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In this paper we consider general port-Hamiltonian formulations of multidimensional Maxwell’s viscoelastic fluids. Two different cases are considered to describe the energy fluxes in isentropic compressible and incompressible fluids. In the compressible case, the viscoelastic effects of shear and dilatational strains on the stress tensor are described individually through the corresponding constitutive equations. In the incompressible case, an approach based on the bulk modulus definition is proposed in order to obtain an appropriate characterization, from the port-Hamiltonian point of view, of the pressure and nonlinear terms in the momentum equation, associated with both dynamic pressure and vorticity of the flow.

This paper proposes a fractal viscoelastic element via He?s fractal derivative, its properties are analyzed in details by the two-scale transform for the first time. The element is used to establish a fractal Maxwell-rheological model, which unifies the fractal creep equation and relaxation equation, and includes the classic elastic model and the classical Maxwell-rheological model as two special cases. This paper sheds a bright light on viscoelasticity, and the model can find wide applications in rock mechanics, plastic mechanics, and non-continuum mechanics.

SUMMARYA complex slowness vector governs the 3-D propagation of harmonic plane waves in a dissipative elastic medium with general anisotropy. In any sagittal plane, this dual vector is specified with phase direction, propagation velocity and coefficients for attenuation. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at the stress free boundary of the medium. Each reflected wave at the boundary is characterized by its propagation direction, propagation velocity, inhomogeneity, amplitude ratio, phase shift and energy flux. These propagation characteristics are exhibited graphically for a numerical example of anisotropic viscoelastic medium.

Fluctuating hydrodynamics (FH) is one of the theories that describes the dynamics of the fluctuations for fluids at mesoscopic scales. However, it is only valid for Markovian processes. Here we extend this approach for a viscoelastic liquid by using a generalized Langevin equation (GLE). We obyain general analytic expressions for the density fluctuations correlation function, the dynamic structure factor and the light scattering spectrum. In particular, we calculate the intermediate scattering function when the time memory and the noise correlation function are power-laws. We find that the difference in values of this quantity as functions of the viscoelasticity may be ∼62% and might be measurable.

To predict the nonlinear viscoelastic behavior of polymer melts and solutions under medium amplitude oscillatory shear (MAOS) flow, we summarized known analytical MAOS material functions and derived new analytical solutions from several continuum- or molecular-based constitutive models [Johnson–Segalman, Phan-Thien–Tanner, Leonov, Larson, Pom-Pom, coupled double-convection-reptation with chain stretch (cDCR-CS), and Rouse linear entangled polymers (Rolie-Poly)]. All constitutive models discussed in this study were classified as time-strain separable or inseparable models. Whereas linear viscoelastic behavior of all constitutive models under small amplitude oscillatory shear flow was identical, the frequency-dependent signatures of four MAOS moduli (first-harmonic elastic and viscous MAOS moduli and third-harmonic elastic and viscous MAOS moduli) were model-specific, though all analytical solutions exhibited negative first-harmonic elastic MAOS moduli. In particular, tube-based constitutive models displayed a sign change in first-harmonic viscous MAOS modulus when chain retraction of the models after deformation was not instantaneous. In addition, two models for entangled linear polymers, that is, the Rolie-Poly and cDCR-CS models, displayed a second sign change in third-harmonic elastic MAOS modulus when finite chain extensibility was introduced. These results suggest that chain relaxation dynamics can be reflected in signatures of MAOS moduli. We extended single-mode predictions into multimode versions to predict the behavior of weakly or moderately entangled polystyrene solutions (effective entanglement number

Our aim in this paper is to prove the weak-strong uniqueness property of solutions to a hydrodynamic system that models the dynamics of incompressible magneto-viscoelastic flows. The proof is based on the relative energy approach for the compressible Navier-Stokes system.

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various kinematical quantities, such as area change and curvature, on the elastic and inelastic strains is discussed. This is essential for the development of general constitutive models. In order to fully explore the coupling between elastic and different inelastic deformations, the surface balance laws for mass, momentum, energy and entropy are examined in the context of the multiplicative decomposition. Based on the second law of thermodynamics, the general constitutive relations are then derived. Two cases are considered: Independent inelastic strains, and inelastic strains that are functions of temperature and concentration. The constitutive relations are illustrated by several nonlinear examples on growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells. The formulation is fully expressed in curvilinear coordinates leading to compact and elegant expressions for the kinematics, balance laws and constitutive relations.

Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Stress release experiments show that nonuniform anisotropic elastic stresses can be distributed throughout. The elastic stresses are maintained by structural proteins and adhesive molecules, and can be actively relaxed by a variety of biophysical processes. In this paper, we present a new continuum model to investigate how the growth-induced elastic stresses and active stress relaxation, in conjunction with cell size control feedback machinery, regulate the cell density and stress distributions within growing tumors as well as the tumor sizes in the presence of external physical confinement and gradients of growth-promoting chemical fields. We introduce an adaptive reference map that relates the current position with the reference position but adapts to the current position in the Eulerian frame (lab coordinates) via relaxation. This type of stress relaxation is similar to but simpler than the classical Maxwell model of viscoelasticity in its formulation. By fitting the model to experimental data from two independent studies of tumor spheroid growth and their cell density distributions, treating the tumors as incompressible, neo-Hookean elastic materials, we find that the rates of stress relaxation of tumor tissues can be comparable to volumetric growth rates. Our study provides insight on how the biophysical properties of the tumor and host microenvironment, mechanical feedback control and diffusion-limited differential growth act in concert to regulate spatial patterns of stress and growth. When the tumor is stiffer than the host, our model predicts tumors are more able to change their size and mechanical state autonomously, which may help to explain why increased tumor stiffness is an established hallmark of malignant tumors., Author summary The mechanical state of cells can modulate their growth and division dynamics via mechanotransduction, which affects both the cell size distribution and the tissue size as a whole. Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Besides external confinement and compression on the tumor border, a heterogeneous stress field can be generated inside the tumor by nutrient-driven differential growth. Such growth-induced mechanical stresses can be relaxed by tissue rearrangement, which happens during cell neighbor exchanges, cell divisions, and extracellular matrix renewal. In this study, we have developed a continuum model that describes the above mechanical interactions and the dynamics of tissue rearrangement explicitly. Motivated by published experimental data, we consider mechanotransduction where the local compressive stress slows down cell growth and cell size reduction limits cell division. We have analyzed how external mechanical stimuli and internal processes influence the outcome of cell-and-tissue sizes and spatial patterns of cell density and mechanical stress in growing tumors.

The SARS-CoV-2 virus, which has emerged as a Covid-19 pandemic, has had the most significant impact on people's health, economy, and lifestyle around the world today. In the present study, the SARS-CoV-2 virus is mechanically simulated to obtain its deformation and natural frequencies. The virus under analysis is modeled on a viscoelastic spherical structure. The theory of shell structures in mechanics is used to derive the governing equations. Whereas the virus has nanometric size, using classical theories may give incorrect results. Consequently, the nonlocal elasticity theory is used to consider the effect of interatomic forces on the results. From the mechanical point of view, if a structure vibrates with a natural frequency specific to it, the resonance phenomenon will occur in that structure, leading to the destruction of the structure. Therefore, it is possible that the protein chains of SARS-CoV-2 would be destroyed by vibrating it at natural frequencies. Since the mechanical properties of SARS-CoV-2 are not clearly known due to the new emergence of this virus, deformation and natural frequencies are obtained in a specific interval. Researchers could also use this investigation as a pioneering study to find a non-vaccine treatment solution for the SARS-CoV-2 virus and various viruses, including HIV.

Analysis of nonlocal axial vibration in a nanorod is a crucial subject in science and engineering because of its wide applications in nanoelectromechanical systems. The aim of this paper is to show how these vibrations can be modelled within the framework of port-Hamiltonian systems. It turns out that two port-Hamiltonian descriptions in physical variables are possible. The first one is in descriptor form, whereas the second one has a non-local Hamiltonian density. In addition, it is shown that under appropriate boundary conditions these models possess a unique solution which is non-increasing in the corresponding ‘energy’, i.e., the associated infinitesimal generator generates a contraction semigroup on a Hilbert space, whose norm is directly linked to the Hamiltonian.

