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Elastic nonlinearity in sandstones is given by the combination of slow and fast effects, leading to hysteresis and relaxation of the viscoelastic properties after the sample is perturbed (conditioning). While a lot of experimental evidences of slow dynamics are available, quantification of nonclassical nonlinearity is still difficult: nonlinear indicators must be introduced which are independent of both experimental configuration and on conditioning strain amplitude, which is often difficult to quantify in an accurate way. In this contribution, we introduce and analyze some possible quantities describing nonlinear viscoelasticity in sandstones, derived from a non-equilibrium strain model. We will show that they identify real material properties, in the sense that they are not dependent on experimental details (such as experiment duration, conditioning protocol, frequency,...) and can be measured easily with good repeatability. Highlights: We quantify the temporal relaxation of viscoelastic properties of sandstones; We introduce measurable indicators allowing to quantify hysteresis, anisotropy, and relaxation in sandstones; We propose a non-equilibrium strain model to describe observed hysteresis and anisotropy in nonlinear hysteretic viscoelastic properties; We show a linear correlation exists between modulus and damping evolution during relaxation in sandstones. [ABSTRACT FROM AUTHOR]

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard–Jones particles. [ABSTRACT FROM AUTHOR]

There is a correlation between nonlocal time and space in the nanostructures which are attacked by waves whose length lies in the range of the nanostructure's intrinsic characteristic lengths. This temporal–spatial coupling affects the viscoelastic behaviors of the nanostructures. In such a case, the conventional tempo-spatially decoupled nonlocal viscoelasticity is not able to provide accurate dynamic responses. To resolve this problem, the present paper focuses on the development of a novel fractional nonlocal time–space strain gradient viscoelasticity and shows its application in the wave propagation analysis of functionally graded material (FGM) nanobeams. The fractional constitutive equations are derived on the basis of the combination of the well-known nonlocal strain gradient elasticity and fractional nonlocal time–space hypotheses. The motion equations of the beam-type elements are presented on the basis of the refined higher-order beam theory and Hamilton's principle. With this newly developed nonlocal theory, the governing equations of the nanobeam are extracted. Afterward, an analytical wave solution will be utilized to achieve the loss factor of the problem. The results of this work reveal that an increase in the nonlocal parameter can reduce the loss factor in a remarkable way due to the coupling between the nonlocalities in the spatial and temporal domains. [ABSTRACT FROM AUTHOR]

AbstractIn our research described here, a rheological model was proposed to be used to determine the rheological behavior of drilling mud, which is one of the most important factors in determining a suitable mud used in drilling. The parameters of the rheological model were determined by a curve fitting method using more than 95 experimental data pairs available in the literature for seven different viscoelastic drilling muds. The relationship between shear stress and shear rate obtained from the proposed model was compared with the relationships obtained from the Herschel–Bulkley, Power-law, and Bingham plastic models. The data obtained from the proposed model was also compared with the experimental data existing in the related literature. The average percentage differences between the experimental data and the data obtained from the proposed model for the drilling fluids were 5.16, 0.623, and 8.8, respectively, which were considerably lower than the average differences between the experimental data and the data acquired from the three mentioned models. The Power-law model outperformed our proposed model for only three drilling muds. As a result, we suggest that the rheological model proposed here can be easily used to determine the rheological properties of some kinds of drilling muds. In addition to deriving the rheological model for drilling muds, a comprehensive literature review on the subject was conducted. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is continued. A set of two nonlinear differential equations describing the processes of shear at a constant rate and stress relaxation is obtained. Equation set describing creep is derived; a general solution of the Cauchy problem for the set is constructed in an explicit form (the equations of the families of creep, and structuredness curves are derived). For arbitrary six material parameters and (increasing) material function that govern the model, basic properties of the families stress-strain curves at constant strain rates, stress relaxation curves and creep curves generated by the model, and the features of structuredness evolution under these types of loading are analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain, and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves, relaxation curves, and creep curves of structurally stable materials. In particular, it is proved that creep curves always increase in time and have oblique asymptote, and structuredness under constant stress is always monotonous (unlike other loading modes), but can decrease or increase depending on the relation between the stress level and initial structuredness. The same condition controls creep curves to be convex up or down: at a certain (calculated) critical load creep curves change from convexity up (under smaller loads) to convexity down, and the structuredness becomes ascending instead of descending. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on. [ABSTRACT FROM AUTHOR]

At present, structural analysis of polymer composite materials is a highly relevant issue. The complexity of taking into account the viscoelastic stress–strain dependence and the time-dependent distribution of stress–strain state parameters over the volume occupied by a solid is a limiting factor. The relevance and demand for new efficient methods of mathematical modeling of creep and relaxation processes in viscoelastic structures are obvious. The aim of this work is to verify and validate the method for solving boundary value problems of a linear viscoelastic solid. The proposed approach is based on the formulation of the generalized principle of correspondence between elastic and viscoelastic problems, according to which a viscoelastic solution can be obtained by replacing elastic constants by some time functions, which are hereinafter called time-effective moduli. The results derived from the theoretical validation and the solution of several problems suggest that the proposed method can be used for solving problems on the stress–strain state of viscoelastic structures. [ABSTRACT FROM AUTHOR]

In this study, the viscoelastic properties of porcine kidney in the upper, middle and lower poles were investigated using oscillatory shear tests. The viscoelastic properties were extracted in the form of the storage modulus and loss modulus in the frequency and time domain. Measurements were taken as a function of frequency from 0.1 Hz to 6.5 Hz at a shear strain amplitude of 0.01 and as function of strain amplitude from 0.001 to 0.1 at a frequency of 1 Hz. Measurements were also taken in the time domain in response to a step shear strain. Both the frequency and time domain data were fitted to a conventional Standard Linear Solid (SLS) model and a semi-fractional Kelvin–Voigt (SFKV) model with a comparable number of parameters. The SFKV model fitted the frequency and time domain data with a correlation coefficient of 0.99. Although the SLS model well fitted the time domain data and the storage modulus data in the frequency domain, it was not able to capture the variation in loss modulus with frequency with a correlation coefficient of 0.53. A five parameter Maxwell–Wiechert model was able to capture the frequency dependence in storage modulus and loss modulus better than the SLS model with a correlation of 0.85. [ABSTRACT FROM AUTHOR]

This paper analyzes the effect of crosslinking reactions on a thermoset polymer's viscoelastic properties. In particular, a numerical model to predict the evolution of epoxy's mechanical properties during the curing process is proposed and implemented in an Ansys APDL environment. A linear viscoelastic behavior is assumed, and the scaling of viscoelastic properties in terms of the temperature and degree of conversion is modeled using a modified version of the TNM (Tool–Narayanaswamy–Mohynian) model. The effects of the degree of conversion and structural relaxation on epoxy's relaxation times are simultaneously examined for the first time. This formulation is based on the thermo-rheological and chemo-rheological simplicities hypothesis and can predict the evolution of epoxy's relaxation phenomena. The thermal–kinetic reactions of curing are implemented in a homemade routine written in APDL language, and the structural module of Ansys is used to predict the polymer's creep and stress relaxation curves at different temperatures and degrees of conversion. [ABSTRACT FROM AUTHOR]

