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Due to the widespread applications of sector circular plates in aerospace engineering, this study presents an analysis of the stability and instability of multi-directional functionally graded (MD-FG) sector circular plates with magneto/electrorheological cores under aerodynamic pressures. The system, modeled as a poroelastic system due to porous media, incorporates Krumhaar's modified supersonic piston theory to model the aerodynamic stiffness and damping matrices. To enhance result accuracy, Series-Fourier expansion is applied to two-dimensional displacement fields. Numerical dynamic stability analysis of sandwich sector circular plates is conducted using the mesh-free radial point interpolation method, which employs a radial basis function without adaptive parameters. The accuracy of the results is confirmed by comparing them with outcomes from other literature. The 3D model demonstrates high accuracy in predicting flutter phenomena and supersonic vibrations of MD-FG sector circular plates under aerodynamic pressures, with significant computational cost reduction. Additionally, the study highlights the influential factors affecting dynamic stability/instability, such as MD-FG power index, radius ratio, boundary conditions, poroelastic media, geometry, Mach number, air yaw angle, aerodynamic pressure, and Biot's coefficient. Notably, the critical Mach number is found to increase with decreasing grading indices, thereby enhancing structure stability. [ABSTRACT FROM AUTHOR]

Purpose: The current research examines the thermoelastic interactions in a homogeneous isotropic microstretch saturated porous solid with temperature dependent properties, caused by a mechanical load acting on the surface of the medium. The problem is treated based on Green-Naghdi theory of thermoelasticity without energy dissipation. Methods: Normal mode technique is applied to derive the exact expressions for different field variables such as displacement components, stresses, temperature, pore pressure and microstress tensor. Numerical computations have been performed with the help of MATLAB software, to depict the response of applied mechanical source in the medium for isothermal boundary. Results and conclusions: The effects of time, microstretch parameter, porosity and temperature dependent properties on the field variables are depicted graphically. The numerical results are found to be in close agreement with the theoretical ones. Some special cases of interest have also been presented. Although, studies in the context of generalized microstretch thermoelasticity do exist, little work with respect to temperature dependent properties in microstretch saturated poro-thermoelastic medium can be found in the open domain. Consequently, the systematic framework of microstretch thermoelasticity with poroelastic structure is at present incomplete. The motivation behind this investigation is to address these deficiencies and that the results obtained are advantageous to researchers involved in engineering, material science, geophysics and rock mechanics. [ABSTRACT FROM AUTHOR]

Investigation of hydromechanical behavior of fluid-saturated tight rock is motivated by the need to quantify the effect of changes of fluid pressure p and mean stress P on rock deformation, hydrothermal fluid, and mass transport. In particular, hydromechanical properties of low porosity crystalline rock are required for analysis of geological processes including areal hydration or dehydration, mineral weathering, and fault mechanics. In this study, poroelastic parameters – drained bulk modulus K, and Biot coefficient α – governing the volumetric response of Westerly blue granite, a typical crystalline rock of low porosity are measured. Three additional hydromechanical properties, unjacketed bulk modulus K s ′ , expansion modulus H, and permeability k, are also measured. For the Terzaghi effective mean stress of 1.0 < P′ = P - p < 25.0 MPa, the unjacketed bulk modulus K s ′ = 57.5 GPa is constant within the range of mean stresses investigated but other poroelastic coefficients exhibit effective mean stress dependency; the ranges are 13.2 < K < 32.3 GPa, 19.0 < H < 60.0 GPa, 0.83 > α > 0.38, and 20 > k > 5 nanodarcy. The agreement between poroelastic coefficients determined from various methods suggests that the underlying linear elastic assumption in Biot's theory of poroelasticity is applicable to Westerly blue granite over small increments of effective mean stress. Highlights: A procedure for saturation of tight, low-porosity rock is illustrated. Biot coefficient, unjacketed, expansion, and drained bulk moduli are measured and verified using different approaches. [ABSTRACT FROM AUTHOR]

For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As the main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics. [ABSTRACT FROM AUTHOR]

Cellular contractility, migration, and extracellular matrix (ECM) mechanics are critical for a wide range of biological processes including embryonic development, wound healing, tissue morphogenesis, and regeneration. Even though the distinct response of cells near the tissue periphery has been previously observed in cell-laden microtissues, including faster kinetics and more prominent cell-ECM interactions, there are currently no models that can fully combine coupled surface and bulk mechanics and kinetics to recapitulate the morphogenic response of these constructs. Mailand et al. (Biophys J 117(5):975–986, 2019) had shown the importance of active elastocapillarity in cell-laden microtissues, but modeling the distinct mechanosensitive migration of cells on the periphery and the interior of highly deforming tissues has not been possible thus far, especially in the presence of active elastocapillary effects. This paper presents a framework for understanding the interplay between cellular contractility, migration, and ECM mechanics in dynamically morphing soft tissues accounting for distinct cellular responses in the bulk and the surface of tissues. The major novelty of this approach is that it enables modeling the distinct migratory and contractile response of cells residing on the tissue surface and the bulk, where concurrently the morphing soft tissues undergo large deformations driven by cell contractility. Additionally, the simulation results capture the changes in shape and cell concentration for wounded and intact microtissues, enabling the interpretation of experimental data. The numerical procedure that accounts for mechanosensitive stress generation, large deformations, diffusive migration in the bulk and a distinct mechanism for diffusive migration on deforming surfaces is inspired from recent work on bulk and surface poroelasticity of hydrogels involving elastocapillary effects, but in this work, a two-field weak form is proposed and is able to alleviate numerical instabilities that were observed in the original method that utilized a three-field mixed finite element formulation. [ABSTRACT FROM AUTHOR]

We propose a frequency-domain finite-element (FDFE) method to model the 2-D P–SV waves propagating in porous media. This specific finite-element method (FEM) is based on the framework of variational principles, which differs from previously widely used FEMs that rely on the weak formulations of the governing equations. By applying the calculus of variations, we establish the equivalence between solving the stress–strain relations, equations of motion and boundary conditions that govern the propagation of P–SV waves, and determining the extremum or stationarity of a properly defined functional. The structured rectangular element is utilized to partition the entire computational region. We validate the FDFE method by conducting a comparison with an analytically-based method for models of a horizontal planar contact of two poroelastic half-spaces, and a poroelastic half-space with a free surface. The excellent agreements between the analytically-based solutions and the FDFE solutions indicate the effectiveness of the FDFE method in modelling the poroelastic waves. Modelling results manifest that both propagative and diffusive natures of the Biot slow P wave can be effectively modelled. The proposed FDFE method simulates wavefields in the frequency domain, allowing for easy incorporation of frequency-dependent parameters and enabling parallel computational capabilities at each frequency point (sample). We further employ the developed FDFE method to model two simplified poroelastic reservoirs, one with gas-saturated sandstone and the other with oil-saturated sandstone. The results suggest that changing the fluid phase of the sandstone reservoir from gas to oil can substantially impact the recorded solid and relative fluid–solid displacements. The modelling suggests that the proposed FDFE algorithm is a useful tool for studying the propagation of poroelastic waves. [ABSTRACT FROM AUTHOR]

