Viscoelastic Type Research Articles

On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity

ABSTRACTIn this paper, we address the system made by two coupled one‐dimensional Moore–Gibson–Thompson equations arising in the description of thermoviscoelastic materials. Here, while . When both the MGT equations lie in the subcritical regime, that is, we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when and are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest.

Physical Characteristics, Clinical Application, and Side Effects of Viscoelastics in Ophthalmology.

To explain the physical properties of ophthalmic viscoelastic devices (OVDs), covering their structural units, optimal features, existing viscoelastic materials, clinical applications, and potential side effects. This is a narrative review on the OVDs. A literature review was conducted in PubMed, Google Scholar, and Scopus databases. Studies that investigated physical characteristics, clinical applications, OVD commercial products, and their complications were included. We included 42 articles from 2010 and discussed physical characteristics, properties of a desirable OVD, structural units of common OVDs, OVD commercial products, clinical applications, and also complications of OVDs. Today, viscoelastics hold a distinct and crucial role in intraocular surgery due to their remarkable properties. These materials safeguard the endothelium and epithelium, uphold anterior chamber depth, manage intraocular bleeding, ease tissue handling, and aid intraocular lens placement. Currently, the American market features 12 prevalent viscoelastic types, including 7 sodium hyaluronate derivatives (Healon, Healon-Greater Viscosity, Healon-5, Amvisc, Amvisc Plus, Advanced Medical Optics Vitrax, and Provisc), 2 hydroxypropyl methylcellulose 2% derivatives (OcuCoat and Cellugel), and 3 combinations of sodium hyaluronate and chondroitin sulfate (Viscoat, DisCoVisc, and DuoVisc). Despite the introduction of new viscoelastic materials annually, no single material encompasses all desired properties. Surgeons must select and employ suitable viscoelastics based on surgical conditions and patient requirements. Advancements in material development and understanding of physical properties and clinical applications continue to refine viscoelastic selection.

Effective Governing Equations for Viscoelastic Composites.

We derive the governing equations for the overall behaviour of linear viscoelastic composites comprising two families of elastic inclusions, subphases and/or fibres, and an incompressible Newtonian fluid interacting with the solid phases at the microscale. We assume that the distance between each of the subphases is very small in comparison to the length of the whole material (the macroscale). We can exploit this sharp scale separation and apply the asymptotic (periodic) homogenization method (AHM) which decouples spatial scales and leads to the derivation of the new homogenised model. It does this via upscaling the fluid-structure interaction problem that arises between the multiple elastic phases and the fluid. As we do not assume that the fluid flow is characterised by a parabolic profile, the new macroscale model, which consists of partial differential equations, is of Kelvin-Voigt viscoelastic type (rather than poroelastic). The novel model has coefficients that encode the properties of the microstructure and are to be computed by solving a single local differential fluid-structure interaction (FSI) problem where the solid and the fluid phases are all present and described by the one problem. The model reduces to the case described by Burridge and Keller (1981) when there is only one elastic phase in contact with the fluid. This model is applicable when the distance between adjacent phases is smaller than the average radius of the fluid flowing in the pores, which can be the case for various highly heterogeneous systems encountered in real-world (e.g., biological, or geological) scenarios of interest.

The growth or decay estimates for nonlinear wave equations with damping and source terms.

The spatial decay or growth behavior of a coupled nonlinear wave equation with damping and source terms is considered. By defining the wave equations in a cylinder or an exterior region, the spatial growth and decay estimates for the solutions are obtained by assuming that the boundary conditions satisfy certain conditions. We also show that the growth or decay rates are faster than those obtained by relevant literature. This kind of spatial behavior can be extended to a nonlinear system of viscoelastic type. In the case of decay, we also prove that the total energy can be bounded by known data.

Semilinear sigma -evolution models with friction and visco-elastic type damping

In this paper we study the global (in time) existence of small data Sobolev solutions to the Cauchy problem for semilinear sigma -evolution models with friction and visco-elastic damping and with a power nonlinearity, namely,utt+(-Δ)σu+ut+(-Δ)σut=||D|au|p,u(0,x)=0,ut(0,x)=u1(x),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\left\\{ \\begin{array}{ll} u_{tt}+ (-\\Delta )^\\sigma u + u_t +(- \\Delta )^\\sigma u_t=\\big ||D|^au\\big |^p,\\\\ u(0,x)=0,\\quad u_{t}(0,x)=u_1(x),\\end{array} \\right. \\end{aligned}$$\\end{document}where sigma ge 1, p>1, and the data u1∈Lm(Rn)∩Hqs-2σ(Rn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_1\\in L^m(\\mathbb {R}^n) \\cap H^{s-2\\sigma }_q(\\mathbb {R}^n) $$\\end{document}with sge 2sigma , qin (1,infty ) and min [1,q). In the power nonlinearity we suppose ain [0,2sigma ). We are interested in connections between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.

