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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.

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.

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.

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.

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks., Author summary The cytoskeleton is composed of semiflexible, inextensible actin filaments, dynamic cross linkers, and molecular motors, and makes the primary contribution to the structural properties of the cell. Despite its being so fundamental to cell biology, the biological complexity of the cytoskeleton hinders our ability to understand its mechanical properties through in vitro experiments. In this paper, we perform microscopic simulations of actin fibers and transient cross linkers to quantify the principle timescales involved in the network, study how these timescales influence the morphology and rheology of the system, and examine the role of hydrodynamic interactions in cytoskeletal networks. We find three principle timescales which we associate with fiber flexibility, cross linker detachment, and network remodeling, respectively. We show that the morphology of the network is more important on longer timescales, where the viscosity of links inside of fiber bundles is enhanced. We also show that hydrodynamic interactions reduce the stress inside of bundles because of entrainment flows. Finally, we propose a continuum model which can be used to coarse-grain our agent-based simulations and enable modeling of larger systems.

In this paper, we focus on why intraplate seismic initiation and migration occurs, which has widely been considered to be caused by static stress triggering caused by earthquakes, as well as post-seismic slips. To illustrate the mechanism underlying large earthquakes, in particular the migration caused by two key episodes that occurred after 1500 in the Bohai-Zhangjiakou Fault Zone (BZFZ) of North China, we developed a high-resolution three-dimensional viscoelastic finite element model that includes the active faults with vertical segmentation, their periodical locking, and the lithosphere heterogeneity. We used the birth and death of element groups to simulate stress intensity changes during the two episodes (named Episode I and II), with our results showing that the Tangshan earthquake was primarily triggered by the Sanhe-Pinggu M8.0 earthquake in 1679, whereas the Zhangbei M6.2 earthquake in 1998 was not triggered by earthquakes in Episode I. According to our work, the calculated stress changes in the different segments of the fault zone correspond to the magnitude of the triggered earthquakes. Further, the largest stress decrease was near the Sanhe-Pinggu fault and occurred the largest earthquake in Episode I, whereas the largest stress increase was near the Tangshan fault and occurred during the largest earthquake in Episode II. Given the above, we propose a model for seismic migration to describe the dynamic mechanisms of earthquake migration within the BZFZ and North China, in which the factors affecting both the seismic migration path and intensity primarily include the distance between the triggered active fault and the original fault, the coupling of the active faults, the location and scale of the low-velocity anomaly, its distance from the active fault, and the location and scale of the crustal thinning.

Wheat (Triticum spp.) gluten consists mainly of intrinsincally disordered storage proteins (glutenins and gliadins) that can form megadalton-sized networks. These networks are responsible for the unique viscoelastic properties of wheat dough and affect the quality of bread. These properties have not yet been studied by molecular level simulations. Here, we use a newly developed α-C-based coarse-grained model to study ∼ 4000-residue systems. The corresponding time-dependent properties are studied through shear and axial deformations. We measure the response force to the deformation, the number of entanglements and cavities, the mobility of residues, the number of the inter-chain bonds, etc. Glutenins are shown to influence the mechanics of gluten much more than gliadins. Our simulations are consistent with the existing ideas about gluten elasticity and emphasize the role of entanglements and hydrogen bonding. We also demonstrate that the storage proteins in maize and rice lead to weaker elasticity which points to the unique properties of wheat gluten., Author summary During the breadmaking process, expanding gas bubbles cause the dough to increase volume. Gluten proteins act as an elastic scaffold in that process, allowing the wheat dough to grow more than other kinds of dough. Thus, explaining the unique viscoelastic properties of gluten at the molecular level may be of great interest to the baking industry. Assessing the structural properties of gluten is difficult because its proteins are disordered. We provide the first molecular dynamics model of gluten elasticity, that is able to distinguish gluten and proteins from different plants, like maize and rice. Our model shows the structural changes the gluten proteins undergo during their deformation, which mimics the mixing of dough during kneading. It also allows for a determination of the force required to extend gluten proteins, as during baking. The data confirms existing theories about gluten, but it also provides molecular-level information about the extraordinary elasticity of gluten.

Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions., Author summary Thromboembolism is associated with detachment of small thrombus pieces from the bulk in the blood vessel. These detached pieces, also known as emboli, travel through the blood flow and may block other vessels downstream, e.g., they may plug the deep veins of the leg, groin or arm, leading to venous thromboembolism (VTE). VTE is a significant cause of morbidity and mortality and it affects more than 900,000 people in the United States and result in approximately 100,000 deaths every year. Mechanical interaction between flowing blood and a thrombus is crucial in determining the deformation of the thrombus and the possibility of releasing emboli. In this study, we develop a phase-field model that is capable of describing the structural properties of a thrombus and its biomechanical properties under different blood flow conditions. Moreover, we combine this thrombus model with a particle-based model which simulates the initiation of the thrombus. This combined framework is the first computational study to simulate the development of a thrombus from platelet aggregation to its subsequent viscoelastic responses to various shear flows. Informed by clinical data, this framework can be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.

Dairy products exhibit several physical properties that are crucial to define whether we like the food or not: firmness, creaminess, thickness, or lightness. Viscosity changes the flow properties of food and influences the appearance and the consistency of a product; this control variable is important in most production stages-manufacture, processing, and storage. Viscosity of heterogeneous products at a given temperature depends on its composition and physical state of its substances. Although rheology provides a method to access the product viscosity, it lacks non-contact full-field monitoring. We apply a simple correlation analysis of laser speckle images to evaluate viscosity properties of dairy products. Our approach ensures robust measurements with high degree of detectability.

Knowledge of the biomechanical properties of the human cornea is crucial for understanding the development of corneal diseases and impact of surgical treatments (e.g., corneal laser surgery, corneal cross-linking). Using a Surface Force Apparatus we investigated the transient viscous response of the anterior cornea from donor human eyes compressed between macroscopic crossed cylinders. Corneal biomechanics was analyzed using linear viscoelastic theory and interpreted in the framework of a biphasic model of soft hydrated porous tissues, including a significant contribution from the pressurization and viscous flow of fluid within the corneal tissue. Time-resolved measurements of tissue deformation and careful determination of the relaxation time provided an elastic modulus in the range between 0.17 and 1.43 MPa, and fluid permeability of the order of 10(-13) m(4)/(N.s). The permeability decreased as the deformation was increased above a strain level of about 10%, indicating that the interstitial space between fibrils of the corneal stromal matrix was reduced under the effect of strong compression. This effect may play a major role in determining the observed rate-dependent non-linear stress-strain response of the anterior cornea, which underlies the shape and optical properties of the tissue.

Shear wave elastography is emerging as a clinically valuable diagnostic tool to differentiate between benign and malignant breast masses. Elastography techniques assume that soft tissue can be modelled as a purely elastic medium. However, this assumption is often violated as soft tissue exhibits viscoelastic properties. In order to explore the role of viscoelastic parameters in suspicious breast masses, a study was conducted on a group of patients using shear wave dispersion ultrasound vibrometry in the frequency range of 50-400 Hz. A total of 43 female patients with suspicious breast masses were recruited before their scheduled biopsy. Of those, 15 patients did not meet the data selection criteria. Voigt model based shear elasticity showed a significantly (p = 7.88x10(-6)) higher median value for the 13 malignant masses (16.76±13.10 kPa) compared to 15 benign masses (1.40±1.12 kPa). Voigt model based shear viscosity was significantly different (p = 4.13x10(-5)) between malignant (8.22±3.36 Pa-s) and benign masses (2.83±1.47 Pa-s). Moreover, the estimated time constant from the Voigt model, which is dependent on both shear elasticity and viscosity, differed significantly (p = 6.13x10(-5)) between malignant (0.68±0.33 ms) and benign masses (3.05±1.95 ms). Results suggest that besides elasticity, viscosity based parameters like shear viscosity and time constant can also be used to differentiate between malignant and benign breast masses.

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling., Author summary In this paper, we develop and analyze a minimal model for a 2D network of cross-linked actin filaments and myosin motors, representing the cortical cytoskeleton of eukaryotic cells. We implement coarse-grained representations of force production by myosin motors and stress dissipation through an effective cross-link friction and filament turnover. We use this model to characterize how the sustained production of active stress, and the steady dissipation of elastic stress, depend individually on motor activity, effective cross-link friction and filament turnover. Then we combine these results to gain insights into how microscopic network parameters control steady state flow produced by asymmetric distributions of motor activity. Our results provide a framework for understanding how local modulation of microscopic interactions within contractile networks control macroscopic quantities like active stress and effective viscosity to control cortical deformation and flow at cellular scales.