In this work, we investigate the poroelastic waves by solving the time‐domain Biot‐JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson‐Koplik‐Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time‐domain Biot‐JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative Chebyshev approximation of the square‐root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge‐Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider a locking-free numerical method for the poroelasticity-Forchheimer problem, which exists locking phenomenon when directly using the continuous Galerkin mixed finite element method (MFEM) to be solved due to the influence of special physical parameters. To overcome the locking phenomenon, we reformulate the original problem into a new problem by introducing some new variables. The new problem can be taken as a Stokes-diffusion coupled model, which exists a built-in mechanism to circumvent the locking phenomenon for continuous Galerkin MFEM. Moreover, we prove the existence and uniqueness of weak solution with the help of a priori error estimate, some invariant quantities and the discussion on nonlinear term. After that, we propose a fully discrete numerical scheme to solve the reformulated problem, where the DL-scheme and L-scheme are designed to deal with the nonlinear term, and prove the optimal convergence in both time and space. Finally, numerical tests are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Numerical investigation of wave propagation in transversely isotropic poroelastic half‐space with the use of a new stretched coordinate system through the Meshless Local Petrov–Galerkin (MLPG) formulation is presented in this paper. To this end, the u−p formulation of Biot is adopted as the framework of the porous media. One approach to numerically solve the infinite domain problems is the use of an absorber layer in which the whole half‐space is divided into two parts, that is (i) a finite part, in which the responses are interested, and (ii) the remaining semi‐infinite part, which is replaced by a Perfectly Matched Layer (PML). The stretched coordinates in the PML are introduced in such a way that the wave propagating in it does not generate spurious reflection to the finite part. Comparing the numerical results with some existing exact solutions and evaluating the norm of error demonstrate that the response functions in the finite part are achievable as precise as desired. Some new results are also presented which show the validity of the numerical approach in poroelastic transversely isotropic domain. [ABSTRACT FROM AUTHOR]

We develop a computational algorithm based on a diffuse interface approach to study the design of bioartificial organ scaffold architectures. These scaffolds, composed of poroelastic hydrogels housing transplanted cells, are linked to the patient's blood circulation via an anastomosis graft. Before entering the scaffold, the blood flow passes through a filter, and the resulting filtered blood plasma transports oxygen and nutrients to sustain the viability of transplanted cells over the long term. A key issue in maintaining cell viability is the design of ultrafiltrate channels within the hydrogel scaffold to facilitate advection-enhanced oxygen supply ensuring oxygen levels remain above a critical threshold to prevent hypoxia. In this manuscript, we develop a computational algorithm to analyze the plasma flow and oxygen concentration within hydrogels featuring various channel geometries. Our objective is to identify the optimal hydrogel channel architecture that sustains oxygen concentration throughout the scaffold above the critical hypoxic threshold. The computational algorithm we introduce here employs a diffuse interface approach to solve a multi-physics problem. The corresponding model couples the time-dependent Stokes equations, governing blood plasma flow through the channel network, with the time-dependent Biot equations, characterizing Darcy velocity, pressure, and displacement within the poroelastic hydrogel containing the transplanted cells. Subsequently, the calculated plasma velocity is utilized to determine oxygen concentration within the scaffold using a diffuse interface advection-reaction-diffusion model. Our investigation yields a scaffold architecture featuring a hexagonal network geometry that meets the desired oxygen concentration criteria. Unlike classical sharp interface approaches, the diffuse interface approach we employ is particularly adept at addressing problems with intricate interface geometries, such as those encountered in bioartificial organ scaffold design. This study is significant because recent developments in hydrogel fabrication make it now possible to control hydrogel rheology and utilize computational results to generate optimized scaffold architectures. Author summary: Bioartificial organ is an engineered device made of living cells and a biocompatible scaffold that can be implanted or integrated into a human body to replace a natural organ, or to augment a specific organ function. The biocompatible scaffold serves as the structural foundation, embedding cells and growth factors to form substitute tissue. A key challenge in bioartificial organ design is ensuring the long-term survival of transplanted cells. Specifically, a critical challenge is creating a hydrogel architecture with ultrafiltrate channels that act as pathways to deliver oxygen and nutrients to the cells, supporting their sustained viability. In this work, we developed a mathematical and computational framework to investigate optimal hydrogel architecture and oxygen supply to transplanted cells. Our findings show that a hexagonal channel architecture significantly outperforms both the commonly used vertical channels and branching channel designs, providing a substantial increase in oxygen delivery to the cells. In the hexagonal architecture, oxygen concentration remains above the critical threshold for hypoxia throughout the scaffold, which is not achieved with other designs. This is particularly important given recent advances in hydrogel fabrication, allowing for precise control of hydrogel elasticity and rheology, making these results valuable for developing improved scaffold designs. [ABSTRACT FROM AUTHOR]

Extracellular matrix (ECM) viscoelasticity broadly regulates cell behavior. While hydrogels can approximate the viscoelasticity of native ECM, it remains challenging to recapitulate the rapid stress relaxation observed in many tissues without limiting the mechanical stability of the hydrogel. Here, we develop macroporous alginate hydrogels that have an order of magnitude increase in the rate of stress relaxation as compared to bulk hydrogels. The increased rate of stress relaxation occurs across a wide range of polymer molecular weights (MWs), which enables the use of high MW polymer for improved mechanical stability of the hydrogel. The rate of stress relaxation in macroporous hydrogels depends on the volume fraction of pores and the concentration of bovine serum albumin, which is added to the hydrogels to stabilize the macroporous structure during gelation. Relative to cell spheroids encapsulated in bulk hydrogels, spheroids in macroporous hydrogels have a significantly larger area and smaller circularity because of increased cell migration. A computational model provides a framework for the relationship between the macroporous architecture and morphogenesis of encapsulated spheroids that is consistent with experimental observations. Taken together, these findings elucidate the relationship between macroporous hydrogel architecture and stress relaxation and help to inform the design of macroporous hydrogels for materials-based cell therapies. [ABSTRACT FROM AUTHOR]

