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Polyvinyl alcohol (PVA) hydrogels are extensively used as scaffolds for tissue engineering, although their biodegradation properties have not been optimized yet. To overcome this limitation, partially oxidized PVA has been developed by means of different oxidizing agents, obtaining scaffolds with improved biodegradability. The oxidation reaction also allows tuning the mechanical properties, which are essential for effective use in vivo. In this work, the compressive mechanical behavior of native and partially oxidized PVA hydrogels is investigated, to evaluate the effect of different oxidizing agents, i.e., potassium permanganate, bromine, and iodine. For this purpose, PVA hydrogels are tested by means of indentation tests, also considering the time-dependent mechanical response. Indentation results show that the oxidation reduces the compressive stiffness from about 2.3 N/mm for native PVA to 1.1 ÷ 1.4 N/mm for oxidized PVA. During the consolidation, PVA hydrogels exhibit a force reduction of about 40% and this behavior is unaffected by the oxidizing treatment. A poroviscoelastic constitutive model is developed to describe the time-dependent mechanical response, accounting for the viscoelastic polymer matrix properties and the flow of water molecules within the matrix during long-term compression. This model allows to estimate the long-term Young's modulus of PVA hydrogels in drained conditions (66 kPa for native PVA and 34–42 kPa for oxidized PVA) and can be exploited to evaluate their performances under compressive stress in vivo, as in the case of cartilage tissue engineering. [ABSTRACT FROM AUTHOR]

In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage layers are often modelled as a poroviscoelastic material. To model the relative motion, noting the separation of scales between the pore level and the macroscale, a homogenization based on multiple scale asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and their interaction is captured in the derived model via a set of interfacial conditions, including a generalization of the Beavers–Joseph condition at the interface between a viscous fluid and a porous medium. In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under load influences the peak force the cartilage experiences and the extent of the associated deformations. In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed charges, manifests in cartilage mechanics at much higher lengthscales. [ABSTRACT FROM AUTHOR]

Conventional technical means are no longer sufficient to fully explain the intrinsic linkage between exogenous fillers and structural changes of meat gels. In this study, poroviscoelasticity (PVE) as a new perspective was introduced. Firstly, the effects of regenerated cellulose microspheres (RCM) and spherical nanocellulose (SNC) in varying amounts (0, 2.5, 5.0, 7.5, 10.0 wt%) on the meat gels were investigated. The incorporation of both RCM and SNC resulted in a denser and more uniform microstructure of meat gels. Compared to pure meat gels, the cooking loss was reduced by 23.8 % and 33.6 %, respectively. The better effect of SNC on meat gels was correlated with its smaller size. Secondly, the mechanical responses of meat gels at different indentation depths were characterized by the spherical indentation method. The results showed that the force relaxation during the indentation process of meat gels was primarily due to the combined effects of poroelasticity (PE) and viscoelasticity (VE). Specifically, a quick VE relaxation was observed with a relaxation time of 10.0 s and 14.5 s for RCM-meat gels and SNC-meat gels, respectively. When RCM and SNC were added at 5.0 wt% and 7.5 wt%, the permeability of gels was significantly lower than that of pure meat gels (p < 0.05), especially when the indentation depth was 2 mm and 3 mm. On the whole, the PVE parameters aligned well with the results of hydration properties and microstructure, so the meat gels could be regarded as a type of porous viscoelastic material, and this study can provide a theoretical basis for the in-depth analysis of the structural properties of meat products using the PVE model. [Display omitted] • Cellulose improves the microstructure and hydration properties of meat gels. • SNC provides a superior filling effect. • Indentation technique applied to obtain material parameters of meat gels. • Hydration capacity of meat gels can explain poroviscoelasticity characteristics. [ABSTRACT FROM AUTHOR]

Poroviscoelastic models have been widely employed to the modeling of hydrated biological tissues, since they allow to investigate the biomechanical responses associated with the interstitial fluid flow. Such problems present strong physical couplings arising from material and geometrical nonlinearities. In this regard, the present study investigates the numerical performance of five biphasic solution algorithms within the context of soft biological tissues: monolithic, drained, undrained, fixed‐strain, and fixed‐stress scheme. To this end, two classical tests were studied within a finite element framework: confined and unconfined compression tests. Since these tests behave differently in terms of biphasic coupling, the sensitivity of different permeability values and time increments to the algorithms' performance were assessed. The results highlight that iterative techniques perform well over the monolithic one for weak coupling cases but suffer from lack of convergence when the coupling strength increases. This means that, in contrast to what is recommended in the vast majority of geomechanics papers, the iteratively‐coupled schemes are not always well‐suited methods for problems related to soft biological tissues mechanics. The monolithic scheme thus emerges as the most reliable choice to solve biphasic problems in a biomechanics context, specifically when high coupling strength problems and small time increments take place. [ABSTRACT FROM AUTHOR]

