Poroelastic Material Research Articles

Biofilms as poroelastic materials

Biofilms are bacterial aggregates encased in a self-produced polymeric matrix which attach to moist surfaces and are extremely resistant to chemicals and antibiotics. Recent experiments show that their structure is defined by the interplay of elastic deformations and liquid transport within the biofilm, in response to the cellular activity and the interaction with the surrounding environment. We propose a poroelastic model for elastic deformation and liquid transport in three dimensional biofilms spreading on agar surfaces. The motion of the boundaries can be described by the combined use of Von Kármán type approximations for the agar/biofilm interface and thin film approximations for the biofilm/air interface. Bacterial activity informs the macroscopic continuous model through source terms and residual stresses, either phenomenological or derived from microscopic models. We present a procedure to estimate the structure of such residual stresses, based on a simple cellular automata description of bacterial activity. Inspired by image processing, we show that a filtering strategy effectively smooths out the rough tensors provided by the stochastic cellular automata rules, allowing us to insert them in the macroscopic model without numerical instability.

On the Mechanical Effects of Poroelastic Crystal Mush in Classical Magma Chamber Models

AbstractImproved constraints on the mechanical behavior of magma chambers is essential for understanding volcanic processes; however, the role of crystal mush on the mechanical evolution of magma chambers has not yet been systematically studied. Existing magma chamber models typically consider magma chambers to be isolated melt bodies surrounded by elastic crust. In this study, we develop a physical model to account for the presence and properties of crystal mush in magma chambers and investigate its impact on the mechanical processes during and after injection of new magma. Our model assumes the magma chamber to be a spherical body consisting of a liquid core of fluid magma within a shell of crystal mush that behaves primarily as a poroelastic material. We investigate the characteristics of time‐dependent evolution in the magma chamber, both during and after the injection, and find that quantities such as overpressure and tensile stress continue to evolve after the injection has stopped, a feature that is absent in elastic (mushless) models. The time scales relevant to the postinjection evolution vary from hours to thousands of years, depending on the micromechanical properties of the mush, the viscosity of magma, and chamber size. We compare our poroelastic results to the behavior of a magma chamber with an effectively viscoelastic shell and find that only the poroelastic model displays a time scale dependence on the size of the chamber for any fixed mush volume fraction. This study demonstrates that crystal mush can significantly influence the mechanical behaviors of crustal magmatic reservoirs.

Acoustic characterization of ducts lined with poroelastic materials based on wave finite element method

A wave finite element (FE) approach is presented for investigating acoustic characteristics of an axisymmetric duct lined with poroelastic materials. A short segment of the poroelastic lined duct is modelled using commercial FE software package, and an eigenvalue problem is established by applying periodic conditions, which greatly reduces the complexity associated with the formulation of eigenvalue problem especially when the intricate two-phase interaction within the poroelastic material is of significance. The predicted wavenumbers agree with those by forced response simulation with full FE simulations. The acoustic characteristics of poroelastic lined duct is analyzed based on the numerical model, which is verified by a full FE model, with emphasis on the effect of skeleton elasticity. For the structure-borne modes, a strong coupling between the fluid phase and solid phase is observed; while for the fluid-borne modes, such coupling is found to be negligible. For a poroelastic lined duct silencer, it is found that the structure-borne mode accounts for the spectral peaks in transmission loss spectrum through enhanced absorption and reflection effects. Meanwhile, the boundary condition of poroelastic material has significant effect on the structure-borne mode. In the simulated case, the change of boundary condition from fixed to rolling causes the first structure-borne mode to change from an evanescent higher-order-like mode to a propagating plane-wave-like mode in low frequency range, which affects the acoustic characteristics of the poroelastic lined silencers noticeably.

Extended Poroelasticity: An Analytical Solution and Its Application to p-Wave Propagation in Cervical Tissues

This work presents a semianalytical solution based on Laplace transform to study the behaviour of poroelastic materials in the context of the Extended Nonequilibrium Thermodynamics. In this framework, the fluid phase incorporates a relaxation time and, consequently, a frequency-dependence appears. This rheological behaviour could explain the frequency-dependence experimentally observed in biological tissues, which has traditionally attributed to the solid phase of tissues. In particular, the analytical solution is applied to two cases, heaviside and sinusoidal inputs, of a semi-infinite domain, which is filled with a material such as the human cervix. From the results, it is observed that the frequency-dependence of the fluid phase could be relevant to high relaxation times while for null relaxation times the classical poroelastic theory is recovered. Finally, the present analytical solution could be used to validate future computational codes and experimental settings.