SUMMARYThe viscoelastic load Love numbers encapsulate the Earth’s rheology in a remarkably efficient fashion. When multiplied by a sudden increment of spherical harmonic load change, they give the horizontal and vertical surface displacements and gravity change at all later times. Incremental glacial load changes thus need only be harmonically decomposed, multiplied by the Love numbers and summed to predict the Earth’s response to glacial load redistributions. The computation of viscoelastic Love numbers from the elastic, viscous and adiabatic profiles of the Earth is thus the foundation upon which many glacial isostatic adjustment models are based. Usually, viscoelastic Love numbers are computed using the Laplace transform method, employing the correspondence principle to convert the viscoelastic equations of motion into the elastic equations with complex material parameters. This method works well for a fully non-adiabatic Earth, but can accommodate realistic partially adiabatic and fully adiabatic conditions only by changing the Earth’s density profile. An alternative method of Love number computation developed by Cathles (1975) avoids this dilemma by separating the elastic and viscous equations of motion. The separation neglects a small solid-elastic/fluid-elastic transition for compressible deformation, but allows freely defining adiabatic, partially adiabatic or fully non-adiabatic profiles in the mantle without changing the Earth’s density profile. Here, we update and fully describe this method and show that it produces Love numbers closely similar to those computed for fully non-adiabatic earth models computed by the correspondence principle, finite element and other methods. The time-domain method produces Love numbers as good as those produced by other methods and can also realistically accommodate any degree of mantle adiabaticity. All method implementations are available open source.

This paper is concerned with the propagation of SH-waves in an inhomogeneous viscoelastic layer overlying an inhomogeneous isotropic half-space. For the study of viscoelastic layer Kelvin–Voigt type model has been considered. The exponential type inhomogeneity is considered in viscoelastic layer with different parameters for viscoelastic part and for density of medium whereas for the half-space, it is quadratic type with single inhomogeneity parameter for rigidity and density. The solutions are obtained analytically for both the layer and half-space. Dispersion relation is obtained and subjected to continuity conditions at interfaces of viscoelastic layer and half-space and the upper boundary of layer as free surface. The effects of the inhomogeneity parameter are studied for both viscoelastic layer and inhomogeneous isotropic half-space. The numerical results are shown by plotting the graph between phase velocity and wave number for different values of inhomogeneity parameter and for the variation of depth of the layer. Keywords: SH-waves, Inhomogeneity parameter, Viscoelastic layer, Phase velocity, Wave number

[EN] In this paper we present a novel formulation for phenomenological anisotropic finite visco-hyperelasticity. The formulation is based on a multiplicative decomposition of the equilibrated deformation gradient into nonequilibrated elastic and viscous contributions. The proposal in this paper is a decomposition reversed respect to that from Sidoroff allowing for anisotropic viscous contributions. Independent anisotropic stored energies are employed for equilibrated and non-equilibrated parts. The formulation uses logarithmic strain measures in order to be teamed with spline-based hyperelasticity. Some examples compare the results with formulations that use the Sidoroff decomposition and also show the enhanced capabilities of the present model. (C) 2015 Elsevier Ltd. All rights reserved., Partial financial support for this work has been given by grant DPI2011-26635 from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of Spain

The basis of the Energy Structure Theory can be introduced in references [1-5] presented in 2020. Energy Structure Theory explains some new thermo-physical concepts including energy space, energy structure equation, dependent and independent energy components, irreversibility components, irreversibility structure, etc. Since this theory is presented considering the first and second laws of thermodynamics as well as energy components of the system as the basis of the energy structure equation, this theory can be expanded for a variety of the scientific applications. For example, in this note, we will try to introduce some of these scientific applications in general physics and engineering analysis. Also, using relevant concepts, 2D viscoelasticity problems will be studied. Also, the viscoelasticity and kinematic energy will be calculated for 2D viscoelasticity problems. Energy structure theory let us to study physical processes from the perspective of the componential energy exchange as well as independent and dependent energy component concept introduced by this theory.