Fluid injection can induce seismicity by altering stresses on pre‐existing faults. Here, we investigate minimizing induced earthquake potential by optimizing injection operations in a physics‐based forecasting framework. We built a 3D finite element model of the poroelastic crust for the Raton Basin, Central US, and used it to estimate time dependent Coulomb stress changes due to ∼ ${\sim} $25 years of wastewater injection in the region. Our finite element model is complemented by a statistical analysis of the seismogenic index (SI), a proxy for critically stressed faults affected by variations in the pore pressure. Forecasts of seismicity rate from our hybrid physics‐based statistical model suggest that induced seismicity in the Raton Basin, from 2001 to 2022, is still driven by wastewater injection despite declining injection rates since 2011. Our model suggests that pore pressure diffusion is the dominant cause of Coulomb stress changes at seismogenic depth, with poroelastic stress changes contributing about 5% to the driving force. Linear programming optimization for the Raton Basin reveals that it is feasible to reduce earthquake potential for a given amount of injected fluid (safety objective) or maximize fluid injection for a prescribed earthquake potential (economic objective). The optimization tends to spread out high‐rate injectors and shift them to regions of lower SI. The framework has practical importance as a tool to manage injection rate per unit field area to reduce induced earthquake potential. Our optimization framework is both flexible and adaptable to mitigate induced earthquake potential in other regions and for other types of subsurface fluid injection. Plain Language Summary: The Raton Basin, in the central United States, has had a remarkable increase in seismicity coincident with large wastewater injection since 2001. This seismicity primarily occurs at depths greater than several kilometers where preexisting faults in the crystalline basement are reactivated by increasing pore pressure due to fluid diffusion. The spatial extent and rate of the induced earthquakes can inform earthquake probability maps which display the probability of an earthquake occurrence within a specific time period. We use the physics‐based and statistical models to develop an optimization framework that may help inform well operations. The proposed method allows for the maximization of injected fluid (the economic objective) and the reduction of earthquake potential (the safety objective). Key Points: Poroelastic and statistical model suggests induced seismicity in Raton Basin is still primarily driven by wastewater injectionOptimization reduces earthquake potential for a given amount of injected fluid or maximizes injection for a prescribed earthquake potentialOptimization tends to spread out higher rate injection wells and may be a useful tool to reduce basin‐scale induced earthquake potential [ABSTRACT FROM AUTHOR]

Axisymmetric contact problems on the interaction of a rigid stamp and a poroelastic layer, the bottom boundary of which is located on a Winkler base, were considered based on the equations of the Cowin–Nunziato theory of poroelastic bodies. It was assumed that the base of the cylindrical stamp has the flat or parabolic shape and there is no friction in the contact area. With the help of the Hankel integral transformation, the problems posed were reduced to the integral equations for an unknown contact stresses, which were solved with the use of the collocation methods, while the transformants of the kernels of the integral equations were obtained in explicit form. The values of contact stresses and size of the contact area in the case of the parabolic stamp were determined. The relationship, which is one of the main characteristics, when determining the mechanical parameters of a material by the indentation method, between the force acting on the stamp and its displacement, was studied. A comparative analysis of the studied quantities for various values of the poroelastic parameters and the coefficient of subgrade resistance of the Winkler base was carried out. The model of contact interaction considered and the solution obtained can be used in calculation of the structures foundations located on ground bases. [ABSTRACT FROM AUTHOR]

Malignant brain tumours represent a significant medical challenge due to their aggressive nature and unpredictable locations. The growth of a brain tumour can result in a mass effect, causing compression and displacement of the surrounding healthy brain tissue and possibly leading to severe neurological complications. In this paper, we propose a multiphase mechanical model for brain tumour growth that quantifies deformations and solid stresses caused by the expanding tumour mass and incorporates anisotropic growth influenced by brain fibres. We employ a sharp interface model to simulate localised, non-invasive solid brain tumours, which are those responsible for substantial mechanical impact on the surrounding healthy tissue. By using patient-specific imaging data, we create realistic three-dimensional brain geometries and accurately represent ventricular shapes, to evaluate how the growing mass may compress and deform the cerebral ventricles. Another relevant feature of our model is the ability to simulate therapeutic protocols, facilitating the evaluation of treatment efficacy and guiding the development of personalized therapies for individual patients. Overall, our model allows to make a step towards a deeper analysis of the complex interactions between brain tumours and their environment, with a particular focus on the impact of a growing cancer on healthy tissue, ventricular compression, and therapeutic treatment. [ABSTRACT FROM AUTHOR]

A high-precision and high-resolution vertical velocity for the Chinese mainland is obtained by integrating precise levelling and Global Navigation Satellite System data, using a Helmert joint adjustment method. The results show that the surface vertical rates range between −3.0 and 3.9 mm yr−1 with continuous deformation in most areas, except the obvious subsidence at the rates of −15.0 to −94.2 mm yr−1 induced by groundwater exploitation in the North China Plain. Particularly, the central and southern Tibet, Tien Shan, Alashan, Ordos, eastern Cathaysia and Northeast China uplift at the rates of 0.5–3.9 mm yr−1; the southeastern Tibetan Plateau, Sichuan basin and Yangtze block are dominated by surface subsidence at the rates of −3.3 to −0.5 mm yr−1. Furthermore, the vertical rates vary little between the eastern and western regions of the Chinese mainland despite their pronounced differences in horizontal deformations. The effects of gravity isostasy and non-tectonic factors, including the environmental mass loads, Glacier Isostatic Adjustment (GIA), poroelastic expansion/compression, and mining operations have partially contributed to the vertical deformation of the Chinese mainland. Overall, this velocity reflects the complicated deformation features induced by the multiple geodynamic processes of the Chinese mainland. These geodynamic processes include isostasy, orogenic processes and geothermal anomalies associated with slab subduction/plate collision. [ABSTRACT FROM AUTHOR]

Adsorption and capillarity, in the order of high free energy to low, are the two soil–water interaction mechanisms controlling the hydro-mechanical behaviour of soils. Yet most of the poroelasticity theories of soil are based on capillarity only, leading to misrepresentations of hydro-mechanical behaviour in the low free energy regime beyond vaporisation. This inability is reasoned to be caused by two major limitations in the existing theories: missing interparticle attraction energy and incomplete definition of adsorption-induced pore-water pressure. A poroelasticity theory is formulated to incorporate the two soil–water interaction mechanisms, and the transition between them – that is, condensation/vaporisation, by expanding the classical three-phase mixture system to a four-phase mixture system with adsorptive water as an additional phase. An interparticle attractive stress is identified as one of the key sources for deformation and strength of soils induced by adsorption and is implemented in the poroelasticity theory. A recent breakthrough concept of soil sorptive potential is utilised to establish the physical link between adsorption-induced pore-water pressure and matric suction. The proposed poroelasticity theory can be reduced to several previous theories when interparticle attractive stress is ignored. The new theory is used to derive the effective stress equation for variably saturated soil by identifying energy-conjugated pairs. The derived effective stress equation leads to Zhang and Lu's unified effective stress equation, and can be reduced to Bishop's effective stress equation when only the capillary mechanism is considered and to Terzaghi's effective stress equation when a saturated condition is imposed. The derived effective stress equation is experimentally validated for a variety of soil in the full matric suction range, substantiating the validity and accuracy of the poroelasticity theory for soil under variably saturated conditions. [ABSTRACT FROM AUTHOR]