Towards acoustic metafoams: The enhanced performance of a poroelastic material with local resonators

Acoustic foams are commonly used for sound attenuation purposes. Due to their porous microstructure, they efficiently dissipate energy through the air flowing in and out of the pores at high frequencies. However, the low frequency performance is still challenging for foams, even after optimisation of their microstructural design. A new, innovative, approach is therefore needed to further improve the acoustic behaviour of poroelastic materials. The expanding field of locally resonant acoustic metamaterials shows some promising examples where resonating masses incorporated within the microstructure lead to a significant enhancement of low frequency wave attenuation. In this paper, a combination of traditional poroelastic materials with locally resonant units embedded inside the pores is proposed, showing the pathway towards designing acoustic metafoams: poroelastic materials with properties beyond standard foams. The conceptual microstructural design of an idealised unit cell presented in this work consists of a cubic pore representing a foam unit cell with an embedded micro-resonator and filled with a viscothermal fluid (air). Analysis of complex dispersion diagrams and numerical transmission simulations demonstrate a clear improvement in wave attenuation achieved by such a microstructure. It is believed that this demonstrates the concept, which serves the future development of novel poroelastic materials.

Nanoscale Topography and Poroelastic Properties of Model Tissue Breast Gland Basement Membranes

Basement membranes (BMs) are thin layers of condensed extracellular matrix proteins serving as permeability filters, cellular anchoring sites, and barriers against cancer cell invasion. It is believed that their biomechanical properties play a crucial role in determining cellular behavior and response, especially in mechanically active tissues like breast glands. Despite this, so far, relatively little attention has been dedicated to their analysis because of the difficulty of isolating and handling such thin layers of material. Here, we isolated BMs derived from MCF10A spheroids—three-dimensional breast gland model systems mimicking in vitro the most relevant phenotypic characteristics of human breast lobules—and characterized them by atomic force microscopy, enhanced resolution confocal microscopy, and scanning electron microscopy. By performing atomic force microscopy height-clamp experiments, we obtained force-relaxation curves that offered the first biomechanical data on isolated breast gland BMs to our knowledge. Based on enhanced resolution confocal microscopy and scanning electron microscopy imaging data, we modeled the system as a polymer network immersed in liquid and described it as a poroelastic material. Finite-element simulations matching the experimental force-relaxation curves allowed for the first quantification, to our knowledge, of the bulk and shear moduli of the membrane as well as its water permeability. These results represent a first step toward a deeper understanding of the mechanism of tensional homeostasis regulating mammary gland activity as well as its disruption during processes of membrane breaching and metastatic invasion.

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions

The homogenization of a very rough three-dimensional interface separating two dissimilar isotropic poroelastic solids with time-harmonic motions was considered by Gilbert and Ou (Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: A homogenization approach. Int J Multiscale Comput Eng 2003; 1(4): 431–440). The homogenized equations have been derived; however, they are still in implicit form. In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar generally anisotropic poroelastic solids with time-harmonic motions is investigated. The main aim of the investigation is to derive homogenized equations in explicit form. By employing the homogenization method, along with the matrix formulation of the poroelasticity theory, the explicit homogenized equations have been derived. Since these equations are totally explicit, they are very useful in solving practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of the tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients are obtained. Based on these expressions, the dependence of the reflection and transmission coefficients on some parameters is examined numerically.

Effects of external and air gap flows on sound transmission through finite clamped double-panel sandwich structures

In this paper, previous theories on the prediction of sound transmission loss (STL) through a finite clamped double-panel sandwich structure lined with poroelastic material are extended to address the influence of both external and air gap flows. Biot’s theory is employed to describe wave propagation in poroelastic material. The clamped boundary condition along the panel edge introduces the modal superposition theory and a double Fourier series solution for the STL is obtained by employing the weighted residual (Galerkin) method. The analytical model is validated against theoretical results of a single incident wave under normal and oblique incidences. Various parameters such as flow velocity and gap flow orientations are considered. The numerical results suggest that the STL performance can be enhanced dramatically below the fundamental (1,1) resonance frequency with the increasing gap flow Mach numbers. Opposite orientation of air gap flows further improve the STL in the low-frequency range, and reduces the limiting angle of incidence which can trigger total internal reflection across the panel system. Although the air gap flows have less influence than the external flow, their noticeable effects on the STL show the potential in active/passive noise control.