The inferred density of Enceladus' core, together with evidence of hydrothermal activity within the moon, suggests that the core is porous. Tidal dissipation in an unconsolidated core has been proposed as the main source of Enceladus' geological activity. However, the tidal response of its core has generally been modeled assuming it behaves viscoelastically rather than poroviscoelastically. In this work, we analyze the poroviscoelastic response to better constrain the distribution of tidal dissipation within Enceladus. A poroviscoelastic body has a different tidal response than a viscoelastic one; pressure within the pores alters the stress field and induces a Darcian porous flow. This flow represents an additional pathway for energy dissipation. Using Biot's theory of poroviscoelasticity, we develop a new framework to obtain the tidal response of a spherically symmetric, self‐gravitating moon with porous layers and apply it to Enceladus. We show that the boundary conditions at the interface of the core and overlying ocean play a key role in the tidal response. The ocean hinders the development of a large‐amplitude Darcian flow, making negligible the Darcian contribution to the dissipation budget. We therefore infer that Enceladus' core can be the source of its geological activity only if it has a low rigidity and a very low viscosity. A future mission to Enceladus could test this hypothesis by measuring the phase lags of tidally induced changes of gravitational potential and surface displacements. Plain Language Summary: With a young surface, a subsurface water ocean and water plumes rising above its limb, tiny Enceladus is one of the most interesting bodies in the Solar System. The moon's geological activity is likely powered by Saturnian tides that periodically deform Enceladus, producing internal heat due to friction by a process known as tidal dissipation. Data from the Cassini mission shows that Enceladus' core is likely a porous medium throughout which water can circulate. We develop a model to study the tidally induced deformation of the core and how water flows within it. We find that for tidal heating to explain the moon's geological activity, Enceladus' core must be exceptionally weak. We show how a future mission could measure whether this is the case or not. Key Points: We present a new method to compute the tidal response of moons with porous layersThe boundary conditions at the porous layer boundaries control the moon's responseTidal dissipation in Enceladus' core can only account for the moon's observed thermal output if it is in a highly deformable state [ABSTRACT FROM AUTHOR]

• The viscoelastic solid frame is modeled based on the fractional derivatives. • The influences of fractional index on the reflected and transmitted behavior are studied. • The influences of the gas saturation on the reflection and transmission behavior are studied. • The characteristic gas saturation is found where the energy dissipation increase drastically. • The sensitivity range of the energy dissipation and the reflection/transmission coefficients on gas saturation are found. The reflection and transmission problems of elastic waves through a partially saturated porous interlayer sandwiched between two elastic solid half-spaces are investigated. The partially saturated porous interlayer contains solid phase, gas phase and liquid phase. The solid frame is modeled by the fractional Zener model where the fractional order derivatives are used to describe the complex history-dependent viscoelastic behavior. Due to the coupled effects of the multiple fields, there exist three longitudinal waves and one transverse wave in the porous medium. The numerical results of reflection and transmission coefficients and the energy dissipation ratios are provided and shown graphically. The effects of the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame are discussed based upon the numerical results. It is observed that the reflection and transmission coefficients and the energy dissipation ratios are affected noticeably by the gas saturation, the interlayer thickness and the viscoelasticity of the solid frame. In particular, there exists the characteristic gas saturation where the energy dissipation increases drastically. [ABSTRACT FROM AUTHOR]