Understanding the dynamic behavior of poroelastic soil adjacent to an axially vibrating pile is crucial to the seismic design and vibration reduction of various geotechnical engineering projects; however, few analytical studies exist on this issue to this point. In this study, to obtain the dynamic response of fully saturated soil around and beneath a vibrating pile, the solving scheme of the pile-fictitious soil pile (FSP) coupled model is extended to the pile-porous FSP coupled model and surrounded by multiple poroelastic medium layers with finite thickness. The semianalytical solutions of the pile-porous FSP-saturated soil-coupled vibration system are resolved and verified by existing solutions under different degradation situations. The developed model and the solutions are then employed to investigate the wave propagation mechanism in the fully saturated soil. The results show a certain degree of hysteresis in the fluid phase response during the vibration. As the permeability of the poroelastic material decreases, the hysteresis effect of the fluid phase relative to the solid phase weakens, resulting in an increase in excess pore-fluid pressure and a wider range of influence from the vibration. The conclusions derived from this study can also provide practical guidance for pile testing techniques, such as the parallel seismic (PS) method and low-strain pile integrity test (PIT) onsite. [ABSTRACT FROM AUTHOR]

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring). [ABSTRACT FROM AUTHOR]

Poroelastic coupling between fractures and the surrounding rock is important to numerous applications in geosciences. We measure the in‐situ fluid pressure and local strain response of a fractured carbonate sample to hydrostatic pressure oscillations. A linear poroelastic model that represents the rock sample is parameterized using X‐ray imaging and ultrasonic wave transmission measurements. The numerical solution, based on Biot's quasistatic equations, is consistent with the measured frequency dependent dispersion of the apparent bulk modulus of the background matrix and the in‐situ pore pressure response, which is caused by fluid pressure diffusion from the compliant fractures into the stiffer matrix. The observed fluid pressure diffusion is causally related to the numerically quantified intrinsic attenuation at seismic frequencies, which is a major contributor to the dissipation of seismic waves. Our analysis supports the use of a simple approximation of fractures as compliant and planar inclusions in numerical simulations based on linear poroelasticity. Plain Language Summary: Fractures control the flow of fluids through rocks as well as their mechanical properties. Finding ways to accurately simulate coupled hydro‐mechanical processes in fractured rock is important to a variety of applications in geosciences (e.g., subsurface storage of carbon dioxide or enhanced geothermal energy extraction). Physics‐based simulations require accurate parameterization and validation against experiments. In our experiment on a fluid saturated fractured rock sample, we applied an oscillating confining pressure to the sample and measured the corresponding deformation and the change in the pore fluid pressure in a fracture and the porous matrix. By adjusting the frequency of the oscillations, we observed a divergence in the pore pressure amplitude in the fracture and the matrix, which is a consequence of flow from the fracture into the porous matrix becoming restricted at elevated frequencies. The laboratory measurements were in close agreement with the results of our simulations, which were based on a simplified model of the rock sample. The outcome of our work supports the use of a widely applied approximation of fractures as simple planar inclusions in numerical simulations based on linear poroelasticity. Key Points: We observe the poroelastic coupling of fractures to the rock matrix in in‐situ fluid pressure measurements during stress oscillationsThe geometrically complex fractures can be modeled as compliant and planar poroelastic inclusionsThe numerically quantified intrinsic seismic (<100 Hz) attenuation is due to fluid pressure diffusion, which is experimentally observed [ABSTRACT FROM AUTHOR]

A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman coupling conditions are taken. In the inertial, linear, and non‐degenerate case, the hyperbolic‐parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes‐Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non‐standard maximality argument. The latter employs a mixed‐variational formulation in order to invoke the Babuška‐Brezzi theorem. The Lumer‐Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot‐Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the dynamics of poroelastic media using the finite element analysis based on the u‐v‐p full formulation, where u${{\bm u}}$, v${{\bm v}}$, and p denote the solid displacement, relative fluid velocity with respect to solid velocity, and pore fluid pressure. It incorporates the effect of relative fluid acceleration with respect to solid acceleration on soil dynamic response. The u${ {\bm u}}$‐v${ {\bm v}}$‐p formulation is first verified through the comparison with the analytical solution. After that, the response of one‐dimensional saturated soil column and two‐dimensional partially saturated soil layer subjected to vertical loading with different combinations of soil permeability and loading frequency are investigated using the analyses with the u${ {\bm u}}$‐v${ {\bm v}}$‐p and u${ {\bm u}}$‐p formulations, based on which the effect of relative pore fluid motion is discussed and the differences in the soil response between two kinds of analysis approaches are examined. Results reveal that the rapid fluid flow has a pronounced effect on soil dynamics and the soil with a greater degree of saturation is more sensitive to the increase of loading frequency and soil permeability. The soil dynamic response can basically be divided into two main categories that represent insignificant and significant flow motion depending on loading frequency and soil permeability. Furthermore, despite vertical loading, horizontal soil response can also be affected by the large relative pore fluid flow when loading frequency and soil permeability are large. In addition, the simplified formulation can still be applicable to predict dynamics of poroelastic media in cases with high loading frequency and low soil permeability. [ABSTRACT FROM AUTHOR]

We present a numerical method to simulate seismic wave propagation in coupled fluid and porous media. We developed a numerical finite element–based algorithm to approximate solutions to viscoacoustic and Biot's equations, considering the open pore conditions at the interfaces between both media. The algorithm architecture allows to simulate arbitrary distributions of viscoacoustic and poroelastic regions, facilitating the modelling of heterogeneous systems involving complex geometries. The algorithm includes a double parallelization scheme whose efficiency in terms of computing time and memory requirements was tested for different core distributions and mesh sizes. We validate our proposal by performing a comparison between its results and those obtained with a well‐known freely available code. We test its capabilities by studying two different scenarios with geophysical interest: a lake with an irregular bottom and a fractured porous medium. [ABSTRACT FROM AUTHOR]