Spontaneous buckling of contractile poroelastic actomyosin sheets

Shape transitions in developing organisms can be driven by active stresses, notably, active contractility generated by myosin motors. The mechanisms generating tissue folding are typically studied in epithelia. There, the interaction between cells is also coupled to an elastic substrate, presenting a major difficulty for studying contraction induced folding. Here we study the contraction and buckling of active, initially homogeneous, thin elastic actomyosin networks isolated from bounding surfaces. The network behaves as a poroelastic material, where a flow of fluid is generated during contraction. Contraction starts at the system boundaries, proceeds into the bulk, and eventually leads to spontaneous buckling of the sheet at the periphery. The buckling instability resulted from system self-organization and from the spontaneous emergence of density gradients driven by the active contractility. The buckling wavelength increases linearly with sheet thickness. Our system offers a well-controlled way to study mechanically induced, spontaneous shape transitions in active matter.

An Analytical Model of Tumors With Higher Permeability Than Surrounding Tissues for Ultrasound Elastography Imaging

Cancerous tissues are known to possess different poroelastic properties with respect to normal tissues. Interstitial permeability is one of these properties, and it has been shown to be of diagnostic relevance for the detection of soft tissue cancers and for assessment of their treatment. In some cases, interstitial permeability of cancers has been reported to be lower than the surrounding tissue, while in other cases interstitial permeability of cancers has been reported to be higher than the surrounding tissue. We have previously reported an analytical model of a cylindrical tumor embedded in a more permeable background. In this paper, we present and analyze a poroelastic mathematical model of a tumor tissue in cylindrical coordinate system, where the permeability of the tumor tissue is assumed to be higher than the surrounding normal tissue. A full set of analytical expressions are obtained for radial displacement, strain, and fluid pressure under stress relaxation testing conditions. The results obtained with the proposed analytical model are compared with corresponding finite element analysis results for a broad range of mechanical parameters of the tumor. The results indicate that the proposed model is accurate and closely resembles the finite element analysis. The availability of this model and its solutions can be helpful for ultrasound elastography applications such as for extracting the mechanical parameters of the tumor and normal tissue and, in general, to study the impact of poroelastic material properties in the assessment of tumors.

Time-dependent behavior of axisymmetric thermal consolidation for multilayered transversely isotropic poroelastic material

The governing equations for axisymmetric thermal consolidation of transversely isotropic poroelastic material are treated by employing Laplace–Hankel transforms to deduce the standard differential equations. Then the extended precise integration method is applied to solve the above standard differential equations. Combining with the continuity conditions and the boundary conditions, the solution in the transformed domain can be achieved. The actual solution can be acquired by inverting the integral transformations. Several numerical examples are provided to examine the accuracy of the theory and to discuss the effects of the properties of materials and the stratification on the time-dependent behavior of thermal consolidation for multilayered transversely isotropic poroelastic material.

Radial vibrations of an infinitely long poroelastic composite hollow circular cylinder

The problem of radial vibrations of an infinitely long poroelastic composite hollow circular cylinder is solved by employing Biot’s theory of wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each poroelastic material as homogeneous and isotropic. The boundaries of composite hollow poroelastic cylinder are free from stress. The frequency equations of radial vibrations of poroelastic composite hollow cylinder with rigid core, poroelastic composite solid cylinder, poroelastic composite solid cylinder with rigid casing and of rigid core and poroelastic composite bore are derived as particular cases. Non-dimensional frequency is computed as a function of ratio of thickness to inner radius of core. The results are presented graphically for two types of poroelastic composite cylinders and then discussed.Keywords:Radial vibrations, Poroelasticity, Composite cylinder, Frequency, Rigid.