Polyvinyl alcohol (PVA) hydrogels are extensively used as scaffolds for tissue engineering, although their biodegradation properties have not been optimized yet. To overcome this limitation, partially oxidized PVA has been developed by means of different oxidizing agents, obtaining scaffolds with improved biodegradability. The oxidation reaction also allows tuning the mechanical properties, which are essential for effective use in vivo. In this work, the compressive mechanical behavior of native and partially oxidized PVA hydrogels is investigated, to evaluate the effect of different oxidizing agents, i.e., potassium permanganate, bromine, and iodine. For this purpose, PVA hydrogels are tested by means of indentation tests, also considering the time-dependent mechanical response. Indentation results show that the oxidation reduces the compressive stiffness from about 2.3 N/mm for native PVA to 1.1 ÷ 1.4 N/mm for oxidized PVA. During the consolidation, PVA hydrogels exhibit a force reduction of about 40% and this behavior is unaffected by the oxidizing treatment. A poroviscoelastic constitutive model is developed to describe the time-dependent mechanical response, accounting for the viscoelastic polymer matrix properties and the flow of water molecules within the matrix during long-term compression. This model allows to estimate the long-term Young’s modulus of PVA hydrogels in drained conditions (66 kPa for native PVA and 34–42 kPa for oxidized PVA) and can be exploited to evaluate their performances under compressive stress in vivo, as in the case of cartilage tissue engineering.

Focused fluid flow is common in sedimentary basins worldwide, where flow structures often penetrate through sandy reservoir rocks, and clay‐rich caprocks. To better understand the mechanisms forming such structures, the impacts of the viscoelastic deformation and strongly nonlinear porosity‐dependent permeability of clay‐rich materials are assessed from an experimental and numerical modeling perspective. The experimental methods to measure the poroviscoelastic and transport properties of intact and remolded shale have been developed, and the experimental data is used to constrain the numerical simulations. It is demonstrated that viscoelastic deformation combined with nonlinear porosity‐dependent permeability triggers the development of localized flow channels, often imaged as seismic chimneys. The permeability inside a channel increases by several orders of magnitude compared to the background values. In addition, the propagation time scale and the channel size strongly depend on the material properties of the fluid and the rock. The time‐dependent behavior of the clay‐rich rock may play a key role in the long‐term integrity of the subsurface formations. Key Points: Clay‐rich rocks exhibit bulk viscous deformation in laboratory experimentsFocused fluid flow might develop through clay‐rich rock with implications for injectivity and leakage riskModel simulations based on experimental parameters give estimates for expected leakage rates [ABSTRACT FROM AUTHOR]

Abstract Focused fluid flow is common in sedimentary basins worldwide, where flow structures often penetrate through sandy reservoir rocks, and clay‐rich caprocks. To better understand the mechanisms forming such structures, the impacts of the viscoelastic deformation and strongly nonlinear porosity‐dependent permeability of clay‐rich materials are assessed from an experimental and numerical modeling perspective. The experimental methods to measure the poroviscoelastic and transport properties of intact and remolded shale have been developed, and the experimental data is used to constrain the numerical simulations. It is demonstrated that viscoelastic deformation combined with nonlinear porosity‐dependent permeability triggers the development of localized flow channels, often imaged as seismic chimneys. The permeability inside a channel increases by several orders of magnitude compared to the background values. In addition, the propagation time scale and the channel size strongly depend on the material properties of the fluid and the rock. The time‐dependent behavior of the clay‐rich rock may play a key role in the long‐term integrity of the subsurface formations.

The effect of crosslinker concentration on the mechanical behaviour of polyacrylamide based hydrogels is established by using depth sensing indentation. In this work, hydrogels are considered as poroviscoelastic solids, being viscoelasticity and poroelasticity taken into account at intermediate length scales such as those here explored. A constrained fitting method is derived to implement a multiplicative rule that accommodates the contribution of each deformation mechanism on the global material response. The proposed method is robust enough to properly separate poroelastic and viscoelastic contributions from relaxation curves measured at different indentation depths and strain rates. At the length scales here tested viscoelasticity appears as dominant, but the poroelastic contribution becomes increasingly important as the crosslinker concentration is reduced.

• An analytical approach is developed to model the indentation of a spherical indenter with a fixed contact radius on a poroviscoelastic medium. • Closed-form expressions in the Laplace-transformed domain for both the normal approach and the contact force of the spherical indenter are provided. • The formulation can aid in interpreting spherical indentation tests on poroviscoelastic media to determine material properties. The research aims to understand the force relaxation that occurs when a spherical indenter is pressed into poroviscoelastic materials, which exhibit viscoelastic properties of solid network and drainage behavior of infiltrated fluid. To achieve this, an analytical approach is proposed to model spherical indentation on a poroviscoelastic medium under the condition of a constant contact radius. This analysis is conducted in the Laplace-transformed domain, and provides closed-form expressions in the transformed domain for both the normal approach and the contact force of the indenter while maintaining a fixed contact radius. These expressions are then numerically inverse-transformed to the time domain for practical analysis. To account for different scenarios, we consider various combinations of drainage conditions at the top and smoothness conditions at the bottom of the medium. We examine three categories of viscoelastic solid behavior, as understanding how they respond under indentation is crucial for characterizing their mechanical behavior. Additionally, we conduct finite element simulations of spherical indentation on poroviscoelastic media, serving as a comparison to the semi-analytic results obtained. Notably, the thickness of the medium relative to the contact radius and the Poisson's ratio play significant roles in the evolution of both the normal approach and contact force of the spherical indenter over time. [ABSTRACT FROM AUTHOR]