We investigate the emergence of global alignment in colonies of dividing rod-shaped cells under confinement. Using molecular dynamics simulations and continuous modeling, we demonstrate that geometrical anisotropies in the confining environment give rise to imbalance in the normal stresses, which, in turn, drives a collective rearrangement of the cells. This behavior crucially relies on the colony's solid-like mechanical response at short time scales and can be recovered within the framework of active hydrodynamics upon modeling bacterial colonies as growing viscoelastic gels characterized by Maxwell-like stress relaxation., Comment: 10 pages, 8 figures

International audience; Solid tumour growth is often associated with the accumulation of mechanical stresses acting on the surrounding host tissue. Due to tissue nonlinearity, the shear modulus of the peri-tumoural region inherits a signature from the tumour expansion which depends on multiple factors, including the soft tissue constitutive behaviour and its stress/strain state. Shear waves used in MR-elastography (MRE) sense the apparent change in shear modulus along their propagation direction, thereby probing the anisotropic stiffness field around the tumour. We developed an analytical framework for a heterogeneous shear modulus distribution using a thick-shelled sphere approximation of the tumour and soft tissue ensemble. A hyperelastic material (plastisol) was identified to validate the proposed theory in a phantom setting. A balloon-catheter connected to a pressure sensor was used to replicate the stress generated from tumour pressure and growth while MRE data were acquired. The shear modulus anisotropy retrieved from the reconstructed elastography data confirmed the analytically predicted patterns at various levels of inflation. An alternative measure, combining the generated deformation and the local wave direction and independent of the reconstruction strategy, was also proposed to correlate the analytical findings with the stretch probed by the waves. Overall, this work demonstrates that MRE in combination with non-linear mechanics, is able to identify the apparent shear modulus variation arising from the strain generated by a growth within tissue, such as an idealised model of tumour. Investigation in real tissue represents the next step to further investigate the implications of endogenous forces in tissue characterisation through MRE

Rupture of the scapholunate interosseous ligament can cause the dissociation of scaphoid and lunate bones, resulting in impaired wrist function. Current treatments (e.g., tendon-based surgical reconstruction, screw-based fixation, fusion, or carpectomy) may restore wrist stability, but do not address regeneration of the ruptured ligament, and may result in wrist functional limitations and osteoarthritis. Recently a novel multiphasic bone-ligament-bone scaffold was proposed, which aims to reconstruct the ruptured ligament, and which can be 3D-printed using medical-grade polycaprolactone. This scaffold is composed of a central ligament-scaffold section and features a bone attachment terminal at either end. Since the ligament-scaffold is the primary load bearing structure during physiological wrist motion, its geometry, mechanical properties, and the surgical placement of the scaffold are critical for performance optimisation. This study presents a patient-specific computational biomechanical evaluation of the effect of scaffold length, and positioning of the bone attachment sites. Through segmentation and image processing of medical image data for natural wrist motion, detailed 3D geometries as well as patient-specific physiological wrist motion could be derived. This data formed the input for detailed finite element analysis, enabling computational of scaffold stress and strain distributions, which are key predictors of scaffold structural integrity. The computational analysis demonstrated that longer scaffolds present reduced peak scaffold stresses and a more homogeneous stress state compared to shorter scaffolds. Furthermore, it was found that scaffolds attached at proximal sites experience lower stresses than those attached at distal sites. However, scaffold length, rather than bone terminal location, most strongly influences peak stress. For each scaffold terminal placement configuration, a basic metric was computed indicative of bone fracture risk. This metric was the minimum distance from the bone surface to the internal scaffold bone terminal. Analysis of this minimum bone thickness data confirmed further optimisation of terminal locations is warranted.