The viscoelasticity of mechanically sensitive tissues such as periodontal ligaments (PDLs) is key in maintaining mechanical homeostasis. Unfortunately, PDLs easily lose viscoelasticity (e.g., stress relaxation) during periodontitis or dental trauma, which disrupt cell–extracellular matrix (ECM) interactions and accelerates tissue damage. Here, Pluronic F127 diacrylate (F127DA) hydrogels with PDL‐matched stress relaxation rates and high elastic moduli are developed. The hydrogel viscoelasticity is modulated without chemical cross‐linking by controlling precursor concentrations. Under cytomechanical loading, F127DA hydrogels with fast relaxation rates significantly improved the fibrogenic differentiation potential of PDL stem cells (PDLSCs), while cells cultured on F127DA hydrogels with various stress relaxation rates exhibited similar fibrogenic differentiation potentials with limited cell spreading and traction forces under static conditions. Mechanically, faster‐relaxing F127DA hydrogels leveraged cytomechanical loading to activate PDLSC mechanotransduction by upregulating integrin–focal adhesion kinase pathway and thus cytoskeletal rearrangement, reinforcing cell–ECM interactions. In vivo experiments confirm that faster‐relaxing F127DA hydrogels significantly promoted PDL repair and reduced abnormal healing (e.g., root resorption and ankyloses) in delayed replantation of avulsed teeth. This study firstly investigated how matrix nonlinear viscoelasticity influences the fibrogenesis of PDLSCs under mechanical stimuli, and it reveals the underlying mechanobiology, which suggests novel strategies for PDL regeneration. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media is continued. For arbitrary six material parameters and an (increasing) material function that control the model, the basic properties of the families of stress-strain curves at constant strain rates and relaxation curves generated by the model, and the features of the evolution of the structuredness under these types of loading are analytically studied. The dependences of these curves on time, shear rate, initial strain and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves and relaxation curves of structurally stable materials. In particular, it has been proved that stress-strain curves can be both increasing functions and can have decreasing sections resembling a "yield tooth" or damped oscillations, that all stress-strain curves (SSCs) possess horizontal asymptotes (steady flow stress), monotonically dependent on shear rate, and flow stress increases with shear rate growth, that the instantaneous shear modulus, on the contrary, depends on the initial structuredness, but does not depend on shear rate. Under certain restrictions on the material parameters, the model is also capable of providing a bilinear form of stress-strain curves, which is typical for an ideal elastoplastic model, but with strain rate sensitivity. It has been established that the family of stress-strain curves does not have to be increasing either in initial structuredness or in shear rate: in a certain range of shear rates, in which the equilibrium position is a "mature" focus and pronounced oscillations of stress-strain curves are observed, it is possible to intertwine stress-strain curves with different shear rates. It is proved that for any material parameters and functions, all stress relaxation curves decrease and have a common zero asymptote as time tends to infinity. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on. [ABSTRACT FROM AUTHOR]

Developing a viscoelastic model for the cyclic thermomechanical loading of thermosetting polymers is the main goal of this study. The model includes memory for residual thermal stresses and can consider stress accumulation across many loading cycles. By considering stress accumulation, we can improve predictions and understand how thermosetting polymers' stress–strain state changes under cyclic thermomechanical loading. This approach was validated through experimental verification to ensure its applicability in practical engineering scenarios. The experiment showed that the thermosetting polymer can accumulate stress during cycles of heating and mechanical loading during use. The results of the modeling and experiment are compared. The results have led to corrections in the way this model is applied to thermosetting polymers like the epoxy resin in this study. The corrected results matched well with the experimental measurements of stress under cyclic thermomechanical load, with a difference of only 1 to 6%. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model of the shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is carried out. A set of two nonlinear differential equations describing shear at a constant rate and stress relaxation was obtained. Assuming six material parameters and an (increasing) material function that control the model are arbitrary, the basic properties of the families of stress-strain curves at constant strain rates, stress relaxation curves (Part 2) and creep curves (Part 3) generated by the model, and the features of the evolution of the structuredness under these types of loading were analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain and initial structuredness of material (for example, degree of physical crosslinking), as well as on material parameters and function governing the model, were studied. Several indicators of the model applicability are found, which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (properties) are generated by structuredness changes in comparison to typical stress-strain, relaxation and creep curves of structurally stable materials. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: the effects of creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves at a constant rate, strain rate and strain hardening, flow under constant stress, etc. The first part of the article is devoted to formulation of the model and preparation of basis for the second part: the proof of the uniqueness and stability of the equilibrium point of the nonlinear equations set, analytical study of the equilibrium point dependence on all material parameters, possible types of phase portraits and the properties of integral and phase curves of the model. [ABSTRACT FROM AUTHOR]

The viscoelasticity of a carbon nanotube (CNT)-laden air–water interface was characterized using two different experimental methods. The first experimental method used a Langmuir-Pockels (LP) trough coupled with a pair of oscillating barriers. The second method is termed the Bicone-Trough (BT) method, where a LP trough was custom-built and fit onto a rheometer equipped with a bicone fixture to standardize the preparation and conditioning of a particle-laden interface especially at high particle coverages. The performance of both methods was evaluated by performing Fast Fourier Transform (FFT) analysis to calculate the signal-to-noise ratios (SNR). Overall, the rheometer-based BT method offered better strain control and considerably higher SNRs compared to the Oscillatory Barriers (OB) method that oscillated barriers with relatively limited positional and speed control. For a CNT surface coverage of 165 mg/m2 and a frequency of 100 mHz, the interfacial shear modulus obtained from the OB method increased from 39 to 57 mN/m as the normal strain amplitude increased from 1 to 3%. No linear viscoelastic regime was experimentally observed for a normal strain as small as 0.5%. In the BT method, a linear regime was observed below a shear strain of 0.1%. The interfacial shear modulus decreased significantly from 96 to 2 mN/m as the shear strain amplitude increased from 0.025 to 10%. [ABSTRACT FROM AUTHOR]

The response of a body described by a quasi-linear viscoelastic constitutive relation, whose material moduli depend on the mechanical pressure (that is one-third the trace of stress) is studied. The constitutive relation stems from a class of implicit relations between the histories of the stress and the relative deformation gradient. A-priori thresholding is enforced through the pressure that ensures that the displacement gradient remains small. The resulting mixed variational problem consists of an evolutionary equation with the Volterra convolution operator; this equation is studied for well-posedness within the theory of maximal monotone graphs. For isotropic extension or compression, a semi-analytic solution of the quasi-linear viscoelastic problem is constructed under stress control. The equations are studied numerically with respect to monotone loading both with and without thresholding. In the example, the thresholding procedure ensures that the solution does not blow-up in finite time. [ABSTRACT FROM AUTHOR]