Existence of multiple solutions for magnetohydrodynamic flows of second-grade and Walter’s B fluids due continuously contracting flat sheet with partial slip

In the present investigation, an attempt is performed to analyse the existence of multiple exact solutions for magnetohydrodynamic flows of second-grade and Walter’s B fluids due continuously contracting flat sheet with partial slip condition at the boundary. After transforming basic governing equations by suitable similarity transformations, single and double closed-form exact solutions of the flow are achieved on certain restrictions on flow variables of two aforesaid fluids. The impacts of magnetic field and partial slip on existence and non-existence of solutions are revealed. The changes of flow surface drag and velocity with various involved parametric values are also explored. For both viscoelastic type fluids, i.e., second-grade and Walter’s B fluids, double solutions exist for certain flow conditions. In second-grade case, if viscoelastic parameter exceeds a definite value, then double similarity solutions are achieved for any type of flow, i.e., slip flow or no-slip flow. For Walter’s B fluid similar results are obtained with unique similarity slip flow solution if magnitude of viscoelastic parameter exceeds certain fixed value. Importantly, the magnetic field and its MHD effect stabilize the uncertainty situation in existence of similarity solution for both fluids and produce unique solution for a suitable choice.

Stability analysis of a spinning soft-core sandwich beam with CNTs reinforced metal matrix nanocomposite skins subjected to residual stress

The stability of a soft-cored spinning viscoelastic sandwich beam and carbon nanotubes (CNTs) reinforced metal matrix nanocomposites (MMNCs) skin subjected to residual stress have been investigated. The metal matrix nanocomposites (MMNCs) skins are symmetrical and isotropic. In addition, these skins reinforced with uniform and functionally graded (FG) distributions of carbon nanotubes (CNTs) are considered. The soft-core of the sandwich beam is deemed to be elastomeric and has internal damping of viscoelastic type. The skin layers of the sandwich beam are subject to residual stresses caused by the production process. Also, the effective material properties of skins are obtained using the rule of mixture (ROM) and Halpin-Tsai (H-T) micromechanics models. First, the governing equations of motion of a spinning viscoelastic sandwich beam are obtained using the Hamilton principle. Then, the sandwich beam's natural frequencies are calculated using the differential quadrature method (DQM). The effects of CNTs distribution, nanotube volume fraction, spinning speed, critical loading, the thickness of the core, axial force, and residual stress on the sandwich beam's natural frequency and stability regions are investigated. According to the results of this study, based on the sandwich beam's different spinning speeds, it is possible to estimate the optimal amount of core thickness to prevent instability, which can be very important in the design of spinning sandwich structures.

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Stability result for a variable-exponent viscoelastic double-Kirchhoff type inverse source problem with nonlocal degenerate damping term

Effect of Pulmonary Hypertension on Biaxial Viscoelastic Properties of the Right Ventricle at Rest and Exercise Conditions