Energy loss in porous media containing fluids is typically caused by a variety of dynamic mechanisms. In the Biot theory, energy loss only includes the frictional dissipation between the solid phase and the fluid phase, resulting in underestimation of the dispersion and attenuation of the waves in the low frequency range. To develop a dynamic model that can predict the high dispersion and strong attenuation of waves at the seismic band, we introduce viscoelasticity into the Biot model and use fractional derivatives to describe the viscoelastic mechanism, and finally propose a new wave propagation model. Unlike the Biot model, the proposed model includes the intrinsic dissipation of the solid frame. We investigate the effects of the fractional order parameters on the dispersion and attenuation of the P- and S-waves using several numerical experiments. Furthermore, we use several groups of experimental data from different fluid-saturated rocks to testify the validity of the new model. The results demonstrate that the new model provides more accurate predictions of high dispersion and strong attenuation of different waves in the low frequency range. [ABSTRACT FROM AUTHOR]

Swelling pressure in the interstitial fluid within the pores of cartilage tissue is known to have a significant effect on the rheology of cartilage tissue. The swelling pressure varies rapidly within thin regions inside pores known as Debye layers, caused by the presence of fixed charge, as observed in cartilage. Tissue level calculation of cartilage deformation therefore requires resolution of three distinct spatial scales: the Debye lengthscale within individual pores; the lengthscale of an individual pore; and the tissue lengthscale. We use asymptotics to construct a leading order approximation to the swelling pressure within pores, allowing the swelling pressure to be systematically included within a fluid-solid interaction model at the level of pores in cartilage. We then use homogenization to derive tissue level equations for cartilage deformation that are very similar to those governing the finite deformation of a poroviscoelastic body. The equations derived permit the spatial variations in porosity and electric charge that occur in cartilage tissue. Example solutions are then used to confirm the plausibility of the model derived and to consider the impact of fixed charge heterogeneity, illustrating that local fixed charge loss is predicted to increase deformation gradients under confined compression away from, rather than at, the site of loss. [ABSTRACT FROM AUTHOR]

Hydrogels are peculiar soft materials formed by a 3D polymeric network surrounded by water molecules. In these systems the mechanical and the chemical energy are well balanced and an applied external stimulus (mechanical or chemical) can cause a distinctive response, where the contributions of the mechanics and the mass transport are combined to form a "poroviscoelastic" behavior. In this work the poroviscoelastic behavior of the agarose gels has been investigated, from the experimental and modeling points of view, by applications of external mechanical stimuli. The pure gel, brought in the non-equilibrium condition, showed that the combined effect of mechanical viscoelasticity and water transport were essential to reach the new equilibrium condition. Furthermore, the agarose gel loaded with a model drug, theophylline, showed that the mechanical stimulus can enhance the drug release from the system by stretching the polymeric chains, modifying the mesh size and therefore the drug diffusion coefficient. [ABSTRACT FROM AUTHOR]

An hp- and memory-adaptive discontinuous Galerkin time-domain algorithm is presented to efficiently model wave propagation in poroelastic media, with the incorporation of 3-D fully anisotropic intrinsic attenuation. From the perspective of physics, the attenuation from the triclinic rock frame, the loss in the pore fluid, and the friction for their interaction are all considered. From the perspective of implementation, a new frequency-domain constitutive equation is introduced, involving complex-valued poroelasticity matrix. A new Q value is defined as the ratio between its real and imaginary parts for every entry. Then, a generalized Maxwell body is adopted to approximate this frequency-dependent Q in the time domain. Mathematically speaking, the hyperbolicity is preserved for the new viscous poroelastic system. Our results corroborate that the intrinsic attenuation anisotropy makes tangible effects in fluid-saturated porous formations. [ABSTRACT FROM AUTHOR]