Conventional seismic rehabilitation methods may not be suitable for some buildings owing to their high cost and time-consuming foundation work. In recent years, viscoelastic dampers (VEDs) have been widely used in many mid- and high-rise buildings. This study introduces a viscoelastic passive control system called rotary rubber braced damper (RRBD). The RRBD is an economical, lightweight, and easy-to-assemble device. A finite element model considering nonlinearity, large deformation, and material damage is developed to conduct a parametric study on different damper sizes under pushover cyclic loading. The fundamental characteristics of this VED system are clarified by analyzing building structures under cyclic loading. The result show excellent energy absorption and stable hysteresis loops in all specimens. Additionally, by using a sinusoidal shaking table test, the effectiveness of the RRBD to manage the response displacement and acceleration of steel frames is considered. The RRBD functioned at early stages of lateral displacement, indicating that the system is effective for all levels of vibration. Moreover, the proposed damper shows significantly better performance in terms of the column compression force resulting from the brace action compared to chevron bracing (CB).

Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters.

Differentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascular networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous, resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally, our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types., Author Summary The development of an organism involves a coordination between the differentiation of cells in well-defined spatial patterns and the growth of tissues towards their target shapes. While extensive research has addressed each of these key processes, their coordination has received less attention. In particular, when a pattern has formed and the tissue continues growing, is the pattern passively dilated like a drawing on an inflated balloon, or does the pattern remodel during tissue expansion? We address this question in the context of leaf vasculature and examine the role of mechanics in leaf growth. We model the growing vascular network and identify quantities that compare network growth to background tissue growth. We apply this quantification to mature leaves that are stretched mechanically; we find that vasculature does not dilate passively and that veins reorient in the direction of external forces. This is reminiscent of the reinforcement of bones or of the cytoskeleton so as to resist to mechanical stress. In a developmental context, this might be an essential process to match patterns and growth.

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the shape of the air-mucus interface. Simulations show that viscoelasticity captures normal stress generation in shear leading to a peak in the air-mucus interface at the middle of the culture and a depression at the walls. Linear and nonlinear viscoelastic regimes can be observed in cultures by varying the hurricane radius and mean rotational velocity. The advection-diffusion of a drug concentration dropped at the surface of the mucus flow is simulated as a function of Peclet number., Author Summary In the lungs, the airway surface liquid protects the airway epithelium from inhaled pathogens and particulates. It is well known that failure to properly clear mucus from the airways leads to chronic, even fatal, lung infections. To date, there is no validated constitutive model capable of recapitulating mucus rheology under diverse, physiological stress and deformation conditions. This gap has hindered studies into the causal relationship between mucus rheology and mucociliary clearance. Our modeling-experimental approach fulfills several purposes: to implement linear and nonlinear constitutive modeling of mucus from micro- and macro-rheology, to test constitutive modeling in an independent experimental system, to build a coarse-grained model of the PCL-mucus boundary condition, to measure and understand modifications in mucociliary transport during and after deposition of a controlled drug concentration, to measure and simulate both the flow and stress fields throughout the mucus layer, and to measure and simulate how the advection profiles in the culture couple with diffusion of particulates landing on the air-mucus interface. These results lay the groundwork for extension of the code to three dimensions and more realistic metachronal wave boundary conditions, both in cell cultures and in airways.

A theory of reciprocating contacts for linear viscoelastic materials is presented. Results are discussed for the case of a rigid sphere sinusoidally driven in sliding contact with a viscoelastic half-space. Depending on the size of the contact, the frequency and amplitude of the reciprocating motion, and on the relaxation time of the viscoelastic body, we establish that the contact behavior may range from the steady-state viscoelastic solution, in which traction forces always oppose the direction of the sliding rigid punch, to a more elaborate trend, never observed before, which is due to the strong interaction between different regions of the path covered during the reciprocating motion. Practical implications span a number of applications, ranging from seismic engineering to biotechnology., Comment: 8 pages, 5 figures, accepted for publication on Physical Review E, March 22, 2016