IntroductionRight ventricle failure (RVF) secondary to pulmonary hypertension (PH) is a key risk factor for PH patients. The RV mechanical behavior is an important determinant of its function. However, compared to the nonlinear anisotropic elasticity, it remains unclear how RV biaxial viscoelasticity alters with PH. Our goal is to characterize the changes in RV biaxial viscoelasticity at rest and exercise conditions in response to PH. We hypothesize that PH alters RV anisotropy, viscoelasticity type and the response to exercised heart rate.MethodsAll procedures were approved by Colorado State University IACUC. Briefly, adult male rats were treated by monocrotaline (MCT, 60 mg/kg) for 3 weeks to induce PH. Healthy rats were used as controls (CTL). After euthanasia, ex vivo equibiaxial stress relaxation tests were performed to quantify the RV viscoelasticity. The outflow track direction was defined as the longitudinal direction.Two sets of stress relaxation tests were included: 1) Using different strain levels (3‐15%) at three fixed ramp speeds (2, 5 and 8 Hz); and 2) using different ramp speeds (0.1‐8 Hz) mimicking non‐physiological and physiological heart rates at rest and exercise at a fixed strain level (20%). The relaxation modulus and the normalized stress were used to indicate the RV viscoelasticity. The logarithmic scale plot from the first set data was used to analyze the type of RV viscoelasticity. A student’s t‐test was performed and p<.05 was treated as significant.ResultsThe establishment of RVF was confirmed by echocardiography. As shown in Fig. 1, we observed frequency‐dependent viscoelasticity in both groups and directions, except for the elasticity of CTL RV in C direction. PH development led to more significant increase in viscoelasticity in L direction compared to the C direction (Fig. 1). The examination of the viscoelasticity at physiological strain‐rates showed that compared to the CTL RV, the MCT RV 1) became anisotropic in elasticity and stiffer in the L direction (Fig. 2A); 2) had increased viscosity in the L direction (Fig. 2B); and 3) had reduced viscoelasticity from the rest to exercise states (Fig. 2). Our results suggested that during exercise, the healthy RV’s viscoelastic behavior was maintained, whereas the diseased RV had decreased viscoelasticity. Finally, we found that the CTL RV was quasi‐linear viscoelastic at all testing frequencies, whereas the MCT RV was nonlinear viscoelastic in all testing conditions, except for the L behavior at sub‐physiological frequency. Therefore, PH changed the RV viscoelasticity from a quasi‐linear to fully nonlinear type.ConclusionThis is the first report of RV biaxial viscoelasticity changes with PH in rats. In the diseased RV, increased viscoelasticity and altered anisotropy and viscoelasticity type were observed, and the viscoelasticity was reduced during exercise. These novel findings improve our understanding of RV biomechanics in response to pulsatile mechanical loadings at rest and exercise conditions.

Computational Galerkin Finite Element Method for Thermal Hydrogen Energy Utilization of First Grade Viscoelastic Hybrid Nanofluid Flowing Inside PTSC in Solar Powered Ship Applications

Parabolic trough solar collectors (PTSCs) are commonly used in solar thermal implementations to achieve high-temperatures. The current investigation looks at entropy formation and the effect of nano solid particles on a parabolic trough surface collector (PTSC) mounted aboard a solar-powered ship (SPS). The non-Newtonian first grade viscoelastic type, as well as a porous medium and Darcy-Forchheimer effects, were utilised in the current study. The flowing of PTSC was created by a non-linear stretching sheet, and the changing thermal conductivity, heat source, and viscous dissipation effects were used to calculate the heat flux in the thermal boundary layer. To convert partial differential equations (PDEs) into solvable ordinary differential equations (ODEs) with boundary-constraints, a similarity transformation strategy was used. The boundary-constraints and PDEs have been reduced to a set of non-linear ODEs (ordinary differential equations). To reach the approximated solution of ODEs, the Galerkin finite element method (G-FEM) is used. As working fluids, copper-sodium alginate (Cu-SA) and molybdenum disulfide-copper/sodium alginate (MoS2-Cu/SA) hybrid nanofluids were used. According to the findings, the permeability factor diminished the Nusselt number whilst boosting the skin friction factor. Furthermore, overall entropy variance throughout the domain was increased for flow speeds using the Reynolds number, and viscosity changes were tracked using the Brinkman number. When compared to MoS2-Cu/SA, using Cu-SA nanofluid boosted thermal efficiency by 1.3–18.8%.

On a mixture of an MGT viscous material and an elastic solid

A lot of attention has been paid recently to the study of mixtures and also to the Moore–Gibson–Thompson (MGT) type equations or systems. In fact, the MGT proposition can be used to describe viscoelastic materials. In this paper, we analyze a problem involving a mixture composed by a MGT viscoelastic type material and an elastic solid. To this end, we first derive the system of equations governing the deformations of such material. We give the suitable assumptions to obtain an existence and uniqueness result. The semigroups theory of linear operators is used. The paper concludes by proving the exponential decay of solutions with the help of a characterization of the exponentially stable semigroups of contractions and introducing an extra assumption. The impossibility of location is also shown.

Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves

We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for self-gravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes.

Characterization of postoperative "fibrin web" formation after canine cataract surgery.