Mudstone interlayer is a weak layer in rock engineering. When it is subjected to continuous stress higher than its damage threshold, due to the dislocation of particles in mudstone crystals and the expansion of cracks, mudstone strength is gradually damaged and deteriorated and the strain gradually increases, thus accelerating the phenomenon of creep damage. In order to describe the characteristics of the whole process of mudstone aging deformation, based on the damage evolution of strength parameters (cohesion and internal friction coefficient) with stress and time in mudstone creep tests, a novel damage nonlinear viscoelastoplastic body (D-NVPB) is proposed through improving traditional plastic element. D-NVPB describes the nonlinear characteristics of the accelerated creep stage of mudstone. With the element combination method, D-NVPB is connected with the Burgers model in series to form a new nonlinear damage creep model (D-NVEP model). The analysis results of creep characteristics theoretically verified the rationality of the model in describing the instantaneous elasticity, viscoelasticity, and nonlinear viscoplastic characteristics of the complete creep curve of mudstone. With the data obtained in the uniaxial compression creep test of mudstone under the action of a stress level of 14 MPa, based on the Levenberg-Marquardt nonlinear least squares method, the fitting calculation was performed through piecewise fitting and overall fitting. The correlation coefficient was 0.9909, which verified the applicability of the model. The obtained model parameters by the identification were used to predict the mudstone creep curve under the stress levels of 13 MPa and 15 MPa. The good prediction results further verified the feasibility of the model. Compared with the traditional creep model, the D-NVEP model can better describe the nonlinear characteristics of the accelerated creep stage and quantitatively display the strength damage evolution process of rock in the creep failure process.

The rheological properties parameters of paddy soil affect the interaction between the tillage tools and soil, thus influencing the operation quality and power consumption. In order to study the effects of tillage methods and moisture content on the rheological properties parameters of paddy soil in the middle and lower reaches of the Yangtze River, uniaxial compression creep tests of paddy soils with four moisture contents under no tillage (moisture contents: 26.71%, 24.52%, 23.26%, 21.28%) and plough tillage (moisture contents: 26.77%, 25.55%, 23.40%, 20.56%) were carried out using a TMS-PRO texture analyzer. The creep properties curves obtained from the tests, and the rheological constitutive equation of paddy soil under compression was established by Burgers viscoelastic model. Respectively, the quantitative change rules of creep properties of paddy soil with different moisture contents under different tillage methods and the correlation between these parameters were explored. The results showed that the moisture content under the three-year plough tillage and no tillage methods had significant influence on the rheological properties parameters of paddy soil (P < 0.05). The instantaneous elastic modulus, delay elastic modulus, and viscosity coefficient of the two paddy soils (no tillage and plough tillage soils) decreased with the increase of moisture content. However, the variation rules of relaxation time and delay viscosity coefficient with moisture content differed between these two paddy soils. Specifically, the strain rate of the two paddy soils decreased as moisture content decreased, where the total strain combines elastic strain, viscous strain, and viscoelastic strain. The initial strain rate and steady strain rate of the plough tillage paddy soils were lower than that of the no tillage paddy soils. The established creep model equation could be used to obtain viscoelastic rheological parameters of paddy soil in a wide range. The fitting equations between rheological parameters and moisture content were introduced into Burgers model, and the coupling equations between creep deformation and moisture content and time were derived, which could be used to predict the creep properties and deformation behavior of paddy soil in a certain range of no tillage and ploughed field. Overall, this study has a certain theoretical significance for the development and improvement of paddy soil rheology theory, and can also provide theoretical basis and technical support for the research of agricultural machinery design optimization, field water, soil conservation, soil tillage and compaction related simulation analysis in the middle and lower reaches of the Yangtze River.

A local universal relation is an equation between the stress components and the position vector components which holds for any material in an assigned constitutive family. Although universal relations may be of great help to modellers in characterizing the material behaviour, they are often ignored. In this paper we briefly discuss the valuable insights that universal relations may offer in solid mechanics and determine novel universal relations associated with shearing motions in nonlinearly elastic and nonlinearly viscoelastic materials of differential type.

Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction., 14 pages, 1 figure

We show that the correct dual hydrodynamic description of homogeneous holographic models with spontaneously broken translations must include the so-called "strain pressure" -- a novel transport coefficient proposed recently. Taking this new ingredient into account, we investigate the near-equilibrium dynamics of a large class of holographic models and faithfully reproduce all the hydrodynamic modes present in the quasinormal mode spectrum. Moreover, while strain pressure is characteristic of equilibrium configurations which do not minimise the free energy, we argue and show that it also affects models with no background strain, through its temperature derivatives. In summary, we provide a first complete matching between the holographic models with spontaneously broken translations and their effective hydrodynamic description., Comment: minor improvements, references added, matches the published version in Physics Letters B