Theoretical and numerical analyses are conducted to rigorously construct master curves that can be used for interpretation of displacement-controlled poroelastic spherical indentation test. A fully coupled poroelastic solution is first derived within the framework of Biot's theory using the McNamee-Gibson displacement function method. The fully saturated porous medium is assumed to consist of slightly compressible solid and fluid phases and the surface is assumed to be impermeable over the contact area and permeable everywhere else. In contrast to the cases in our previous studies with an either fully permeable or impermeable surface, the mixed drainage condition yields two coupled sets of dual integral equations instead of one in the Laplace transform domain. The theoretical solutions show that for this class of poroelastic spherical indentation problems, relaxation of the normalized indentation force is affected by material properties through weak dependence on a single-derived material constant only. Finite element analysis is then performed in order to examine the differences between the theoretical solution, obtained by imposing the normal displacement over the contact area, and the numerical results where frictionless contact between a rigid sphere and the poroelastic medium is explicitly modeled. A four-parameter elementary function, an approximation of the theoretical solution with its validity supported by the numerical analysis, is proposed as the master curve that can be conveniently used to aid the interpretation of the poroelastic spherical indentation test. Application of the master curve for the ramp-hold loading scenario is also discussed. [ABSTRACT FROM AUTHOR]

A general solution to harmonic excitation of beam-shaped specimens made from porous, fluid-saturated, transversely isotropic, and viscoelastic materials is developed and presented. The solution draws from Biot's theory of dynamic poroviscoelasticity and adopts a modification of Timoshenko beam model to account for the moment due to pore fluid pressure. Closed-form expressions for transverse displacement and rotation angle of the beam are obtained for the case of three-point bending experiments. Solutions for Rayleigh and Euler-Bernoulli beam models are recovered as special cases. Implications for possible characterization through relevant dynamic mechanical analysis testing are discussed for materials which exhibit certain anisotropy in both the mechanical and flow properties. Three timescale groups shape the dynamic response of the vibrating beam. These timescales pertain to energy dissipation rate within the solid phase, viscous flow of the pore fluid, as well as the natural frequencies of the test specimen. The interplay of a varying excitation frequency with the described timescales is shown to enable simultaneous characterization of the viscoelastic and poroelastic parameters of the specimen constitutive behavior through the obtained dynamic moduli and loss angles of beam vibrations. [ABSTRACT FROM AUTHOR]

Changes in biomechanical properties such as elasticity modulus, viscosity, and poroelastic features are linked to the health status of biological tissues. Ultrasound elastography is a non-invasive imaging tool that quantitatively maps these biomechanical characteristics for diagnostic and treatment monitoring purposes. Mathematical models are essential in ultrasound elastography as they convert the raw data obtained from tissue displacement caused by ultrasound waves into the images observed by clinicians. This article reviews the available mathematical frameworks of continuum mechanics for extracting the biomechanical characteristics of biological tissues in ultrasound elastography. Continuum-mechanics-based approaches such as classical viscoelasticity, elasticity, and poroelasticity models, as well as nonlocal continuum-based models, are described. The accuracy of ultrasound elastography can be increased with the recent advancements in continuum modelling techniques including hyperelasticity, biphasic theory, nonlocal viscoelasticity, inversion-based elasticity, and incorporating scale effects. However, the time taken to convert the data into clinical images increases with more complex models, and this is a major challenge for expanding the clinical utility of ultrasound elastography. As we strive to provide the most accurate imaging for patients, further research is needed to refine mathematical models for incorporation into the clinical workflow. [ABSTRACT FROM AUTHOR]

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver's energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware. [ABSTRACT FROM AUTHOR]

In this work, poroelastic properties of Sierra White granite namely elastic moduli, Biot's effective stress coefficient, α, and Skempton's pore pressure coefficient, B, are determined. The Biot's coefficient of this rock was determined using two different approaches. It is found that overall, the Biot's coefficient decreases from 0.77 at low effective stress (3–4 MPa) to 0.45–0.55 at high effective stress levels (30–40 MPa). Unlike the Biot's effective stress coefficient, which is related only to the solid rock, Skempton's B is a property related to both solid rock and the pore fluid. Although a single undrained hydrostatic compression test can theoretically be used to measure B, two types of laboratory tests were performed to fully reveal this parameter's behavior. In the first test, back pressure and confining pressure are increased stepwise to maintain a constant effective stress (usually very low), and Skempton's B is measured at different back pressure levels. This test reveals the Skempton's B behavior related to pore fluid compressibility, and consequently, this test can be used to evaluate if the pore fluid is free of air. In the second test, the back pressure is maintained at a constant level, and the confining pressure is increased stepwise, and then Skempton's B is determined at different confining pressure levels. This test correlates Skempton's B with effective stress. Details of the laboratory test protocol for combining these two types of tests are described and the results for Sierra White granite are provided. It is also found that the dead volume of the drainage system during the undrained compression test for the measurement of Skempton's B has an obvious impact on the measurement accuracy, with smaller dead volume yielding more accurate results. Highlights: The development of laboratory test protocol for Skempton's B measurement with consideration of both fluid and solid properties by two types of tests under two different boundary conditions. A comparison of using two different approaches to measure the Biot's effective stress coefficient. Determination of Biot's effective stress coefficient, α, and Skempton's pore pressure coefficient, B, for Sierra White granite. [ABSTRACT FROM AUTHOR]

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes. [ABSTRACT FROM AUTHOR]

In this paper, we develop two discontinuous Galerkin (DG) finite element methods to solve the linear poroelasticity in the total pressure formulation, where displacement, fluid pressure, and total pressure are unknowns. The fully-discrete standard DG and conforming DG methods are presented based on the discontinuous approximations in space and the implicit Euler discretization in time. Compared to the standard DG method with penalty terms, the conforming DG method removes all stabilizers and maintains conforming finite element formulation by utilizing weak operators defined over discontinuous functions. The two methods provide locally conservative solutions and achieve locking-free properties in poroelasticity. We also derive the well-posedness and optimal a priori error estimates, which show that our methods satisfy parameter-robustness with respect to the infinitely large Lamé constant and the null-constrained specific storage coefficient. Several numerical experiments are performed to verify these theoretical results, even in heterogeneous porous media. [ABSTRACT FROM AUTHOR]