To describe the occurrence and associated factors for "fibrin web" (FW) formation following phacoemulsification in dogs. A retrospective review of medical records of all dogs undergoing phacoemulsification (MU-Veterinary Health Center, 2014-2018) was conducted to associate FW formation with signalment, systemic co-morbidities, cataract stage, surgeon (resident vs faculty), phacoemulsification time, IOL, and intracameral injections including viscoelastic type. Both univariate and multivariate statistical analyses were performed to evaluate associations among variables with FW formation. Data from 398 eyes on 201 dogs were included; 4 left eyes (4 dogs) developed presumptive endophthalmitis and were excluded from further analysis. Forty-eight eyes did not have cataract surgery. Hence, 350 eyes on 201 dogs were included in the analyses. Among these, 84 eyes (59 dogs) developed a FW. Univariate analyses showed that the odds of FW increased with age and phacoemulsification time. Additionally, FW web was associated lens type, lens brand, and viscoelastic type. Multivariate analyses showed that when comparing lens types in combination with a particular viscoelastic, viscoelastic impacted the estimated prevalence of FW formation the most. In contrast, when the data were analyzed by lens brand, lens brand impacted prevalence more than viscoelastic type. Diabetes mellitus was not associated with FW formation. Based on the available data, intraocular lens implantation, viscoelastic type, dog age, and phacoemulsification time were associated with FW formation. Diabetes mellitus, gender, cataract stage, surgeon, intracameral injections other than viscoeleastic, and intra- and postoperative complications were not associated with FW formation.

Support Surfaces for Pressure Ulcer Prevention in Intensive Care Patients: A Short Review Article

Objective: This short review seeks to present the effectiveness of support surfaces for pressure ulcer prevention in intensive care patients. Methods: A literature search was undertaken of international databases (PubMed, CINAHL, and Cochrane Library). A time limited criteria was applied with respect to articles publication; articles published in the last decade (2010-2020). As key words, the following terms were used: “pressure ulcers”, “support surfaces”, “intensive care unit”, “prevention”, “mattresses”. Randomized controlled trials (RCTs), which assessed the effectiveness of mattresses for the prevention of pressure ulcers, in intensive care unit (ICU) patients were included in this review. Results: Many researchers have compared support surfaces and revealed the effectiveness between different types of support surfaces. From the present short review of the literature, researchers made an effort to compare the standard hospital mattress with viscoelastic mattress. It was found that the viscoelastic type of mattress reduced the incidence of PUs in critical ill patients. Moreover, some researchers underline the need for systematic and ongoing assessment of the patient’s skin as well as implementation of prevention measures. Conclusions: Viscoelastic mattress seems to be more effective compared to standard foam mattresses in prevention of PUs, in ICU patients. Coping strategies can be developed through an organized intensive care team for PUs prevention.

Flow of magnetized Oldroyd-B nanofluid over a rotating disk

Nanofluids have been getting considerable attention in recent years owing to their great importance in an enhanced thermophysical heat transfer as well as the potential usage in various applications like drug delivery and oil recovery. In this study, the characteristics of an Oldroyd-B nanofluid flow caused by axially symmetric rotating disk are analyzed with the features of vertically applied magnetic field. The speciality of current viscoelastic type fluid model involves relaxation and retardation times characteristics. An innovative Buongiorno model is introduced to characterize the heat and mass transport of Oldroyd-B nanofluid considering the impacts of thermophoresis and Brownian diffusion. Consideration is focused on mathematical formulation of momentum equations based on boundary layer approximation theory. The conversion of governing continuity, momentum, energy and concentration expressions into dimensionless forms is based on von Karman similarity variables. The numerical integration of resultant problem is performed through BVP Midrich scheme in Maple. The attained outcomes are exhibited through flow fields, temperature and concentration of nanoparticles distributions as well as local Nusselt and Sherwood numbers. Results reveal that the occurrence of magnetic field in the flow region leads to loss of fluid movement. Also, the thermal and solutal distributions enhance substantially with rising values of retardation time parameter. Moreover, the temperature of liquid boosts up for up growing values of thermophoresis and Brownian motion parameters, respectively.