Mechanical forces play an important role in various physiological processes, such as morphogenesis, cytokinesis, and migration. Thus, in order to illuminate mechanisms underlying these physiological processes, it is crucial to understand how cells deform and respond to external mechanical stimuli. During recent decades, the mechanical properties of cells have been studied extensively using diverse measurement techniques. A number of experimental studies have shown that cells are far from linear elastic materials. Cells exhibit a wide variety of nonlinear elastic and inelastic properties. Such complicated properties of cells are known to emerge from unique mechanical characteristics of cellular components. In this review, we introduce major cellular components that largely govern cell mechanical properties and provide brief explanations of several experimental techniques used for rheological measurements of cell mechanics. Then, we discuss the representative nonlinear elastic and inelastic properties of cells. Finally, continuum and discrete computational models of cell mechanics, which model both nonlinear elastic and inelastic properties of cells, will be described.

Motivated by the classical expressions of the mean-square displacement and the velocity autocorrelation function of Brownian particles either suspended in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all timescales the mean-square displacement of Brownian microspheres with mass m and radius R suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance m_{R}=m/6πR. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean-square displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer timescales. The viscous-viscoelastic correspondence principle established in this paper by introducing the concept of the inerter is equivalent to the viscous-viscoelastic analogy adopted by Mason and Weitz [T. G. Mason and D. A. Weitz, Phys. Rev. Lett. 74, 1250 (1995)10.1103/PhysRevLett.74.1250].

The experimental quantification and modeling of the multiaxial mechanical response of polymer membranes of coronary balloon catheters have not yet been carried out. Due to the lack of insights, it is not shown whether isotropic material models can describe the material response of balloon catheter membranes expanded with nominal or higher, supra-nominal pressures. Therefore, for the first time, specimens of commercial polyamide-12 balloon catheters membranes were investigated during uniaxial and biaxial loading scenarios. Furthermore, the influence of kinematic effects on the material response was observed by comparing results from quasi-static and dynamic biaxial extension tests. Novel clamping techniques are described, which allow to test even tiny specimens taken from the balloon membranes. The results of this study reveal the semi-compliant, nonlinear, and viscoelastic character of polyamide-12 balloon catheter membranes. Above nominal pressure, the membranes show a pronounced anisotropic mechanical behavior with a stiffer response in the circumferential direction. The anisotropic feature intensifies with an increasing strain-rate. A modified polynomial model was applied to represent the realistic mechanical response of the balloon catheter membranes during dynamic biaxial extension tests. This study also includes a compact set of constitutive model parameters for the use of the proposed model in future finite element analyses to perform more accurate simulations of expanding balloon catheters.

The time-dependent properties of rubber-like synthesized and biological materials are crucial for their applications. Currently, this behavior is mainly measured using axial tensile test, compression test, or indentation. Limited studies performed on using multi-axial loading measurements of time-dependent material behavior exist in the literature. Therefore, the aim of this study is to investigate the viscoelastic response of rubber-like materials under multi-axial loading using cavity expansion and relaxation tests. The tests were performed on PVA hydrogel specimens. Three hyperelasitc models and one term Prony series were used to characterize the viscoelastic response of the hydrogels. Finite element (FE) simulations were performed to verify the validity of the calibrated material coefficients by reproducing the experimental results. The excellent agreement between the experimental, analytical and numerical data proves the capability of the cavity expansion technique to measure the time-dependent behavior of viscoelastic materials.

We show the analogy between a generalization of the Rayleigh-Plesset equation of bubble dynamics including surface tension, elasticity and viscosity effects with a reformulation of the Friedmann-Lema\^itre set of equations describing the expansion of space in cosmology assuming a homogeneous and isotropic universe. By comparing both fluid and cosmic equations, we propose a bold generalization of the newly-derived cosmic equation mapping three continuum mechanics contributions. Conversely, the addition of a cosmological constant-like term in the fluid equation would lead also to a new phenomenology., Comment: 5 pages