In this work, we study the locking-free numerical method for a Barenblatt-Biot poroelastic model. When solving by the continuous Galerkin mixed finite element method, the model exists two kind of locking phenomena for special physical parameters. To overcome these locking phenomena, we introduce new variables to reformulate the original problem into a new problem, which exists a built-in mechanism to keep the continuous Galerkin mixed finite element method stable. It can be regarded as a generalized Stokes problem for two given β and η and two diffusion problems for a given δ. The generalized Stokes problem can be adopted by some stable solver and the diffusion problems can be solved by continuous Galerkin finite element. Moreover, the existence and uniqueness of weak solution is proved by using the standard Galerkin method and combining with priori estimates and some invariant quantities. After that, we design fully discrete time-stepping schemes to use mixed finite element method with P 2 − P 1 − P 1 − P 1 element pairs for space variables and backward Euler method for time variable, and analyze the coupled and decoupled time stepping methods based on the proposed scheme. The optimal convergence order is obtained in both space and time. Finally, some numerical examples are presented to show the optimal convergence rates about variables and the robustness of proposed method with respect to ν , and to verify that there is no locking phenomenon. [ABSTRACT FROM AUTHOR]

An analytical solution is presented for spherically symmetric growth of a fluid-saturated, poroelastic inhomogeneity inclusion embedded within a compressible elastoplastic matrix. A fluid source at the center causes the inclusion growth. The solution considers full poroelastic coupling of the inclusion pore fluid flow and solid phase deformation while solving for large deformation of the matrix via incremental elastoplasticity with associated flow rule and modified Mohr-Coulomb or Drucker-Prager yield models. Results obtained from the compressible (drained) solution are compared against the previously published solution pertaining to incompressible (undrained) matrix. Drained deformation is found to generally cause larger deviatoric stress, less compressive radial and hoop stresses, as well as faster growth of the plastic region, in the matrix. An example case study shows that compared with the undrained case, the drained matrix reaches the same elastoplastic strain with substantially smaller volume of injected fluid inside the embedded inclusion. The solution may be used as a proxy model of caprock integrity problem in CO2 geo-sequestration applications and further as a rigorous benchmark to verify the related numerical solvers. [ABSTRACT FROM AUTHOR]

In shallow water regions, ocean waves commonly propagate in the form of cnoidal waves, with the response induced in the seabed obviously being different from that involving conventional linear waves. Computational models of waves and seabeds were established based on cnoidal wave theory and Biot's completely dynamic consolidation theory, respectively. A semianalytical solution for the dynamic response of the multilayered, transversely isotropic (TI), poroelastic seabed induced by cnoidal waves was derived via the scalar potential function and the dual variable and position method. The reliability and accuracy of the developed semianalytical solution was verified against existing solutions and experimental data. This parametric study demonstrated that cnoidal waves have a significant effect on the dynamic response of the seabed compared to linear waves. Also, the induced pore pressure/stresses and corresponding liquefaction potential were significantly affected by the anisotropy and layering of the seabed material. The newly developed solution can serve as a useful tool for estimating the liquefaction potential of a TI and multilayered poroelastic seabed in shallow water. [ABSTRACT FROM AUTHOR]

A computational homogenization framework is proposed for solving transient wave propagation in the linear regime in heterogeneous poroelastic media that may exhibit local resonances due to microstructural heterogeneities. The microscale fluid‐structure interaction problem and the macroscale are coupled through an extended version of the Hill‐Mandel principle, leading to a variationally consistent averaging scheme of the microscale fields. The effective macroscopic constitutive relations are obtained by expressing the microscale problem with a reduced‐order model that contains the longwave basis and the so‐called local resonance basis, yielding the closed‐form expressions for the homogenized material properties. The resulting macroscopic model is an enriched porous continuum with internal variables that represent the microscale dynamics at the macroscale, whereby the Biot model is recovered as a special case. Numerical examples demonstrate the framework's validity in modeling wave transmission through a porous layer. [ABSTRACT FROM AUTHOR]

In areas of induced seismicity, earthquakes can be triggered by stress changes due to fluid injection and static deformation from fault slip. Here we present a method to distinguish between injection‐driven and earthquake‐driven triggering of induced seismicity by combining a calibrated, fully coupled, poroelastic stress model of wastewater injection with interpretation of a machine learning algorithm trained on both earthquake catalog and modeled stress features. We investigate seismicity from Paradox Valley, Colorado as an ideal test case: a single, high‐pressure injector that has induced thousands of earthquakes since 1991. Using feature importance analysis, we find that injection‐driven earthquakes are approximately 22± $\pm $5% of the total catalog but act as background events that can trigger subsequent aftershocks. Injection‐driven events also have distinct spatiotemporal clustering properties with a larger b‐value, closer proximity to the well, and earlier occurrence in the injection history. Generalization of our technique can help characterize triggering processes in other regions where induced seismicity occurs. Plain Language Summary: The Paradox Valley Unit, Colorado in the central United States has had a remarkable increase in seismicity coincident with over 8 million cubic meters of brine fluid injection since 1991, inducing thousands of earthquakes within an aquifer 4.5 km below the surface. We use a physics‐based model of the Earth combined with statistical and machine learning techniques to help discern which earthquakes are triggered by other earthquakes and which earthquakes are directly triggered by the stress changes from the well as well as their comparative characteristics. Discerning which earthquakes are directly caused from pressure changes due to the fluid injected by the well can inform our understanding of earthquake physics and provide useful information to operators of energy production sites. Key Points: Physics‐based models with interpretable machine learning can identify likely triggering mechanism of earthquakes within an induced sequenceWith this technique, we show that only 22土5% of earthquakes in Paradox Valley are primarily injection‐drivenInjection‐driven events have a larger b‐value, are closer to the well, and occur earlier in the injection history [ABSTRACT FROM AUTHOR]

AbstractThe most popular model of the bone healing considers the fracture callus as poroelastic medium. As such it requires an assumption of the callus’ external permeability. In this work a systematic study of the influence of the permeability of the callus boundary on the simulated bone healing progress is performed. The results show, that these conditions starts to play significant role with the decrease of the callus size. Typically enforced impermeability inhibits the progress of healing during simulation. A remedy for this effect is imposing drainage conditions at the callus’ boundary. [ABSTRACT FROM AUTHOR]