Application of computationally efficient TR-BDF2 scheme for the finite element implementation of explicit non-linear viscoelastic models for filled elastomers

This paper presents the implementation of a nonlinear viscoelastic multi-configurational rate type material model within the general framework of the commercial finite element package Abaqus (Implicit). A user-defined subroutine, UMAT for continuum elements, is employed to implement a model similar to the one developed and extensively validated experimentally by Devendiran et al. One of the major challenges of using an implicit finite element (FE) solver is the description of material Jacobian, which may be difficult to obtain in the form of an analytical equation for multi-configurational models. Hence, numerical approximations are used to implement the consistent material Jacobian used in the global Newton iterations. We have used a Jacobian that is formulated by perturbing the deformation gradient, by extending an idea developed by Miehe and widely implemented in hyperelasticity. In order to determine the multiple intermediate configurations that keep evolving with time, this study also examines the computational efficiency of a fully second order integrator in comparison to traditional first order BDF integrator. A highly efficient TR-BDF2 integrator, originally developed for simulating transients of silicon VLSI devices, is utilised to determine the “current relaxed configuration”, which to the author’s knowledge is the first implementation in literature for rate type viscoelastic constitutive equations. Coupling the numerically approximated Jacobian and TR-BDF2 integrator, the UMAT is generic and can easily be modified for various combinations of stored energy potential functions and rate of dissipation equations. The UMAT is validated against material point solution of the constitutive model in MATLAB; and is found to be exact within a tight tolerance. The implemented UMAT is used to determine the rolling resistance of a Grosch wheel which demonstrates the practical application of such a material model focussed towards the workflows for tyre analysis.

Hysteretic Loops in Correlation with the Maximum Dissipated Energy, for Linear Dynamic Systems

This paper presents the outcomes of the theoretical and experimental research carried out on a real model at natural scale using Voigt–Kelvin linear viscoelastic type m, c, and k models excited by a harmonic force F(t) = F0 sinωt, where F0 is the amplitude of the harmonic force and ω is the excitation angular frequency. The linear viscous-elastic rheological system (m, c, k) is characterized by the fact that the c linear viscous damping—and, consequently, the fraction of the critical damping ζ—may be changed so that the dissipated energy can reach maximum W d max values. The optimization condition between the W d max maximum dissipated energy and the amortization ζ 0 = ± ( 1 − Ω 2 ) / 2 Ω modifies the structure of the relation F = F(x), which describes the elliptical hysteresis loop F–x in the sense that it has its large axis making an angle less than 90° with respect to the x-axis in Ω < 1 ante-resonance, and an angle greater than 90° in post-resonance for Ω > 1 . The elliptical Q–x hysteretic loops are tilted with their large axis only at angles below 90°. It can be noticed that the equality between the arias of the hysteretic loop, in the two representations systems Q–x and F–x, is verified, both being equal with the maximum dissipated energy W d max .

Corneal endothelial cell loss associated to phacoemulsification and ophthalmologist experience: prospective analysis of individual secondary data.

Phacoeresis is the procedure through which the lens is surgically removed to treat cataracts. A corneal endothelial loss is a recognized sequel. Although several factors associated with this harm have been described, the surgeon’s prior experience has been scarcely evaluated. To assess the association between the surgeon’s experience and other variables associated with a corneal endothelial cell loss in the context of phacoeresis. Clinical records of 198 patients undergoing cataract operations were prospectively reviewed. The experience of the surgeon and other variables were recorded, including cumulative dissipated energy, viscoelastic type, the use of trypan blue, amount of fluidics, ultrasound time, combined phacoemulsification energy, and pre- and postoperative corneal endothelial cell counts. No differences were observed in the postoperative corneal endothelial cell count between surgeons with more or less than five years of experience. Nevertheless, ophthalmologists with more than five years’ experience used less trypan blue, but more cumulative dissipated energy in each procedure, while less experienced ophthalmologists used less fluidics. Although there were differences in the surgical management regarding the surgeons’ experience in factors known to influence corneal endothelial cell loss, no differences in endothelial cell loss were observed as an outcome.

Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping

In this paper, we deal with the uniform stabilization to the mixed problem for a nonlinear wave equation and acoustic boundary conditions on a non-locally reacting boundary. The main purpose is to study the stability when the internal damping acts only over a subset $$\omega $$ of the domain $$\Omega $$ and the boundary damping is of the viscoelastic type.

Approximation and characterization of quasi-static $H^1$-evolutions for a cohesive interface with different loading-unloading regimes

We consider the quasi-static evolution of a prescribed cohesive interface: dissipative under loading and elastic under unloading. We provide existence in terms of parametrized BV -evolutions, employing a discrete scheme based on local minimization, with respect to the H^1 -norm, of a regularized energy. Technically, the evolution is fully characterized by: equilibrium, energy balance and Karush–Kuhn–Tucker conditions for the internal variable. Catastrophic regimes (discontinuities in time) are described by gradient flows of visco-elastic type.