Motivated by the observation of comets and asteroids rotating in non-principal axis (NPA) states, we investigate the relaxation of a freely precessing triaxial ellipsoidal rotator towards its lowest energy spin state. Relaxation of the precession arises from internal dissipative stresses generated by self-gravitation and inertial forces from spin. We develop a general theory to determine the viscoelastic stresses in the rotator, under any linear rheology, for both long-axis (LAM) and short-axis (SAM) modes. By the methods of continuum mechanics, we calculate the power dissipated by the stress field and the viscoelastic material strain, which enables us to determine the time-scale of the precession dampening. To illustrate how the theory is used, we apply our framework to a triaxial 1I/2017 (‘Oumuamua) and 4179 Toutatis under the Maxwell regime. For the former, employing viscoelastic parameters typical of very cold monolithic asteroids renders a dampening time-scale longer by a factor of 1010 and higher than the time-scales found in the works relying on the $\, Q$-factor approach, while the latter yields a time-scale shorter by 107 as a consequence of including self-gravitation. We further reduce our triaxial theory to bodies of an oblate geometry and derive a family of relatively simple analytic approximations determining the NPA dampening times for Maxwell rotators, as well as a criterion determining whether self-gravitation is negligible in the relaxation process. Our approximations exhibit a relative error no larger than $0.2{{\ \rm per\ cent}}$, when compared to numerical integration, for close to non-dissipative bodies and $0.003{{\ \rm per\ cent}}$ for moderately to highly energy dissipating rotators.

We determine the nonlocal stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we go beyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection operator formalism by introducing the proper irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently from these authors, we include transverse contributions as well. This recovers the expression for the stress autocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, in case that those are evaluated in the overdamped limit. Finally, we argue that the found memory function reduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations and derive the corresponding hydrodynamic equations., Comment: 10 pages, 0 figure

To study the shrinkage rule of borehole diameter and its effect on gas extraction, a visco-elastoplastic model for boreholes considering strain softening and the dilatancy characteristic was established to obtain the expressions of the coal stress, variation in diameter, and pressure relief range. The stress distribution and pressure relief effect of the boreholes in soft and hard coal seams were comparatively analyzed. The shrinkage rule of the borehole diameter was studied. The reasons for the rapid reduction in the extraction concentration of the borehole in soft coal seams were described. A technology of improving the gas extraction effect in soft coal seams was developed. The research results showed that the radius of the plastic softening zone is 0.405 m for a borehole in a soft coal seam and 0.224 m for that in a hard coal seam. This indicates that the borehole in a soft coal seam has a better pressure relief effect. The boreholes in both hard and soft coal seams will incur a shrinkage phenomenon; however, the soft coal seam has low strength and a weak ability to resist damage, and thus the surrounding coal will have a more intense creep deformation, leading to an instability failure during a short period of time and thus, a blocking of the extraction channel, thereby causing a rapid reduction in the gas extraction concentration. The borehole in a hard coal seam also shows a shrinkage phenomenon, but remains in a stable state without a blockage; thus, high-concentration gas can be extracted from this borehole for a long period of time. The geo-stress and coal strength are the two main factors controlling the amplitude of borehole shrinkage. From an increase in stress, the borehole in a hard coal seam shows a more intense creep deformation in a deep mine, which may lead to blockage. The key to improving the gas extraction effect in soft coal seams is to maintain a smooth extraction channel. The full screen pipe is installed through the drill pipe to retain an extraction channel, leading to an average gas extraction increase from 0.043 m3/min to 0.12 m3/min, an increase of 2.77 times. These research results are consistent with actual production, and can provide theoretical guidance for determining the gas extraction parameters.

With desirable physical performances of impressive actuation strain, high energy density, high degree of electromechanical coupling and high mechanical compliance, dielectric elastomer actuators (DEAs) are widely employed to actuate the soft robots. However, there are many challenges to establish the dynamic models for DEAs, such as their inherent nonlinearity, complex electromechanical coupling, and time-dependent viscoelastic behavior. Moreover, most previous studies concentrated on the planar DEAs, but the studies on DEAs with some other functional shapes are insufficient. In this paper, by investigating a conical DEA with the material of polydimethylsiloxane and considering the influence of inertia, we propose a dynamic model based on the principles of nonequilibrium thermodynamics. This dynamic model can describe the complex motion characteristics of the conical DEA. Based on the experimental data, the differential evolution algorithm is employed to identify the undetermined parameters of the developed dynamic model. The result of the model validation demonstrates the effectiveness of the model.