The Accelerated Pseudo-Transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization. With the advent of the memory-wall phenomenon around 2005, where memory access speed overtook floating-point operations as the bottleneck in high-performance computing, the APT method has gained prominence as a powerful tool for tackling various PDEs in geosciences. Recent advancements have demonstrated the APT method's computational efficiency, particularly when applied to quasi-static nonlinear problems using Graphical Processing Units (GPUs). This manuscript presents a comprehensive analysis of the APT method, focusing on its application to quasi-static elastic, viscoelastic, and coupled hydro-mechanical problems, specifically those governed by quasi-static Biot's poroelastic equations, across 1D, 2D, and 3D domains. We systematically investigate the optimal numerical parameters required to achieve rapid convergence, offering valuable insights into the method's applicability and efficiency for a range of physical models. Our findings are validated against analytical solutions, underscoring the robustness and accuracy of the APT method in both homogeneous and heterogeneous media. We explore the influence of boundary conditions, non-linearities, and coupling on the optimal convergence parameters, highlighting the method's adaptability in addressing complex and realistic scenarios. To demonstrate the flexibility of the APT method, we apply it to the nonlinear mechanical problem of strain localization using a poro-elasto-viscoplastic rheological model, achieving extremely high resolutions – 10,0002 voxels in 2D and 5123 voxels in 3D – that, to our knowledge, have not been previously explored for such models. Our study contributes significantly to the field by providing a robust framework for the effective implementation of the APT method in solving challenging geophysical problems. Importantly, the results presented in this paper are fully reproducible, with Matlab, symbolic Maple scripts, and CUDA C codes made available in a permanent repository. [ABSTRACT FROM AUTHOR]

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration. [ABSTRACT FROM AUTHOR]

This research delves into the radial vibrations of dissipative poroelastic spherical shells, which are embedded within an elastic foundation and subjected to rotational dynamics. The analysis identifies that the inclusion of dissipative effects gives rise to a transcendental, complex-valued frequency equation. A numerical approach, specifically the bisection method, is employed in MATLAB for solution derivation. In instances where the argument is relatively small, the study leverages the asymptotic expansions of Bessel functions, facilitating the bifurcation of the frequency equation into two distinct real-valued equations. These equations are instrumental in computing the natural frequency as a function of the shell's thickness. Furthermore, the research rigorously examines how rotational forces influence the natural frequency. The culmination of this study is presented through a series of graphical depictions, which succinctly illustrate the impact of rotational dynamics on the radial vibrations of thick-walled hollow structures situated in various elastic media. The overall findings contribute significantly to our understanding of the behavior of poroelastic materials in rotational environments, with implications for both theoretical and practical applications in material science and engineering. The results can benefit the theoretical development of orthopedic study projects connected to spherical poroelastic medium. [ABSTRACT FROM AUTHOR]

The most significant and protracted phase of the installation of a dental prosthesis is osseointegration of a metal implant with bone tissue. It is important to accelerate this process, for example, by the use of extracorporeal shock wave therapy. The objective of this study is to investigate numerically the conditions for osseointegration of the implant in the dental region employing a poroelastic model implemented in the movable cellular automaton method. The mandibular segment under consideration includes a spongy tissue covered with a cortical layer 600 μm thick and a gum 400 μm thick. Additionally, the second premolar and second molar exhibited periodontal membranes of their roots, while the implant of the first molar was situated within a shell of soft fibrous tissue. The obtained fields of hydrostatic pressure and interstitial fluid pressure were analyzed according to the mechanobiological principles. The results obtained have indicated that shock wave therapy has a beneficial impact on the creation of conditions conducive to the differentiation and transfer of bone tissue cells along the main volume of the fibrous tissue surrounding the implant during the initial osseointegration stage. [ABSTRACT FROM AUTHOR]

This work deals with a coupled acoustic problem involving a compressible fluid and a poroelastic material contained in a cavity whose walls are all rigid except for the top, where a flexible plate is placed. The fluid is described utilizing its acoustic pressure, whereas, for the plate, the Naghdi shell model is used. The mechanical behaviour of the absorbing layer attached to the plate is described by using the Biot-Allard model, where the governing equations are written in the displacement-based formulation. The main novelty of this work lies in addressing the coupling between the plate and the poroelastic medium using the Reissner-Mindlin formulation for the Naghdi's shell model and the displacement-based formulation for the Biot-Allard model. A comprehensive three-dimensional analysis is performed, comparing numerical and experimental results and showing the advantages of using the Biot-Allard poroelastic model in combination with the Naghdi shell model to predict the in-plane displacements of the plate structure over other fluid-equivalent formulations, such as the Allard-Champoux model. [ABSTRACT FROM AUTHOR]

Within this work, we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid cylinder. We provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure, stresses, and elastic displacement. We obtain the solution by performing a Laplace transform on the governing equations, which are those of Biot's poroelasticity in cylindrical polar coordinates. We enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time domain. The sensitivity analysis is then carried out, considering only the derived pressure solution. This analysis finds that the time t, Biot's modulus M, and Poisson's ratio v have the highest influence on the pressure whereas the initial value of pressure P0 plays a very little role. [ABSTRACT FROM AUTHOR]

In this work, we propose a space-time multigrid method for solving a finite difference discretization of the linear Biot's model in two space dimensions considering random hydraulic conductivity. This method is an extension of the one developed by Franco et al. [1] and which was applied to the heat equation. Particularly for the poroelasticity problem, we need to use the Tri-Diagonal Matrix Algorithm (TDMA) for systems of equations with multiple variables (block TDMA) solver on the planes xt and yt with zebra-type wise-manner (the domain is divided into planes and solve each odd plane first and then each even plane independently [2]). On the planes xy, the F-cycle multigrid with fixed-stress smoother is improved by red-black relaxation. A fixed-stress smoother is compound solver, where the mechanical and flow parts are addressed by two distinctive solvers and symmetric Gauss-Seidel iteration. This is the basis of the proposed method which does not converge only with the standard line-in-time red-black solver [1]. This combination allows the code parallelization. The use of standard coarsening associated with line or plane smoothers in the strong coupling direction allows an application in real world problems and, in particular, the random hydraulic conductivity case. This would not be possible using the standard space-time method with semicoarsening in the strong coupling direction. The spatial and temporal approximations of the problem are performed, respectively, by using Central Difference Scheme (CDS) and implicit Euler methods. The robustness and excellent performance of the multigrid method, even with random hydraulic conductivity, are illustrated with numerical experiments through the average convergence factor. [ABSTRACT FROM AUTHOR]

A theoretical simulation is performed to evaluate how microcracks affect the flow resistance in tumors during the convection-enhanced delivery (CED) of nanofluids. Both Darcy's law and the theory of poroelasticity are used to understand fluid transport with or without microcrack introduction and/or enlargement. The results demonstrate significantly altered pressure and velocity fields in a spherical tumor with a radius of 10 mm due to the presence of a microcrack with a radius of 0.05 mm and length of 3 mm. The non-uniform fluid pressure field enlarges the original cylindrical microcrack to a frustum, with the crack volume more than doubled. Due to the larger permeability and porosity in the microcrack, flow in the tumor is much easier. One finds that the flow resistance with the enlarged microcrack is reduced by 14% from the control without a microcrack. Parametric studies are conducted to show that larger crack radii, longer crack lengths and higher infusing pressures result in further resistance reductions. The largest resistance reduction occurs when the infusing pressure is 4 × 105 Pa and the microcrack is 9 mm long, up to 18% from the control. We conclude that introducing a microcrack is an effective way to facilitate nanofluid delivery in porous tumors using CED. [ABSTRACT FROM AUTHOR]