We propose an anisotropic and nonlinear generalization of the Kelvin–Voigt viscoelastic model obtained considering the additive splitting of the Cauchy stress tensor in an elastic and a dissipative part. The former one corresponds to a fiber-reinforced hyperelastic material while the dissipative effect is described by the most general linear transverse-isotropic tensorial function of symmetric part of the velocity gradient. In a such a way we characterize the dissipative contribution via three viscoelastic moduli. We then show, by a detailed analysis of the simple shear quasistatic motion and the corresponding creep phenomena, that this motion may be used to determine experimentally the viscoelastic parameters. [ABSTRACT FROM AUTHOR]

Understanding the time-dependent mechanical behavior of tough and viscoelastic hydrogels under complex external loading is crucial. In this study, we utilized tough and viscoelastic hydrogels synthesized through the copolymerization of methacrylic acid and methacrylamide as a model system to investigate their mechanical behavior under multiaxial stretching across a wide range of strain rates. Three stretching modes examined were uniaxial, pure shear, and equal biaxial stretching. Our findings show that under equal biaxial stretching, the hydrogels exhibit higher mechanical properties and energy dissipation compared to uniaxial and pure shear stretching, owing to the greater contribution of hydrogen bonds to energy dissipation in the former stretching mode. Additionally, employing the time-elongation separability method during the stretching process, we observed that the relaxation of dynamic hydrogen bonds in the hydrogels only depends on stretching time, independent of the elongation ratio and stretching modes. We anticipate that this study will yield valuable contributions to the design of durable load-bearing soft materials, particularly in dealing with complex deformation and strain rate responses. [ABSTRACT FROM AUTHOR]

To understand the geomechanical implications of long-term creep (time-dependent deformation) response of gas shale, short-duration creep was recorded from laboratory triaxial tests on ten Goldwyer gas shale samples in the onshore Canning Basin at in situ stress conditions under constant differential axial stress. A simple power-law function captures primary creep behaviour involving elastic compliance constant B and time-dependent factor n. Experimental creep data revealed larger axial creep strain in clay and organic-rich rocks, than those dominated by carbonates. Anisotropic nature of creep was observed depending upon the direction of constant axial stress application (perpendicular or parallel to the bedding plane). Upon the application of linear viscoelastic theory on laboratory creep fitting coefficients, differential horizontal stress accumulation over a geological time scale was estimated from the viscoelastic stress relaxation concept. Further, this model was used to derive lithology-dependent least principal stress (Shmin) magnitude at depth for two vertical wells intersecting the Goldwyer gas shale formations. This newly proposed Shmin model was found to have a profound influence on designing hydraulic fracture simulation. Further, pore size distribution and specific surface area value SN2 were derived from low-pressure gas adsorption experiments. These physical properties along with weak mineral components were linked with creep constitutive parameters to understand the physical mechanisms of creep. A strong correlation was noted between SN2 and creep parameters n and B. Finally, an attempt was made to investigate how gas shale composition and failure frictional properties can influence shear fracturing. Highlights: Bedding perpendicular gas shales show a higher creep magnitude than their bedding parallel orientation i.e., creep deformation is anisotropic in nature. A viscoelastic stress relaxation approach can explain lithology-dependent least principal stress Shmin profile estimated from 1-D power-law creep constitutive parameters (B—elastic compliance constant, n—time-dependent factor) and with a constrain of relative variation of in situ stress magnitudes ϕ at subsurface depth. Specific surface area SN2 is a first-order proxy for continuous creep constitutive parameters prediction as well as estimation of frictional failure properties of gas shales intersecting different stratigraphic layers. [ABSTRACT FROM AUTHOR]

A high-performance bismaleimide (BMI) resin blends containing the polyaryletherketone (PAEK) were prepared. The nanomechanical behaviors, viscoelasticity, and tribological properties of the bismaleimide resins were investigated by nanoindentation/scratch methods. It was established that the hardness (H) decreased, while the elastic modulus (E) increased, i.e., a reduction of plasticity index (H /E) values through the quasi-static nano-indentation testing. Meanwhile, the indentation response was mainly affected by the plastic deformation in response to a stress. The unmodified bismaleimide resins demonstrated better load-bearing capacity and indentation recovery ability, lower penetration depth than the other three specimens. Effects of angular frequency and average contact force on the viscoelastic properties were also investigated by the dynamic nanoindentation mode. The results revealed that variations of the loss tangent curves nearly were similar to each other, first increased then decreased gradually at contact force of 150 and 300 μN. Topography and profiles of the indentation and scratch surfaces were also discussed. Based on the results of the nanoscratching tests, when the PAEK content was 10 phr, the coefficient of friction during plowing was the lowest, exhibited the better scratch/wear resistance. [ABSTRACT FROM AUTHOR]

• The variable-order fractional viscoelastic models are developed considering three typical viscoelastic behaviors. • The linear form of the order function is chosen to reflect the evolution of mechanical properties in materials. • The sensitivity of the viscoelastic behaviors to the parameters in the order function is analyzed in detail. In variable-order fractional calculus, the order is allowed to be in a functional form, which provides a novel way to describe the time-dependent physical processes. In this work, the performance of variable-order fractional viscoelastic models to the order function parameters is comprehensively investigated. Firstly, the variable-order fractional constitutive model is deduced from the theory of constant-order fractional viscoelasticity. The effect of order function is studied which shows that the linear order function can effectively describe the viscoelastic properties. Then the variable-order fractional viscoelastic models are developed considering three kinds of viscoelastic behaviors, including stress-strain relationship, creep, and stress relaxation. The sensitivity of the viscoelastic behaviors to the parameters in the linear order function is analyzed in detail. Finally, the effectiveness of the proposed models is validated by comparing them to the existing experimental data of typical viscoelastic behaviors, and the laws of the order function for each case are discussed based on the fractional viscoelastic theories. It is proved that the variable-order fractional models can give an accurate description of the viscoelastic behaviors under various loading conditions, and the change of the fractional order can visualize the evolution of the mechanical properties of the material. [ABSTRACT FROM AUTHOR]

This paper deals with a linear theory of thermoviscoelasticity within the framework of Green–Naghdi thermomechanics. We use some notation and terminology introduced by Green and Naghdi, but instead of using the entropy balance law we employ an entropy production inequality. We introduce the entropy flux tensor and present a theory of materials of Kelvin–Voigt type in which the stress tensor depends on the temperature gradients. The theory leads to a fourth-order equation for temperature. The boundary conditions for thermal displacement are presented. In the dynamical theory of anisotropic solids, we formulate boundary-initial value problems and present a uniqueness theorem. We derive the continuous dependence of solutions upon initial data and supply terms. In the case of homogeneous and isotropic bodies, we establish a representation of the solution that is expressed in terms of two potentials and present an application of this result. [ABSTRACT FROM AUTHOR]