The indentation method is widely used for characterizing the mechanical properties of materials because of its simplicity. However, the interpretation of the force relaxation of a flat indenter at a fixed displacement to obtain the properties of polymeric gels is challenging, especially when the viscoelasticity of the solid network and the drainage of the infiltrated fluid both contribute to the relaxation. This paper formulates flat indentation on a poroviscoelastic half-space analytically using displacement functions in a Laplace-transformed domain. The dual integral equations formed by the mixed boundary conditions are solved and the force of the indenter at a fixed displacement is expressed in closed form in the transformed domain and later numerically inverse-transformed to the time domain. The force relaxation is analyzed for three drainage conditions prescribed on the surface of the half-space, namely a completely pervious condition, a completely impervious condition, and a mixed condition that combines an impervious surface underneath the indenter and a pervious surface elsewhere. The closed-form solution can be reduced to that of a flat indentation on a poroelastic half-space. Moreover, finite element simulations of a flat indentation on a poroviscoelastic half-space are carried out and their results are compared with the semi-analytic results. Three categories of viscoelastic solid behavior are considered and the results for a wide variety of polymeric gels are provided. [ABSTRACT FROM AUTHOR]

Abstract Macroscale deformations in a roasting coffee bean are important mechanisms in determining flavour development, moisture loss, and consistency of the bean. In this paper, we model the stresses and strains in the cellulose structure of a roasting coffee bean via temperature-dependent poroviscoelastic constitutive equations. This model accounts for the deformations that are created and controlled by the moisture content, temperature, and gas pressure inside of the roasting coffee bean. The model combines previously derived multiphase heat and mass transfer models for roasting coffee beans with these poroviscoelastic equations, to determine when and where macroscale deformations of the cellular matrix are likely to occur. By exploiting reasonable asymptotic reductions of the poroviscoelastic equations, we find that a large surge of stress is produced in the interior of a coffee bean. We determine that this build-up of stress is due to the viscoelastic interior of the bean being contained by a rigid elastic exterior and unable to expand. Our theoretical results suggest directions for possible improvement in standard industrial coffee roasting techniques, which may allow the macroscale deformations of the cellular matrix to be controlled and thereby improve properties such as flavour, moisture loss, and consistency of the final product. Highlights • The cellulose structure in a roasting coffee bean is modelled. • The governing equations describing the cellulose structure are coupled to existing multiphase models. • Analysis of the aforementioned equations reveals a surge of internal stresses. [ABSTRACT FROM AUTHOR]

The present paper is dedicated to numerical solving of three dimensional boundary-value problems in poroviscoelastic formulation. The poroviscoelastic formulation is treated as a combination of Biot's theory of poroelasticity and elastic-viscoelastic correspondence principle. Kelvin-Voigt model and Standard linear solid model are employed in order to describe viscoelastic media properties. Boundary element method and boundary integral equation method are applied to obtain Laplace domain solution of boundary-value problem. Modified Durbin's algorithm of numerical inversion of Laplace transform is used to perform solutions in time domain. Research is also dedicated to development of numerical modelling technique based on Boundary Element Method (BEM) in Laplace domain for solution of three dimensional transient poroviscoelastic problems. A problem of the three-dimensional poroviscoelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading at another is considered. Viscosity parameter influence on dynamic responses of displacements and tractions is studied. [ABSTRACT FROM AUTHOR]

As the state of the art pushes triboelements toward greater capabilities and longevity, the need for evolving triboelement technology exists. The following work explores a novel coupling of phenomena inspired by biomimetics. A poroviscoelastic substrate coupled to a fluid film load is modeled and compared to its rigid counterpart. It is hypothesized that poroviscoelasticity can improve triboelement properties such as damping and wear resistance and have utility in certain applications where flexibility is desired (e.g., biomechanical joint replacements, flexible rotordynamic bearings, and mechanical seals). This study provides the framework for the analysis of flexible, porous viscoelastic materials and hydrodynamic lubrication. [ABSTRACT FROM AUTHOR]

