasticity-modifying properties, CSA-13 displays therapeutic potential in biofilm-associated infections, especially when combined with mucolytic agents.