The size and viscosity effects are noticeable at the micro-/nano scale. In the present work, the strain gradient viscoelastic solution of the mode-III crack in an infinite quasi-brittle advanced material is proposed based on the strain gradient viscoelasticity theory using the Wiener–Hopf method. The solutions to the gradient-dependent viscoelastic crack problem are obtained directly by using the correspondence principle between the strain gradient viscoelasticity and strain gradient elasticity in Maxwell's standard linear solid model. In this model, the stress near the crack tip is time-dependent and size-dependent. Besides, the stress near the crack tip is more significant than that based on gradient elasticity theory. Compared with the elastic strain gradient effect, the viscous gradient effect makes the stress field at the crack tip harden. The location and the value of maximum stress change with time, which differs from the case in strain gradient elasticity theory. The time that the normalized stress takes to stabilize also changes with the distance from the crack tip. When the viscosity effect is neglected or time tends to infinity, the strain gradient viscoelasticity theory can be reduced to the classical strain gradient elasticity theory. [ABSTRACT FROM AUTHOR]

This study constructs a model to represent the strain–stress field surrounding a splay fault and demonstrates the accumulation processes of both strain and stress around the splay fault. We consider the case of multiple fault dislocations, construct the model as a function of the effective viscosity in the media, and investigate the influence of the effective viscosity on the strain and stress accumulation patterns. The results show that the strain and stress tend to accumulate in the splay fault and the subducting oceanic crust, and the rate of accumulation varies with the effective viscosity. The accumulation and relaxation of strain and stress are simultaneous, and the slower the effective viscosity, the slower the accumulation rate. We discuss the relationship between the splay faults, fluid, and intraslab earthquakes. Finally, the possibility that effective viscosity may contribute to the mode of occurrence of intraslab earthquakes at the Hikurangi subduction margin is discussed. Plain Language Summary: We construct a simple model to explain the evolution of strain and stress over time in a subduction margin. The model constructed in this study is the case where a fault branches from a plate boundary. We investigate the influence of the effective viscosity of its constituents on the temporal evolution of strain and stress. The results show that the rate of strain and stress accumulation varies with the effective viscosity. Our result may suggests the influence of the effective viscosity on the source distribution of the microearthquakes observed at the Hikurangi subduction margin. Key Points: Temporal evolution of strain and stress caused by the dislocation of tri‐materials with different effective viscosities is calculatedStrain and stress accumulation rate depends on the effective viscosityStrain and stress accumulated at the multiple fault edge strongly influence the stress perturbations in the subducting oceanic crust [ABSTRACT FROM AUTHOR]

In recent years, there has been a growing interest in changes in dynamic mechanical properties of mixed rubber during dynamic shear, yet the influence of vulcanized characteristics on the dynamic shear behavior of vulcanized rubber, particularly the effect of cross-linking density, has received little attention. This study focuses on styrene–butadiene rubber (SBR) and aims to investigate the impact of different cross-linking densities (Dc) on dynamic shear behavior using molecular dynamics (MD) simulations. The results reveal a remarkable Payne effect, where the storage modulus experiences a significant drop when the strain amplitude (γ0) exceeds 0.1, which can be attributed to the fracture of the polymer bond and the decrease in the molecular chain's flexibility. The influence of various Dc values mainly resides at the level of molecular aggregation in the system, where higher Dc values impede molecular chain motion and lead to an increase in the storage modulus of SBR. The MD simulation results are verified through comparisons with existing literature. [ABSTRACT FROM AUTHOR]

Purpose: Abnormal iris mechanical properties have been considered to be an important cause of pupillary-block and angle-closure glaucoma. In this research, viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were investigated using uniaxial tensile test. Methods: Iris strips were taken along three directions: inner-circumferential direction (ICD), outer-circumferential direction (OCD) and radial direction (RD), respectively. Quasi-static tensile tests and stress-relaxation tests were applied on the iris strips. Then, the stress-stretch data was fitted with third order Ogden model; the stress-relaxation data was fitted with the third order Prony series model. Through comparing the tangent modulus and relaxation limit of the strips from different directions and locations, the viscoelasticity, anisotropy and location-dependence of mechanical properties of rabbit iris were explored. Results: The tangent moduli of iris at the stretch of 1.05 along ICD, OCD, and RD were 3.2 ± 1.4 kPa, 4.2 ± 2.6 kPa, 1.5 ± 0.8 kPa, respectively. Iris strips in ICD and OCD were found to have almost the same stress-relaxation behavior, and both relaxed slower than iris strips in RD. Conclusions: The mechanical properties of the iris were typically nonlinear, viscoelastic, anisotropic and location-dependent. The stress growth rate of the circumferential direction iris strip is significantly lower than that of RD and the stress-relaxation rate is significantly higher than that of the RD. That is, the iris is more prone to deformation in RD and the stress-retention ability after deformation in RD is weak, which is consistent with the fact that the iris bombe more likely happens in RD in vivo. The results of this study may also help us to establish a more accurate finite element model to simulate the flow field of humor aqueous and find the key factor of pupillary-block. [ABSTRACT FROM AUTHOR]

We consider the equations of motion of a bar, with given density, infinite in both directions, subjected to longitudinal vibrations under the action of an external load, and a stress–strain relation represented by a fractional‐order operator. Using three types of fractional operators, the initial‐boundary value problems associated with the described phenomenon are posed and solved. Through the bivariate Mittag–Leffer function, which has been recently introduced, we find the fundamental solution of these problems and calculate their moments. [ABSTRACT FROM AUTHOR]

The study presents the experimental results of measurements of the relaxation time of cryogels formed from various colloid-dispersed systems based on a poly(vinyl alcohol) aqueous solution. It is shown that the value of relaxation time, which characterizes the relationship between the viscosity and elasticity of real bodies, describes the rheological properties of materials more objectively than the traditional assessment of their physical and mechanical characteristics only by the elasticity modulus of the samples. [ABSTRACT FROM AUTHOR]

Viscoelastic fibre prestressing (VFP) is a promising technique to counterbalance the potential thermal residual stress within a polymeric composite, offering superior mechanical benefits for structural engineering applications. It has been demonstrated that the time required for a desirable creep strain can be significantly reduced by implementing higher creep stress, while its long-term stability is still unknown. Here, we developed the prestress equivalence principle and investigated the durability of viscoelastic fibre prestressing within a composite in order to further enrich the prestress mechanisms. The effectiveness of the prestress equivalence principle was refined through Charpy impact testing of prestressed samples with various pre-strain levels. The durability was investigated by subjecting samples to both natural aging (up to 0.5 years) and accelerated aging (by using the time-temperature superposition principle). It is found that the prestress equivalence principle offers flexibility for viscoelastically prestressed polymeric matrix composite (VPPMC) technology; the impact benefits offered by VFP are still active after being accelerated aged to an equivalent of 20,000 years at 20 °C, inferring long-term reliability of VFP-generated fibre recovery within a polymeric composite. These findings demonstrated that both materials and energy consumption could be conserved for advanced composites. Therefore, they promote further steps of VPPMC technology toward potential industrial applications, especially for impact protection. [ABSTRACT FROM AUTHOR]