Many solid food matrices contain high amounts of solvent, typically water, yet the time dependent mechanical characterization of foods has typically been analyzed following a viscoelastic approach, omitting the effect of the solvent. In solvent rich solids the solvent can flow internally, for example as it is compressed, which is typically understood using poroelastic theory. A poroelastic approach allows the determination of hydrogel parameters, such as the Darcy's diffusivity or the intrinsic permeability, that have a physical meaning. Recently, it has been proposed for polymeric hydrogels a novel experimental methodology, based on relaxation after indentation, that greatly simplifies the poroelastic analysis. This methodology is applied and tested to heat induced whey protein hydrogels. Finite element analysis was performed to simulate the particularities of the indentation experiments. Relaxation data suggest, after a pure poroelastic analysis, that there is also a small fast viscoelastic relaxation in whey protein hydrogels. Poroviscoelastic relaxation was simulated with finite elements modeling, and a forward regression methodology was implemented. Results show that the water diffusivity in the protein hydrogels is larger that the self-diffusivity of water, as expected in a matrix with large pores where solvent flow occurs by convection. Whey protein hydrogels swollen to different degrees using different salt concentrations relaxed to different proportions. This result was unexpected as it leads, in poroelastic theory, to different drained Poisson's ratio, with even negative values for the less swollen gels. [ABSTRACT FROM AUTHOR]

Water, vapor, and heat transport mechanisms and thermomechanical changes occurring inside the expanding extrudate were described using hybrid mixture theory-based unsaturated transport equations. Transport equations were transformed from the Eulerian coordinates to the Lagrangian coordinates. Good agreements between the predicted and experimental values of surface temperature, moisture content, and expansion ratio of the extrudates were obtained. The model was also used to calculate temperature, moisture content, pore-pressure, and viscoelastic-stress distribution in the extrudate. Matrix collapse and glassy crust formation under the surface was calculated as a function of extrusion conditions. Expansion behavior of the extrudate was described using the difference between stress due to pore pressure and viscoelastic stress. The modeling results can serve as a guide for predictably modifying the extrusion parameters for obtaining specific textural attributes of expanded starch for various food, feed, and biomedical applications. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4517-4532, 2015 [ABSTRACT FROM AUTHOR]

In this research, we present a theory of finite deformation poroviscoelasticity. The proposed theory is based on the logarithmic strain and a quadratic free energy function. As an illustration, we apply the theory to the study of the consolidation of a finite porous layer. To show the viscous effect of solid skeleton, we compare the results obtained from poroviscoelasticity with those from poroelasticity. Moreover, we provide the finite element formulation for the one-dimensional problem considered, which can however, be extended straightforward for two- and three-dimensional problems. • A finite strain poroviscoelastic model based on the logarithmic stain has been proposed. • The crucial advantage of the model is to utilize the material properties evaluated at infinitesimal strains to predict the finite deformation response. • The one-dimensional finite element formulation of the proposed theory has been provided to study the consolidation of a finite porous layer. [ABSTRACT FROM AUTHOR]

Interpreting the contact force relaxation between an indenter and a poroviscoelastic material at a fixed displacement to obtain the materials properties is a challenging task, because both fluid drainage and solid viscoelasticity contribute to the relaxation. In this research, the indentation of a poroviscoelastic layer caused by a flat-ended cylindrical indenter is formulated analytically by the displacement functions in the Laplace-transformed domain. The contact force of the indenter at a fixed displacement was expressed by a closed-form in the transformed domain and numerically inverse-transformed to the time domain. The force relaxation is analyzed for combinations of three drainage conditions prescribed on the layer top and two boundary conditions prescribed on the layer bottom. The closed-form solution can approach that of the flat-indentation on a poroviscoelastic half-space, when the layer is very thick compared to the indenter radius. In addition, finite element simulations of the flat-indentation on poroviscoelastic layers were carried out as a comparison for the semi-analytical results. The relaxation ratios at the limits of the drained-nonviscoelastic state, the nondrained-viscoelastic state and the drained-viscoelastic state are shown for different ratios of the layer thickness to the indenter radius, and verified with the corresponding elastic solutions. The effects of the viscoelastic characteristic time on the force relaxations are also presented for different viscoelastic properties and boundary conditions. [ABSTRACT FROM AUTHOR]

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels. Engineering applications often require knowledge of both behaviors separated; however, few methods exist to decouple viscoelastic and poroelastic properties of gels. We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests. The viscoelastic characteristic time and the poroelastic diffusivity of a gel define an intrinsic material length scale of the gel. The experimental setup gives a sample length scale, over which the solvent migrates in the gel. By setting the sample length to be much larger or smaller than the material length, the viscoelasticity and poroelasticity of the gel will dominate at different time scales in a test. Therefore, the viscoelastic and poroelastic properties of the gel can be probed separately at different time scales of the test. We further validate the method by finite-element models and stress-relaxation experiments. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