Viscoelasticity of soft tissue is often related to pathology, and therefore, has become an important diagnostic indicator in the clinical assessment of suspect tissue. Surgeons, particularly within head and neck subsites, typically use palpation techniques for intra-operative tumor detection. This detection method, however, is highly subjective and often fails to detect small or deep abnormalities. Vibroacoustography (VA) and similar methods have previously been used to distinguish tissue with high-contrast, but a firm understanding of the main contrast mechanism has yet to be verified. The contributions of tissue mechanical properties in VA images have been difficult to verify given the limited literature on viscoelastic properties of various normal and diseased tissue. This paper aims to investigate viscoelasticity theory and present a detailed description of viscoelastic experimental results obtained in tissue-mimicking phantoms (TMPs) and ex vivo tissues to verify the main contrast mechanism in VA and similar imaging modalities. A spherical-tip micro-indentation technique was employed with the Hertzian model to acquire absolute, quantitative, point measurements of the elastic modulus (E), long term shear modulus (η), and time constant (τ) in homogeneous TMPs and ex vivo tissue in rat liver and porcine liver and gallbladder. Viscoelastic differences observed between porcine liver and gallbladder tissue suggest that imaging modalities which utilize the mechanical properties of tissue as a primary contrast mechanism can potentially be used to quantitatively differentiate between proximate organs in a clinical setting. These results may facilitate more accurate tissue modeling and add information not currently available to the field of systems characterization and biomedical research.

When synovial joints are loaded, the articular cartilage and the cells residing in it deform. Cartilage deformation has been related to structural tissue damage, and cell deformation has been associated with cell signalling and corresponding anabolic and catabolic responses. Despite the acknowledged importance of cartilage and cell deformation, there are no dynamic data on these measures from joints of live animals using muscular load application. Research in this area has typically been done using confined and unconfined loading configurations and indentation testing. These loading conditions can be well controlled and allow for accurate measurements of cartilage and cell deformations, but they have little to do with the contact mechanics occurring in a joint where non-congruent cartilage surfaces with different material and functional properties are pressed against each other by muscular forces. The aim of this study was to measure in vivo, real time articular cartilage deformations for precisely controlled static and dynamic muscular loading conditions in the knees of mice. Fifty and 80% of the maximal knee extensor muscular force (equivalent to approximately 0.4N and 0.6N) produced average peak articular cartilage strains of 10.5±1.0% and 18.3±1.3% (Mean ± SD), respectively, during 8s contractions. A sequence of 15 repeat, isometric muscular contractions (0.5s on, 3.5s off) of 50% and 80% of maximal muscular force produced cartilage strains of 3.0±1.1% and 9.6±1.5% (Mean ± SD) on the femoral condyles of the mouse knee. Cartilage thickness recovery following mechanical compression was highly viscoelastic and took almost 50s following force removal in the static tests.

Thin liquid films are central to everyday life. They are ubiquitous in modern technology (pharmaceuticals, coatings), consumer products (foams, emulsions) and also serve vital biological functions (tear film of the eye, pulmonary surfactants in the lung). A common feature in all these examples is the presence of surface-active molecules at the air-liquid interface. Though they form only molecular-thin layers, these surfactants produce complex surface stresses on the free surface, which have important consequences for the dynamics and stability of the underlying thin liquid film. Here we conduct simple thinning experiments to explore the fundamental mechanisms that allow the surfactant molecules to slow the gravity-driven drainage of the underlying film. We present a simple model that works for both soluble and insoluble surfactant systems in the limit of negligible adsorption-desorption dynamics. We show that surfactants with finite surface rheology influence bulk flow through viscoelastic interfacial stresses, while surfactants with inviscid surfaces achieve stability through opposing surface-tension induced Marangoni flows.

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time reversal symmetry. In practice, active fluids may have not only liquid crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a 'drag-reduction' effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid., Comment: 11 pages, 4 figures (supplementary information included); v2 has updated PACS numbers, and a note added with one additional citation; v3 fixes a typo in Eq. 6 and a minor correction to top phase diagram in Fig. 1

Formation of bacterial colonies as biofilm on the surface/interface of various objects has the potential to impact not only human health and disease but also energy and environmental considerations. Biofilms can be regarded as soft materials, and comprehension of their shear response to external forces is a key element to the fundamental understanding. A mesoscale model has been presented in this article based on digitization of a biofilm microstructure. Its response under externally applied shear load is analyzed. Strain stiffening type behavior is readily observed under high strain loads due to the unfolding of chains within soft polymeric substrate. Sustained shear loading of the biofilm network results in strain localization along the diagonal direction. Rupture of the soft polymeric matrix can potentially reduce the intercellular interaction between the bacterial cells. Evolution of stiffness within the biofilm network under shear reveals two regimes: a) initial increase in stiffness due to strain stiffening of polymer matrix, and b) eventual reduction in stiffness because of tear in polymeric substrate.

Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The model equations for the poroelastic medium are obtained from continuum force-balance equations that include the relevant mechanical fields and an incompressibility relation for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stresses. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a chemomechanical feedback. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets., Comment: Additional supplemental material is supplied

Studies on integral and differential constitutive equations by the present authors are summarized and some new results are presented. Applicability of various constitutive equations to some typical deformation modes is investigated. In integral equations, superiority of the BKZ model is established. But it is also known that the model fails in a prediction of stress relaxation for double‐step shear strains in which the second step strain is applied in the opposite direction to the first. A stress dependent constitutive model of integral type proposed by the present authors can describe this double‐step stress relaxation very well as well as ordinary single‐step stress relaxation and shear rate dependence of viscosity. Compared to integral equations, applicability of differential equations is limited. The Leonov model is very useful to predict viscoelastic functions in steady shear flow, but it fails in describing both stress relaxations for a step strain and after cessation of steady shear flow. The Giesekus model gives slightly better predictions for steady shear flow and for these stress relaxations, but fundamentally the Giesekus and Leonov models cannot be accepted as exact models for stress relaxation. On the other hand, the Larson model can describe both stress relaxations well, but it gives too strong shear rate dependences for viscosity and coefficient of first normal stress difference. It is concluded that further studies on stress dependent model of either integral or differential type will yield fruitful development of constitutive equations.

By adding minute concentrations of a high-molecular-weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times and high polymer extensibilities, for which the evolution can be divided into two distinct regimes. For times smaller than the polymer relaxation time over which the beads-on-string structure develops, we give a simplified local description, which still retains the essential physics of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops. ispartof: Journal of fluid mechanics vol:556 pages:283-308 status: published

Deformation induced heating of reactive solids is a physically complex process. As such, the effects of meso-structure, component thermomechanical properties, component mass fractions, and porosity on their impact response is not well-understood. In this study, an explicit, 2-D, Lagrangian finite and discrete element technique is used to examine thermomechanical fields in metal-explosive (aluminum-HMX) particle mix- tures due to piston supported uniaxial deformation waves. The meso-scale description uses a plane strain, thermoelastic-viscoplastic and friction constitutive theory to describe the motion and deformation of individual particles, and an energy consistent, penalty based method to describe inter-particle contact. The deformation response of material having an initial solid volume fraction of φ 0 s = 0.835 is characterized for different metal mass fractions and wave strengths. Predictions indicate that the response can be classified into strength dominated and pressure dominated regions depending on wave strength. Average thermomechanical fields that define the macro-scale wave structure are found to differ both qualitatively and quantitatively between the two regions.

Based upon the phenomenological theory of non-linear responses of many variable systems (K. Okano and O. Nakada, J. Phys. Soc. Japan, 16, 2071 (1961)) the non-linear constitutive equations for isotropic viscoelastic materials are presented.Let σ(t) denote the stress tensor at an instant of time t, and D(t) be the displacement gradient ∇S (S being the displacement vector) or velocity gradient ∇V (V being the velocity vector) according as the material concerned is a viscoelastic solid or a viscoelastic liquid, then we have (K. Okono, Japanese J. Appl. Phys., 1, 302 (1961)) the following non-linear constitutive equation (up to the second order terms in D) for an isotropic viscoelastic material:σ(t)=∫t-∞[a(1)(t-τ)D(0)(τ)+b(1)(t-τ)D(2)(τ)]dτ+∫t-∞∫t-∞[a(2)(t-τ1, t-τ2)D(0)(τ1): D(0)(τ2)I+b(2)(t-τ1, t-τ2)D(2)(τ1): D(2)(τ2)I+c(2)(t-τ1, t-τ2)D(0)(τ1)·D(2)(τ2)+d(2)(t-τ1, t-τ2){1/2D(2)(τ1)·D(2)(τ2)+1/2D(2)(τ2)·D(2)(τ1)-1/3D(2)(τ1): D(2)(τ2)I}+e(2)(t-τ1, t-τ2){1/2D(1)(τ1)·D(2)(τ2)-1/2D(2)(τ2)·D(1)(τ1)}]dτ1dτ2+higher order terms.In the above equation I is the unit tensor andD(0)≡1/3∇·SI or 1/3∇·VID(1)≡1/2(D-D)D(2)≡1/2(D+D)-D(0)and a(1)(t), b(1)(t), a(2)(t1, t2), ect. are the scalar material functions characterizing the viscoelastic response of the system concerned. The third order terms in D are given in the text. (eq. 2.5).If the material concerned is incompressible the terms on the right hand of the above constitutive equation which are connected with a dilatational deformation (the terms containing a(1), a(2), b(2), c(2)) should be replaced by an indeterminate hydrostatic pressure: -pI