To illuminate brittle and ductile fracturing of magma, we investigated bubble expansion and fracturing in two contrasting fluids: a Maxwell‐type viscoelastic fluid and a Bingham‐type yield‐strength fluid. Measurements of the complex shear modulus, G′ + iG″ (i is the imaginary unit), under small‐strain oscillation showed that both fluids are elastic (G′ > G″) with similar rigidity. Viscous behavior (G′ < G″) appeared at lower frequency in the Maxwell fluid but at larger strain in the Bingham fluid. When we injected air into the Maxwell fluid, bubbles expanded viscously at low flux, fractured in a brittle manner at high flux, and behaved transitionally at intermediate flux. In contrast, we observed no fracturing in the Bingham fluid. This demonstrates that the G′ > G″ condition is insufficient to infer that brittle fracturing can occur. Brittle fracturing of the Maxwell fluid occurred not at a critical strain rate but under decreasing strain rate and increasing stress. Plain Language Summary: The flow‐to‐fracture transition of magma is an essential process controlling eruption explosivity. This transition has been explained based on the linear Maxwell viscoelastic model: magma can flow slowly but breaks in a brittle manner under rapid deformation. The Bingham model represents another type of fluid‐solid transition: a material flows under a sufficiently large force but behaves elastically below this force. The present study investigates bubble growth and fracture by air injection in Maxwell‐type and Bingham‐type fluids, both having similar elasticity. We demonstrate that brittle fracture occurs in the Maxwell fluid at high air flux but never in the Bingham fluid. Detailed observations of the deformation until brittle fracture reveals a stress increase and strain rate decrease. The fracture onset is not determined by the critical strain rate, contrary to conventional brittle fragmentation criteria widely used in volcanology. These results will help improve brittle‐ductile transition models for complex fluids in volcanic eruptions. Key Points: Rapid air injection generated brittle fracture in a Maxwell fluid but not in a Bingham fluid, although they have similar elasticityThe observation of elasticity in small‐amplitude oscillation tests is not sufficient to infer that the fluid can fractureThe strain rate around a bubble decreased toward fracture, contrary to the conventional critical strain‐rate fracture criterion [ABSTRACT FROM AUTHOR]

We propose a simple 3D nonlinear rate-type constitutive relation with just three parameters for elastomeric dampers capable of emulating double-shear data in frequency and strain sweep mode. The nonlinear relation derived using two scalar functions, namely Helmholtz free energy and the rate of dissipation function [1], result in a partitioned constitutive relation: Cauchy stress tensor is described in terms of the left Cauchy-Green stretch tensor and a tensor describing instantaneous elastic response, and the evolution equation for the instantaneous elastic response is derived by maximizing the rate of dissipation function. A compressible version of this model is implemented in Abaqus® The constitutive relation and the implementation are validated by comparing with known semi-inverse solutions obtained by specializing rate-type relation to special deformations. Material parameters are obtained for dampers made of synthetic and natural rubber by fitting the predictions of the model with that of double shear data. By using the same parameters, three dimensional simulations of a cylindrical damper subjected to sinusoidal force akin to that of an unbalanced machinery predict different hysteresis curves in compression/tension and shear. To that end, we show that the non-linear 3 parameter model is one of the simple models that can be formulated within the thermodynamic framework which can predict the inherent non-linearity of the damper operating under combined harmonic loading situations. A robust implementation (VUMAT) of the developed model is included with the article. We believe that this can aid engineers in tailoring dampers for its controlled dissipation across multiple modes of deformation as well as academicians in adding more value by building and implementing sophisticated models within this framework. [ABSTRACT FROM AUTHOR]

To improve the production yield rate, reliability is one of the important indicators of electronic packaging products. In past research, however, the influence of the fabrication process was rarely taken into consideration. In this thesis, mold flow analysis software Moldex3D is used to develop a series analysis procedure for IC package products. The effects of many factors, including process, structure, and materials were being taken into account. Especially for epoxy molding compound, namely EMC, is studied on its properties during the molding and post-mold cure (PMC) processes. This paper adopted P–V-T-C equations, which consider both volume shrinkage due to thermal mismatch and chemical shrinkage to predict the amount of warpage and residual stresses after the mold filling process. Next, dual shift factor model for viscoelastic analysis was used to model the PMC process and predict the amount of warpage and residual stresses after PMC. And the influence of different PMC process conditions and loading conditions on the warpage results is discussed. The residual stresses after PMC simulation are set as the initial conditions for reliability analysis and then the stress distribution after two thermal cycles is analyzed. It is observed that the deformed shape of the simulation and experiment results after PMC were consistent. Both are concave downwards. In comparison with experiment results, the error of warpage simulation results was between 10% and 50%. The biggest error was found in the short direction. During two thermal cycles, it is can be found that the maximum stress of the lead frame is 505.7 MPa and the location of the possible failure is at the top left of the die. In addition, when considering or not considering the process-induced residual stress in the thermal cycle analysis, the stress states are very different. [ABSTRACT FROM AUTHOR]

This paper presents results from a study of the long-term behaviour of carbon/epoxy composites. The interactions between ageing in water and constant mechanical loads are described, first experimentally then using a simple modelling approach. An identification procedure for the model is carried out and test/model comparisons are discussed. The results show that a four-parameter Burgers model can provide a good fit of the experimental data. The analysis of the results indicates the impact of water diffusion on the viscoelastic behaviour with larger strains for both creep and recovery phases. Those changes tend to appear at the early stage of the moisture diffusion process and stabilize quite quickly. This article is part of the theme issue 'Ageing and durability of composite materials'. [ABSTRACT FROM AUTHOR]