An implicit mixed finite element formulation of hydrated soft biological tissues, based on the Simon model, is presented that incorporates the coupling of solid, fluid, and ion phases as well as the viscoelasticity of soft tissue in the dynamical process. The tissues are modeled as a multi-field viscoelastic body subject to finite deformation. In addition to a three-field (u-w-p) modeling of the porous matrix, the study also includes an ion phase for the ionic solution. After presenting the formulation, an efficient staggered solution scheme is presented: within each time step, the ion charge equation is solved first to give the distribution of the charge concentration, the charge induced osmotic water pressure is then employed in solving the u-w-p equations. The resulting u field becomes a forcing term to the solution of the ion charge concentration equations for iteration. This methodology and codes developed for the study have been verified with one-dimensional (1D) analytical solutions. A 2D chemical electric swelling model illustrates the important role of viscoelasticity. A brain tissue impact example demonstrates the potential application of the model. [ABSTRACT FROM AUTHOR]

Abstract: This work presents a numerical methodology to simulate the physical phenomena in which there is conversion between electromagnetic and mechanical (kinetic) energy. The electroseismic equations linking the diffusive electromagnetic and seismic wavefields are solved using the finite element method. The subsurface is modeled as a 2D fluid-saturated layered porous medium. It is illuminated by two different kinds of electromagnetic sources, one giving rise to transverse electric (TE) fields and the other one to transverse-magnetic (TM) fields; the former are coupled with SH and the latter with PSV mechanical displacements respectively. Examples illustrating the capabilities of the presented methodology, including partially saturated gas regions are presented. [ABSTRACT FROM AUTHOR]

Abstract: The analytical poromechanics solution for the stresses, pore pressure, fluid flux, strains, and displacements of transversely isotropic saturated cylinders under general time-dependent loading is extended in this paper to account for the intrinsic viscoelastic nature of the porous matrix as well as the compressible interstitial fluid flow, simulating saturated poroviscoelastic geo-materials and bio-materials under some of the most encountered laboratory testing conditions: unconfined compression, confined compression, unjacketed triaxial, jacketed triaxial, and oedometer tests. Numerical examples are demonstrated for biological tissues in unconfined and confined compression tests with cyclic loading and rocks under triaxial configuration with confinement and linear-ramp axial loading. [Copyright &y& Elsevier]

Abstract: The mechanical induction of specific cell phenotypes can only be properly controlled if the local stimuli applied to the cells are known as a function of the external applied loads. Finite element analysis of the cell carriers would be one method to calculate these local conditions. Furthermore, the constitutive model of the construct material should be able to describe mechanical events known to be responsible for cell stimulation, such as interstitial fluid flow. The aim of this study was to define a biphasic constitutive model for fibrin, a natural hydrogel often used for tissue engineering but not yet thoroughly characterized. Large strain poroelastic and poroviscoelastic constitutive equations were implemented into a finite element model of a fibrin gel. The parameter values for both formulations were found by either analytically solving equivalent low strain equations, or by optimizing directly the large strain equations based on experimental stress relaxation data. No poroelastic parameters that satisfactorily described the fibrin carrier behaviour could be found, suggesting that network viscoelasticity and fluid-flow time-dependent behaviour must be separately accounted for. It was demonstrated that fibrin can be described as a poroviscoelastic material, but a large strain characterization of the parameter values was necessary. The analytical resolution of the low strain poroviscoelastic equations was, however, accurate enough to serve as a reliable initial condition for further optimization of the parameter values with the large strain formulation. [Copyright &y& Elsevier]

This work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single-phase fluid. The equations of motion, formulated in the space-frequency domain, include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high-frequency range and intrinsic anelasticity of the solids modeled using linear viscoelasticity. This formulation leads to the solution of a Helmholtz-type boundary value problem for each temporal frequency. For the spatial discretization, nonconforming finite element spaces are employed for the solid phases, while for the fluid phase the vector part of the Raviart--Thomas--Nedelec mixed finite element space is used. Optimal a priori error estimates for global standard and hybridized Galerkin finite element procedures are derived. An iterative nonoverlapping domain decomposition procedure is also presented and convergence results are derived. Numerical experiments showing the application of the numerical procedures to simulate wave propagation in partially frozen porous media are presented. [ABSTRACT FROM AUTHOR]

Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-β method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects. [ABSTRACT FROM AUTHOR]