The effect of nature of porous material on diffuse field acoustic transmission of the sandwich aerospace composite doubly curved shell

This paper investigates a diffuse acoustic field to analyze the wave propagation on infinite doubly curved laminated composite shell sandwiching a porous material which is extensively used in aerospace structures. In fact, the main goal is to study the influence of embedded porous core on Sound Transmission Loss (STL) of the structure. Accordingly, Biot's theory is employed to model the poroelastic material which considers three types of wave propagation including two compression and one shear terms. In addition, Shear Deformation Shallow Shell Theory (SDSST) is applied to derive the wave propagation through double-walled laminated composite shell. Moreover, a numerical process is prepared to investigate a random incidence STL in a diffuse acoustic field which results in presenting the Limiting angle of incidence in which no incident wave is transmitted through structure. Then, in order to show the accuracy and the reliability of the present results, some comparisons are made between the achieved results and those of analytical as well as experimental results available in literature. Besides, the importance of using porous material as a core has been presented. Finally, some effective parameters have been studied in numerical results to inspect the insulation property of the current composite structure.

Additional Sound Absorption Within a Poroelastic Lamella Network Under Oblique Incidence

To tackle the lack of efficiency of passive sound absorbing treatments in the low frequency range, a specific arrangement of a poroelastic material is proposed. Compared with the usual uniform layout, giving a lamella network structure to a material provides additional sound absorption below the quarter wavelength resonance frequency at oblique incidence. This is demonstrated experimentally on a sample made of melamine foam lamellas. A numerical approach that incorporates geometric periodicity highlights the mechanisms involved in this additional dissipation, achieved by combining structural and viscous dissi-pation within the lamellas. The shear and bending resonances of the lamellas can be excited at oblique incidence. The frequency of the shear resonance is related to the thickness of the sample, whereas the bending resonance is also a function of the width of the lamellas. These simple dimensional parameters allow adjustable tuning of the associated frequencies at which additional sound absorption can be obtained.

An analytical poroelastic model for laboratorial mechanical testing of the articular cartilage (AC)

The articular cartilage (AC) can be seen as a biphasic poroelastic material. The cartilage deformation under compression mainly leads to an interstitial fluid flow in the porous solid phase. In this paper, an analytical poroelastic model for the AC under laboratorial mechanical testing is developed. The solutions of interstitial fluid pressure and velocity are obtained. The results show the following facts. (i) Both the pressure and fluid velocity amplitudes are proportional to the strain loading amplitude. (ii) Both the amplitudes of pore fluid pressure and velocity in the AC depend more on the loading amplitude than on the frequency. Thus, in order to obtain the considerable fluid stimulus for the AC cell responses, the most effective way is to increase the loading amplitude rather than the frequency. (iii) Both the interstitial fluid pressure and velocity are strongly affected by permeability variations. This model can be used in experimental tests of the parameters of AC or other poroelastic materials, and in research of mechanotransduction and injury mechanism involved interstitial fluid flow.

Fast mean and variance computation of the diffuse sound transmission through finite-sized thick and layered wall and floor systems

A method is developed for computing the mean and variance of the diffuse field sound transmission loss of finite-sized layered wall and floor systems that consist of solid, fluid and/or poroelastic layers. This is achieved by coupling a transfer matrix model of the wall or floor to statistical energy analysis subsystem models of the adjacent room volumes. The modal behavior of the wall is approximately accounted for by projecting the wall displacement onto a set of sinusoidal lateral basis functions. This hybrid modal transfer matrix-statistical energy analysis method is validated on multiple wall systems: a thin steel plate, a polymethyl methacrylate panel, a thick brick wall, a sandwich panel, a double-leaf wall with poro-elastic material in the cavity, and a double glazing. The predictions are compared with experimental data and with results obtained using alternative prediction methods such as the transfer matrix method with spatial windowing, the hybrid wave based-transfer matrix method, and the hybrid finite element-statistical energy analysis method. These comparisons confirm the prediction accuracy of the proposed method and the computational efficiency against the conventional hybrid finite element-statistical energy analysis method.

Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics

In this study, a poroviscoelastic finite element model (FEM) was developed and used in conjunction with an AFM-based wide-bandwidth nanorheology system to predict the frequency-dependent mechanical behavior of tendon and dermis subjected to compression via nanoindentation. The aim was to distinguish between loading rates that are dominated by either poroelasticity, viscoelasticity, or the superposition of these processes. Using spherical probe tips having different radii, the force and tip displacement were measured and the magnitude, E∗, and phase angle, ϕ, of the dynamic complex modulus were evaluated for mouse supraspinatus tendon and mouse dermis. The peak frequencies of the phase angle were associated with the characteristic time constants of poroelastic and viscoelastic material behavior. The developed FE model could predict the separate poroelastic and viscoelastic responses of these soft tissues over a 4 decade frequency range, showing good agreement with experimental results. We observed that poroelasticity was the dominant energy dissipation mechanism for mouse dermis and supraspinatus tendon at higher indentation frequencies (102 to 104 Hz) whereas viscoelasticity was typically dominant at lower frequencies (<102 Hz). These findings show the underlying mechanical behavior of biological connective tissues and give insight into the role played by these different energy dissipation mechanisms in governing the function of these tissues at nanoscale. Statement of SignificanceSoft biological tissues exhibit complex, load- and time-dependent mechanical behavior. Evaluating their mechanical behavior requires sophisticated experimental tools and numerical models that can capture the fundamental mechanisms governing tissue function. Using an Atomic-force-microscopy-based rheology system and finite element models, the roles of the two most dominant time-dependent mechanisms (poroelasticity and viscoelasticity) that govern the dynamic loading behavior of mouse skin and tendon have been investigated. FE models were able to predict and quantify the contribution of each mechanism to the overall dynamic response and confirming the presence of these two distinct mechanisms in the mechanical response. Overall, these results provide novel insight into the viscoelastic and poroelastic properties of mouse skin and tendon and promote better understanding of the underlying origins of each mechanism.

Quasi-static thermal analyses of layered compressible poroelastic materials with a finite depth or half-space

• The Laplace–Fourier transforms are applied to reduce partial differential equations to ordinary ones. • An extended precise integration solution of multilayered materials due to a heat source is derived. • The actual solution in the physical domain is further solved by inverting the Laplace-Fourier transforms. • The effects of compressible constituents and layered characteristic on thermal consolidation are investigated. Quasi-static thermal analyses of layered compressible poroelastic materials with a finite depth or half-space caused by a heat source are carried out via extending the precise integration method in this study. The Laplace-Fourier transforms are applied to reduce partial differential equations of three-dimensional coupled thermo-hydro-mechanical problem to ordinary ones in the transform domain. By means of the precise integration method, a precise solution of layered materials induced by a heat source is deduced, and then, the previous ordinary differential equations are solved by substituting these equations into the extended precise integration solution. The actual solution is solved by applying the Laplace–Fourier inverse transforms. And lastly, numerical computations are performed to validate the method, and to analyze the effects of compressible constituents and layered characteristic as well as the heat source's half-life on thermal consolidation.

An analytical poroelastic model for ultrasound elastography imaging of tumors

The mechanical behavior of biological tissues has been studied using a number of mechanical models. Due to the relatively high fluid content and mobility, many biological tissues have been modeled as poroelastic materials. Diseases such as cancers are known to alter the poroelastic response of a tissue. Tissue poroelastic properties such as compressibility, interstitial permeability and fluid pressure also play a key role for the assessment of cancer treatments and for improved therapies. At the present time, however, a limited number of poroelastic models for soft tissues are retrievable in the literature, and the ones available are not directly applicable to tumors as they typically refer to uniform tissues. In this paper, we report the analytical poroelastic model for a non-uniform tissue under stress relaxation. Displacement, strain and fluid pressure fields in a cylindrical poroelastic sample containing a cylindrical inclusion during stress relaxation are computed. Finite element simulations are then used to validate the proposed theoretical model. Statistical analysis demonstrates that the proposed analytical model matches the finite element results with less than 0.5% error. The availability of the analytical model and solutions presented in this paper may be useful to estimate diagnostically relevant poroelastic parameters such as interstitial permeability and fluid pressure, and, in general, for a better interpretation of clinically-relevant ultrasound elastography results.

Development of boundary-element time-step scheme in solving 3D poroelastodynamics problems

The development of time-step boundary-element scheme for the three dimensional boundaryvalue problems of poroelastodynamics is presented. The poroelastic continuum is described using Biot’s mathematical model. Poroelastic material is assumed to consist of a solid phase constituting an elastic formdefining skeleton and carrying most of the loading, and two fluid phases filling the pores. Dynamic equations of the poroelastic medium are written for unknown functions of displacement of the elastic skeleton and pore pressures of the filling materials. Green’s matrices and, based on it, boundary integral equations are written in Laplace domain. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. Boundary element scheme is based on time-step method of numerical inversion of Laplace transform. A modification of the time-step scheme on the nodes of Runge-Kutta methods is considered. The Runge-Kutta scheme is exemplified with 2-and 3-stage Radau schemes. The results of comparing the two schemes in analyzing a numerical example are presented.