This work derives an approximate solution of the laminar viscoelastic fluid flow through a parallel flat plate microchannel, driven by electroosmotic and external pressure forces. In contrast to other works published in the past, in the present analysis, the fluid's rheology obeys the generalized Phan–Thien–Tanner model that has been proposed recently, which uses the Mittag-Leffler function instead of linear or exponential functions of the trace for the stress tensor. The hydrodynamic analysis considers a non-linear Navier slip law at the wall that follows a power-law behavior on the shear stress. For the electric potential in the electric double layer, the Debye–Hückel approximation was used, and it is assumed that the wall's zeta potentials are symmetric. The solution obtained in this work depends on several dimensionless parameters that allow controlling the flow: ɛ W i 2 characterizes the fluid's viscoelasticity, the electrokinetic parameter κ ̄ , the dimensionless slip coefficient L ̄ , the slip-power exponent m , and the ratio between pressure and electroosmotic forces, G. Besides, the influence of two parameters of the Mittag-Leffler function, α and β , notably affects the flow's characteristics. Our results evidence the important consequences of considering the generalized Phan–Thien–Tanner model and the slippage effect on the flow field compared to that described by the Phan–Thien–Tanner model. • Electroosmotic/pressure-driven flow of a viscoelastic fluid is studied. • The generalized Phan–Thien–Tanner model is considered as the rheological model. • The Nonlinear Navier slip was used as boundary condition. • Mittag-Leffler function parameters influence notably on the fluid flow. • Slip coefficients at the wall may increase up to two orders the volumetric flow rate. [ABSTRACT FROM AUTHOR]

We propose and rigorously analyze a semi- and fully discrete discontinuous Galerkin method for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components and with mixed boundary conditions. The arbitrary-order spatial discretization imposes strongly the symmetry of the stress tensor, and it is combined with a Newmark trapezoidal rule as a time-advancing scheme. We establish stability and convergence properties, and the theoretical findings are further confirmed via illustrative numerical simulations in 2 and 3 dimensions. [ABSTRACT FROM AUTHOR]

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric (FGP) nanoplates deposited in a viscoelastic foundation. It is assumed that (i) the material parameters of the nanoplates obey a power-law variation in thickness and (ii) the uniform porosity exists in the nanoplates. The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory. The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory (NSGT). The motion equations are calculated in accordance with Hamilton's principle. Finally, the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution. The results indicate that the nonlocal parameters (NLPs) and length scale parameters (LSPs) have exactly the opposite effects on the wave frequency. In addition, it is found that the effect of porosity volume fractions (PVFs) on the wave frequency depends on the gradient indices and damping coefficients. When these two values are small, the wave frequency increases with the volume fraction. By contrast, at larger gradient index and damping coefficient values, the wave frequency decreases as the volume fraction increases. [ABSTRACT FROM AUTHOR]

The aim of the study is to investigate the mechanical and creep properties of the bamboo fiber under thermal or hygro conditions. Bamboo fibers were extracted mechanically, and then undergone alkali treatment. The bamboo fiber in this study is actually thin bamboo sticks instead of the real bamboo fibers. This bamboo stick will retain the structure of the original. Tensile tests of the bamboo fiber were. The yield and the tensile strength were found to decrease with the increase of the moisture content or temperature. Creep tests of the bamboo fibers were conducted to investigate the viscoelastic behavior. Results show that the strain creep curve can be divided into three stages. In primary creep phase, strain increases at a decreasing rate. The secondary phase exhibits a linear response with time, also called steady-state creep. The tertiary stage is the stage in which strain response almost increases exponentially, resulting in the failure of the fiber. In the creep test, the applied force was maintained 25 N, and the fracture strain was about 0.7%–0.8%. A mathematical constitutive model was constructed to fit the creep curves. The creep fitting curve only includes the primary and secondary phases, and the fitted curve can roughly show the creep behavior of the bamboo fiber. [ABSTRACT FROM AUTHOR]

We consider a system of evolutionary equations that is capable of describing certain viscoelastic effects in linearized yet nonlinear models of solid mechanics. The constitutive relation, involving the Cauchy stress, the small strain tensor, and the symmetric velocity gradient, is given in an implicit form. For a large class of these implicit constitutive relations, we establish the existence and uniqueness of a global-in-time large-data weak solution. Then we focus on the class of socalled limiting strain models, i.e., models for which the magnitude of the strain tensor is known to remain small a priori, regardless of the magnitude of the Cauchy stress tensor. For this class of models, a new technical difficulty arises. The Cauchy stress is only an integrable function over its domain of definition, resulting in the underlying function spaces being nonreflexive and thus the weak compactness of bounded sequences of elements of these spaces is lost. Nevertheless, even for problems of this type we are able to provide a satisfactory existence theory, as long as the initial data have finite elastic energy and the boundary data fulfill natural compatibility conditions. [ABSTRACT FROM AUTHOR]

The flexural wave propagation in a micro-beam mounted on viscoelastic foundation is considered in the present work. The mechanical behavior of the micro-beam is modeled by nonlocal strain gradient elasticity with the size-effects taken into account. The constraint is modeled by the Pasternak foundation with the rheology behavior modeled by fractional-order viscoelasticity. The main concerns are the dispersion and attenuation feature of five kinds of possible flexural waves derived from the governing equations of the presented micro-beam model. The influences of the nonlocal effects, strain gradient effects and the fractional-order viscoelastic effects are investigated by a parameter study in the numerical examples. This research is helpful for the design of micro-sensor, micro-actuator and energy-harvest devices in micro electric-mechanic system (MEMS). [ABSTRACT FROM AUTHOR]

The maintenance of homeostasis and the retention of ordered epithelial cell self-organization are essential for morphogenesis, wound healing, and the spread of cancer across the epithelium. However, cell–cell interactions in an overcrowded environment introduce a diversity of complications. Such interactions arise from an interplay between the cell compressive and shear stress components that accompany increased cell packing density. They can lead to various kinds of cell rearrangement such as: the epithelial-to-mesenchymal cell state transition; live cell extrusion; and cell jamming. All of these scenarios of cell rearrangement under mechanical stress relate to changes in the strengths of the cell–cell and cell–matrix adhesion contacts. The objective of this review study is twofold: first, to provide a comprehensive summary of the biological and physical factors influencing the effects of cell mechanical stress on cell–cell interactions, and the consequences of these interactions for the status of cell–cell and cell–matrix adhesion contacts; and secondly, to offer a bio-physical/mathematical analysis of the aforementioned biological aspects. By presenting these two approaches in conjunction, we seek to highlight the intricate nature of biological systems, which manifests in the form of complex bio-physical/mathematical equations. Furthermore, the juxtaposition of these apparently disparate approaches underscores the importance of conducting experiments to determine the multitude of parameters that contribute to the development of these intricate bio-physical/mathematical models. [ABSTRACT FROM AUTHOR]