Abstract: A poroviscoelastic constitutive model is developed and used to study coupled rock deformation and fluid flow. The model allows the relaxation of both shear and symmetric components of the effective stress. Experimental results are usually interpreted in terms of the power law viscous material. However, in this work the effect of strain damage on viscosity is considered by treating the viscosity as a dynamic time-dependent parameter that varies proportionally to the second invariant of the strain rate. Healing is also taken into account so that the dynamic power law viscosity has a constant asymptotic at a given strain rate. The theoretical model is implemented in a finite element (FE) formulation that couples fluid flow and mechanical equilibrium equations. The FE method is applied to numerically study the triaxial compression of partially melted rocks at elevated PT conditions. It is found that the numerically calculated stress–strain curves demonstrate maxima similar to those observed in laboratory experiments. Also, the computed pattern of melt redistribution and strain localization at the contact between the rock sample and a stiff spacer is qualitatively similar to the experimental observations. The results also indicate that the matrix sensitivity to damage affects the scale of strain localization and melt redistribution. [Copyright &y& Elsevier]

We present an iterative algorithm formulated in the space-frequency domain to simulate the propagation of waves in a bounded poro-viscoelastic rock saturated by a two-phase fluid. The Biot-type model takes into account capillary forces and viscous and mass coupling coefficients between the fluid phases under variable saturation and pore fluid pressure conditions. The model predicts the existence of three compressional waves or Type-I, Type-II and Type-III waves and one shear or S-wave. The Type-III mode is a new mode not present in the classical Biot theory for single-phase fluids. Our differential and numerical models are stated in the space-frequency domain instead of the classical integrodifferential formulation in the space-time domain. For each temporal frequency, this formulation leads to a Helmholtz-type boundary value problem which is then solved independently of the other frequency problems, and the time-domain solution is obtained by an approximate inverse Fourier transform. The numerical procedure, which is first-order correct in the spatial discretization, is an iterative nonoverlapping domain decomposition method that employs an absorbing boundary condition in order to minimize spurious reflections from the artificial boundaries. The numerical experiments showing the propagation of waves in a sample of Nivelsteiner sandstone indicate that under certain conditions the Type-III wave can be observed at ultrasonic frequencies. [ABSTRACT FROM AUTHOR]

The effect of crosslinker concentration on the mechanical behaviour of polyacrylamide based hydrogels is established by using depth sensing indentation. In this work, hydrogels are considered as poroviscoelastic solids, being viscoelasticity and poroelasticity taken into account at intermediate length scales such as those here explored. A constrained fitting method is derived to implement a multiplicative rule that accommodates the contribution of each deformation mechanism on the global material response. The proposed method is robust enough to properly separate poroelastic and viscoelastic contributions from relaxation curves measured at different indentation depths and strain rates. At the length scales here tested viscoelasticity appears as dominant, but the poroelastic contribution becomes increasingly important as the crosslinker concentration is reduced. [Display omitted] • Polyacrylamide hydrogels are synthesized with different crosslinker concentrations. • Spherical indentation is used to perform relaxation test at the micro length scale. • Poroelastic and viscoelastic mechanisms are overlapped at this contact size. • A constrained fitting procedure has been developed to properly separate the viscoelastic and poroelastic contributions. • Poroelastic contribution is more important as the amount of crosslinker is reduced. [ABSTRACT FROM AUTHOR]

Biomaterials is an emerging field in the study of brain tissue engineering and repair or neurogenesis. The fabrication of biomaterials that can replicate the mechanical and viscoelastic features required by the brain, including the poroviscoelastic responses, force dissipation, and solute diffusivity are essential to be mapped from the macro to the nanoscale level under physiological conditions in order for us to gain an effective treatment for neurodegenerative diseases. This research topic has identified a critical study gap that must be addressed, and that is to source suitable biomaterials and/or create reliable brain-tissue-like biomaterials. This chapter will define and discuss the various types of biomaterials, their structures, and their function-properties features which would enable the development of next-generation biomaterials useful in brain repair. • Injury and neurodegenerative diseases cause irreversible cell loss in brain. • Biomaterials are potential substances that can be engineered to enhance neural repair following brain injury. • Brain's physical, mechanical and poroviscoelastic properties need to be considered to design biomaterials-based scaffolds. • Hydrogels have been shown as the most potential and suitable biomaterials-based scaffold for brain regenerative therapies. [ABSTRACT FROM AUTHOR]