Recent studies showed that wave intensity analysis (WIA) provides clinically valuable information about local and global cardiovascular function. Wave intensity (WI) is computed as the product of the pressure change and the velocity change during short time intervals. The major limitation of WIA in clinical practice is the need for invasive pressure measurement. Since vessel wall displacement can be measured non-invasively, the usage of WI will be expanded if the vessel wall dilation is used instead of pressure in derivation of WI waveform. Our goal in this study is to investigate the agreement between wall displacement-based WI and the pressure-based WI for different vessel wall models including linear elastic, nonlinear and viscoelastic cases. The arbitrary Eulerian Lagrangian finite element method is employed to solve the coupled fluid-structure interaction (FSI). Our computational models also include two types of vascular disease-related cases with geometrical irregularities, aneurysm and stenosis. Our results show that for vessels with linear elastic wall, the displacement-based WI is almost identical to the pressure-based WI. The existence of vessel irregularities does not impact the accuracy of displacement-based WI. However, in a viscoelastic wall where there is a phase difference between pressure and vessel wall dilation, displacement-based WI deviated from pressure-based WI. The error associated with this phase difference increased nonlinearly with increasing viscosity. This results in a maximum error of 6.8% and 7.13% for a regular viscoelastic vessel wall and an irregular viscoelastic vessel wall, respectively. A separate analysis has also been performed on the agreement of backward and forward running waves extracted from a decomposition of the displacement-based and pressure-based WI. Our findings suggest that displacement-based WI is a reliable method of WIA for large central arteries that do not show viscoelastic behaviors. This can be clinically significant since the required information can be measured non-invasively.

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework., 32 pages, 10 figures

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports. peerReviewed

A new polydisperse “toy” constitutive model is derived and developed from fundamental principles and ideas governing the nonlinear rheology of linear flexible polymers [Mead et al., J. Rheol. 59, 335–363 (2015)]. Specifically, the new model is comprised of four fundamental pieces. First, the model contains a simple differential description of the entanglement dynamics of discrete entanglement pairs. Second, the model contains a differential description of the ij entanglement pair orientation tensor dynamics. Third, following a similar development by Mead and Mishler [J. Non-Newtonian Fluid Mech. 197, 61–79 and 80–90 (2013).], a diluted stretch tube is constructed to describe the relative stretch of each component in the molecular weight distribution (MWD). Fourth, a description of configuration dependent friction coefficients is generated by generalizing the monodisperse formulation of Ianniruberto et al. [Macromolecules 45, 8058–8066 (2012)]. The polydisperse stress calculator is developed from the orientation, stretch and entanglement density and is fundamentally different from other molecular models that assume a constant entanglement density. The resulting model is comprised of three differential evolution equations and is simple to code and fast to execute. The model can simulate arbitrary fast nonlinear flows of arbitrary MWD's. In the slow flow linear viscoelastic limit, the model collapses to the double reptation model. This welcome result has positive implications with respect to our model parameter determination [Ye et al., J. Rheol. 47, 443–468 (2003); Ye and Sridhar, Macromolecules 38, 3442–3449 (2005)] for making quantitative calculations.A new polydisperse “toy” constitutive model is derived and developed from fundamental principles and ideas governing the nonlinear rheology of linear flexible polymers [Mead et al., J. Rheol. 59, 335–363 (2015)]. Specifically, the new model is comprised of four fundamental pieces. First, the model contains a simple differential description of the entanglement dynamics of discrete entanglement pairs. Second, the model contains a differential description of the ij entanglement pair orientation tensor dynamics. Third, following a similar development by Mead and Mishler [J. Non-Newtonian Fluid Mech. 197, 61–79 and 80–90 (2013).], a diluted stretch tube is constructed to describe the relative stretch of each component in the molecular weight distribution (MWD). Fourth, a description of configuration dependent friction coefficients is generated by generalizing the monodisperse formulation of Ianniruberto et al. [Macromolecules 45, 8058–8066 (2012)]. The polydisperse stress calculator is developed from the orien...