The dynamic interplay between cells and their native extracellular matrix (ECM) influences cellular behavior, imposing a challenge in biomaterial design. Dynamic covalent hydrogels are viscoelastic and show self-healing ability, making them a potential scaffold for recapitulating native ECM properties. We aimed to implement kinetically and thermodynamically distinct crosslinkers to prepare self-healing dynamic hydrogels to explore the arising properties and their effects on cellular behavior. To do so, aldehyde-substituted hyaluronic acid (HA) was synthesized to generate imine, hydrazone, and oxime crosslinked dynamic covalent hydrogels. Differences in equilibrium constants of these bonds yielded distinct properties including stiffness, stress relaxation, and self-healing ability. The effects of degree of substitution (DS), polymer concentration, crosslinker to aldehyde ratio, and crosslinker functionality on hydrogel properties were evaluated. The self-healing ability of hydrogels was investigated on samples of the same and different crosslinkers and DS to obtain hydrogels with gradient properties. Subsequently, human dermal fibroblasts were cultured in 2D and 3D to assess the cellular response considering the dynamic properties of the hydrogels. Moreover, assessing cell spreading and morphology on hydrogels having similar modulus but different stress relaxation rates showed the effects of matrix viscoelasticity with higher cell spreading in slower relaxing hydrogels. [Display omitted] [ABSTRACT FROM AUTHOR]

In the United States, currently peak-to-peak oscillatory shear stress-strain data is used in the asphalt binder characterization protocols. This practice necessitates the measurement, usage, and reporting of only peak responses for material characterization and specification even though a sinusoidal waveform is applied. However, in this paper it is argued that with the proliferation of modified binding systems, it is critical to capture and examine the complete waveform data when subjected to both small and large strains. This approach will help properly differentiating between materials. In this study, four modified binders were tested at small and large strain levels while recording the complete response waveform. The recorded waveform data was then used to examine the linear and nonlinear viscoelastic characteristics of these binders. The orthogonal stress decomposition technique was used to delineate elastic and viscous contributions in the nonlinear regime. This study examined the time-temperature dependency under both linear and nonlinear regimes. The time-temperature shift factors obtained from linear regime were effectively applied in the nonlinear regime. Further, all the tested binders showed strain stiffening and shear thinning behavior under most of the testing conditions. This study provides useful insights about the material behavior under nonlinear regime and can serve as a benchmark for further investigation of nonlinear viscoelastic behavior of asphalt binders. • Complete response waveform under oscillatory shear used to characterize the asphalt binder response. • Stress decomposition technique used to delineate elastic and viscous contributions in the nonlinear regime. • Application of linear viscoelastic time-temperature shift factors in the nonlinear regime. • Construction of master curves for elastic and viscous Chebyshev coefficients for asphalt binder systems. • Unification of linear and nonlinear characterization of asphalt binder response using complete response waveform and time-temperature superposition principle. [ABSTRACT FROM AUTHOR]

• Elastic instabilities of low-molecular-weight polymers are studied in Taylor-Couette. • An elastically modified wavy vortex flow state is reported for the first time. • This state is characterised by oscillations of both inflow and outflow boundaries. • The amplitude of these oscillations increases at higher fluid elasticities. • This may contribute to the emergence of Rotating Standing Waves. We investigate the transition pathway of low elasticity fluids (E l = 0.003 − 0.008) in a Taylor-Couette configuration using low-molecular-weight polyacrylamide (PAAM) and visualisation experiments in the Reynolds range from 0 to 300. We report here for the first time an elastically modified wavy vortex flow state with altered spectral and structural characteristics, that precedes the onset of the traditional (inelastic) Newtonian wavy instability. This new wavy regime is characterised by oscillations of both the inflow and outflow boundaries, associated with a weakening of the outflow regions due to low hoop stresses. The modification of the boundaries persists at higher Reynolds numbers, where the spectral characteristics are unaltered compared to the inelastic, Newtonian case. In addition, a hysteretic behaviour is observed for increasing elasticity, as instabilities are shifted towards lower critical Reynolds numbers, confirming the importance of even vanishing elasticity on the stability of Taylor-Couette flows. At higher fluid elasticity (E l = 0.06), the amplitude of inflows/outflows oscillations increases, and momentum is transferred axially between adjacent vortices, which may contribute to the emergence of Rotating Standing Waves. [ABSTRACT FROM AUTHOR]

Flexible viscoelastic foams with relative density in the range of 5-50% are widely used to control interaction forces, notably in cushions for impact protection, shoes, mechanical grippers, etc. The design of new foams to improve performance is challenging, due to the lack of efficient models to connect cellular architecture, viscoelasticity of the base resin, and non-linear responses that stem from large deformation of open pores. This paper presents highly efficient solutions for the response of linearly viscoelastic, kinematically non-linear and shear-deformable struts that are loaded at an oblique angle to their axis. The models can be used to predict structure-property relationships for strut-based metamaterials, including non-linear stress-strain response and accompanying hysteresis. To illustrate this, the entire design space of a simple unit cell is mapped in terms of a broad range of strut angles and thicknesses; the unit cell is inspired by features in stochastic foams that dominate their response. An enormous range of stress-strain responses can be obtained from this single foam-like cell, including purely softening, purely stiffening, and non-monotonic stiffness with adjustable tangent moduli. The model is also used to illustrate connections between viscoelastic material parameters, loading rate, and hysteresis for two distinct classifications of non-linear stress-strain response. • Efficient model to quantify the coupling of non-linear stress-strain response and hysteresis in strut-based metamaterials. • Model uses linearly viscoelastic, kinematically non-linear and shear-deformable struts loaded obliquely. • The entire simple unit cell design space is mapped in terms of a broad range of strut angles and thicknesses. • Stress-strain responses include stiffening, plateau and sigmoidal shapes. • Connections between viscoelastic material parameters, loading rate, and hysteresis are shown. [ABSTRACT FROM AUTHOR]

The cross correlation between the two-body density and shear stress of Lennerd-Jones liquids is evaluated by means of equilibrium molecular dynamics (MD) simulation in order to clarify the microscopic structure that determines the shear viscosity. The slowest viscoelastic relaxation is coupled to the shift of the main peak of the static structure factor as is predicted by mode-coupling theory (MCT). The decay of the cross-correlation function in the reciprocal space is explained by the square of the intermediate scattering function, which is also in harmony with MCT. The distortion of the microscopic structure under simple shear is calculated by means of non-equilibrium MD simulation. The linear response relation also holds on the two-body density within the Newtonian regime of shear viscosity, while the structural distortion diminishes in the shear-thinning regime. The transition between the Newtonian and the shear-thinning regimes occurs at the shear rate where the magnitude of the structural distortion becomes as large as that of the equilibrium structure. The breakdown of the Cox-Merz rule is ascribed to the narrow width of the main peak of the static structure factor. [ABSTRACT FROM AUTHOR]

Time‐dependent ground deformation is a key observable in active magmatic systems, but is challenging to characterize. Here we present a numerical framework for modeling transient deformation and stress around a subsurface, spheroidal pressurized magma reservoir within a viscoelastic half‐space with variable material coefficients, utilizing a high‐order finite‐element method and explicit time‐stepping. We derive numerically stable time steps and verify convergence, then explore the frequency dependence of surface displacement associated with cyclic pressure applied to a spherical reservoir beneath a stress‐free surface. We consider a Maxwell rheology and a steady geothermal gradient, which gives rise to spatially variable viscoelastic material properties. The temporal response of the system is quantified with a transfer function that connects peak surface deformation to reservoir pressurization in the frequency domain. The amplitude and phase of this transfer function characterize the viscoelastic response of the system, and imply a framework for characterizing general deformation time series through superposition. Transfer function components vary with the frequency of pressure forcing and are modulated strongly by the background temperature field. The dominantly viscous region around the reservoir is also frequency dependent, through a local Deborah number that measures pressurization period against a spatially varying Maxwell relaxation time. This near‐reservoir region defines a spatially complex viscous/elastic transition whose volume depends on the frequency of forcing. Our computational and transfer function analysis framework represents a general approach for studying transient viscoelastic crustal responses to magmatic forcing through spectral decomposition of deformation time series, such as long‐duration geodetic observations. Plain Language Summary: Ground motions associated with subsurface magma reservoirs are the result both of magma movement and time‐dependent deformation of crustal rocks. We have developed a new computational framework to help interpret surface deformations associated with magmatic systems embedded within viscoelastic rocks as expected in volcanic regions. This framework is general in the sense that a broad range of scientific studies can be explored by specifying particular conditions at domain boundaries or magma reservoir geometries, and we perform rigorous numerical tests to ensure credible solutions. We then apply the model to study a simple but highly generalizable type of transient behavior—the cyclic pressurization and depressurization of a spherical reservoir. We develop a theoretical approach to simply analyze the time‐dependent output, and find that temporal lag and amplification of surface deformation with respect to the reservoir pressure is explained by an aureole of material surrounding the chamber with a dominantly viscous response, whose size is frequency‐dependent. Our results can be extended to many transient deformation scenarios because a sinusoidal response forms the basic element of general pressure time‐series. Key Points: A high‐order numerical framework is derived for time‐dependent viscoelastic deformation around magma reservoirsThe transfer function characterizes phase lag and amplification between pressurization at depth and surface deformationThe spatial extent of viscous response is frequency dependent and well‐characterized by a local Deborah number [ABSTRACT FROM AUTHOR]

Solid propellant is a composite material exhibiting classic nonlinear viscoelastic mechanical characteristic, which is due in a large part to a cumulative damage process caused by the formation and growth of microflaws inside. The standard relaxation tests and uniaxial tension tests under different velocities of hydroxyl-terminated polybutadiene (HTPB) propellant are carried out in this paper, where Digital Image Correlation (DIC) technique is applied to record deformation. The experimental results show that the material mechanical behavior is rate-dependent. It is also observed that the yield stress and failure stress are significantly rate-dependent on the tensile velocity. Based on these experimental results, it can be inferred that the stiffness degradation and damage evolution of HTPB propellant are a rate-dependent processes. Therefore, the damage accumulation of HTPB propellant is considered rate-dependent in this research. In order to describe the mechanical characteristic precisely, a nonlinear viscoelastic constitutive model with rate-dependent cumulative damage is developed. The damage model is developed based on the concept of pseudo strain, in which a Prony series representation of viscoelastic material functions is applied. Besides, a rate-dependent damage variable is introduced into the model through considering the rate-dependent characteristics of cumulative damage process. In addition, a new normalized failure criterion is derived on the basis of the proposed damage model, which is independent of strain-rate after normalization. Finally, it is implemented in commercial finite element software for stress analysis to verify the predictive capacities of the damage model. The accuracy of the constitutive model and failure criterion is validated under uniaxial tensile tests of various strain rates. [ABSTRACT FROM AUTHOR]

To investigate the effects of viscoelasticity on the stick-slip behaviour, a new model reproducing the partial slip of viscoelastic materials under fully coupled conditions is developed in this paper. The ratio of retardation time to relaxation time is employed to characterize the rheological property of a viscoelastic material. It is found that materials with higher ratios exhibit more fluid-like behaviours while those with lower ratios perform more like solid. As long as the contact input (load or displacement) is constant, the stick ratio (ratio of stick area to contacting area) is found to be insensitive to the viscoelasticity of materials. However, the separation pattern of the stick and slip regions varies with time when different contact phenomena (creep or stress relaxation) are encountered in the lateral and normal directions. The transition process from partial slip to gross sliding of viscoelastic materials, unlike the elastic response, tends to be abrupt when fully coupled conditions between shear tractions and pressure are introduced. When identical contact parameters are specified for different viscoelastic materials, the more fluid-like material always experiences a quicker transition from partial slip to gross sliding. [ABSTRACT FROM AUTHOR]

• The analytical integration Legendre polynomial method is developed to study the wave attenuation. • Functionally gradient viscoelastic microstructures sandwiched in two elastic half-spaces are studied. • The couple stress decreases the attenuation, while the inhomogeneity increases the attenuation. • The couple stress effect weakens the viscoelasticity, while the viscoelasticity strengthens the couple stress effect. Taking the viscoelasticity and size-dependent effect into account, the reflection and transmission of elastic waves through functionally graded viscoelastic plate sandwiched in two elastic half-spaces are investigated. The extended analytical integration Legendre polynomial method and Kelvin-Voigt viscoelastic model in the context of the modified couple stress theory are utilized to perform the derivation. The global matrix method is used to confirm the validity of the extended analytical integration Legendre polynomial method. Compared with the global matrix method, the extended analytical integration Legendre polynomial method provides an efficient numerical calculation method without layering and iterative root seeking. The influences of the couple stress, viscoelasticity and inhomogeneity of medium on elastic wave reflection and transmission are discussed. In addition, the attenuation caused by the viscoelasticity is analyzed. It is found that the couple stress effect weakens the influence of the viscoelasticity, while the viscoelasticity strengthens the couple stress effect. The couple stress effect decreases the attenuation, while the inhomogeneity increases the attenuation. [ABSTRACT FROM AUTHOR]

The relationship between pressure (P) and volume (V) in the human lung has been extensively studied. However, the combined effects of gravity and the mechanical properties of elastin and collagen on alveolar and lung P–V curves during breathing are not well understood. Here, we extended a previously established thick-walled spherical model of a single alveolus with wavy collagen fibers during positive pressure inflation. First, we updated the model for negative pressure-driven inflation that allowed incorporation of a gravity-induced pleural pressure gradient to predict how the static alveolar P–V relations vary spatially throughout an upright human lung. Second, by introducing dynamic surface tension and collagen viscoelasticity, we computed the hysteresis loop of the lung P–V curve. The model was tested by comparing its predicted regional ventilation to literature data, which offered insight into the effects of microgravity on ventilation. The model has also produced novel testable predictions for future experiments about the variation of mechanical stresses in the septal walls and the contribution of collagen and elastin fibers to the P–V curve and throughout the lung. The model may help us better understand how mechanical stresses arising from breathing and pleural pressure variations affect regional cellular mechanotransduction in the lung. [ABSTRACT FROM AUTHOR]