The current work deals with the mechanical buckling behavior of saturated porous toroidal shell segments sandwiched by piezoelectric actuator layers. Material properties of the porous shells with nonuniform distributed porosities are assumed to vary as a specific function of the thickness and porosity parameters. The nonlinear equations of the sandwich toroidal shell having either positive or negative Gaussian curvature are obtained on the basis of Biot's poroelasticity theory. The energy method as the minimum potential energy principle is applied to derive the governing equations of the sandwich shells. The buckling equations of the piezo-porous sandwich shells under various types of mechanical loading are established by employing the adjacent equilibrium criterion. The governing equations as a set of the coupled partial differential equations are solved using an analytical method including the Airy stress function. Closed-form solutions are derived for shallow segments of the sandwich toroidal shell with positive/negative Gaussian curvature under lateral pressure, axial compression, and hydrostatic pressure loadings. Novel numerical results are presented in this work to show the effects of important factors such as the piezoelectric layer thickness, applied voltage, shell geometrical ratio, and variation of the porosity coefficient on the buckling behavior of these structures. [ABSTRACT FROM AUTHOR]

Hydraulic stimulation is a critical process for increasing the permeability of fractured geothermal reservoirs. This technique relies on coupled hydromechanical processes induced through pressurized fluid injection into the rock formation. The injection of fluids causes poromechanical stress changes that can lead to fracture slip and shear dilation, as well as tensile fracture opening and propagation, so-called mixed-mechanism stimulation. The effective permeability of the rock is particularly enhanced when new fractures connect with pre-existing fractures. While hydraulic stimulation can significantly improve the productivity of fractured geothermal reservoirs, the process is also related to induced seismicity. Hence, understanding the coupled physics is central, for both reservoir engineering and seismic risk mitigation. This article presents a modelling approach for simulating the deformation, propagation and coalescence of fractures in porous media under the influence of anisotropic stress and fluid injection. It uses a coupled hydromechanical model for poroelastic, fractured media. Fractures are governed by contact mechanics and a fracture propagation model. For numerical solutions, we employ a two-level approach, combining a finite volume method for poroelasticity with a finite element method for fracture propagation. The study investigates the impact of injection rate, matrix permeability and stress anisotropy on stimulation outcomes. This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'. [ABSTRACT FROM AUTHOR]

Articular cartilage (AC) is a load-bearing tissue that covers long bones in synovial joints. The biphasic/poroelastic mechanical properties of AC help it to protect joints by distributing loads, absorbing impact forces, and reducing friction. Unfortunately, alterations in these mechanical properties adversely impact cartilage function and precede joint degeneration in the form of osteoarthritis (OA). Thus, understanding what factors regulate the poroelastic mechanical properties of cartilage is of great scientific and clinical interest. Transgenic mouse models provide a valuable platform to delineate how specific genes contribute to cartilage mechanical properties. However, the poroelastic mechanical properties of murine articular cartilage are challenging to measure due to its small size (thickness ∼ 50 microns). In the current study, our objective was to test whether the poroelastic mechanical properties of murine articular cartilage can be determined based solely on time-dependent cell death measurements under constant loading conditions. We hypothesized that in murine articular cartilage subjected to constant, sub-impact loading from an incongruent surface, cell death area and tissue strain are closely correlated. We further hypothesized that the relationship between cell death area and tissue strain can be used—in combination with inverse finite element modeling—to compute poroelastic mechanical properties. To test these hypotheses, murine cartilage-on-bone explants from different anatomical locations were subjected to constant loading conditions by an incongruent surface in a custom device. Cell death area increased over time and scaled linearly with strain, which rose in magnitude over time due to poroelastic creep. Thus, we were able to infer tissue strain from cell death area measurements. Moreover, using tissue strain values inferred from cell death area measurements, we applied an inverse finite element modeling procedure to compute poroelastic material properties and acquired data consistent with previous studies. Collectively, our findings demonstrate in the key role poroelastic creep plays in mediating cell survival in mechanically loaded cartilage and verify that cell death area can be used as a surrogate measure of tissue strain that enables determination of murine cartilage mechanical properties. [ABSTRACT FROM AUTHOR]

A reconstruction nonconforming virtual element method for the incompressible poroelasticity model is developed and analyzed. We investigate to determine the divergence-free displacement in incompressible poroelasticity model on polygons. The presented method mainly involves the parameter robust for μ also can be considered as the real pressure robustness for the virtual element. Using the H (div) space on the polygons to build the reconstruction operator, the method can be applied on general polygonal meshes, satisfy pressure robustness and overcome Poisson locking in incompressible model. The results are corroborated by theoretical derivations as well as numerical results. [ABSTRACT FROM AUTHOR]

The focus of the present study is to analyze the reflection and refraction of plane-P-wave at the interface between a nonlocal transversely isotropic poroelastic medium (excluding fluid nonlocal effects) and a nonlocal transversely isotropic thermoelastic half-space. The incidence of the plane P (P 1) wave generates three reflected and three transmitted waves in the respective media. Generalized governing equations for the two media are solved assuming plane wave solutions for displacement components and temperature field. The calculation of theoretical expressions for reflection and transmission coefficients involves a system of six non-homogeneous linear equations, based on boundary constraints and are computed utilizing Cramer's rule. The findings demonstrate a significant influence of incidence angle and nonlocal parameter on the amplitude ratios of each reflected and refracted wave. Graphical representations explore the impact of material parameters of both poroelastic medium (porosity, Biot's parameter, and tortuosity), and thermoelastic medium (temperature and thermal relaxation time) on amplitude ratios of waves. Propagation characteristics for different boundary constraints (permeable/impermeable, and thermally insulated/isothermal) are numerically compared. In addition, variations of velocities of all reflected and transmitted waves showing the impact of nonlocal parameter and incidence angle are shown graphically. This study enhances the comprehension of wave behavior in anisotropic nonlocal materials, with potential applications in geophysics, seismology, and material science. Understanding these interactions can improve the design and performance of devices, systems, and structures utilizing poroelastic and thermoelastic materials. [ABSTRACT FROM AUTHOR]

Groundwater level tidal analysis is a powerful technique to monitor aquifer's permeability and hence its change over time. Earthquakes are known to affect aquifer's properties, in their vicinity through static stress changes but also further away through dynamic stresses. Most often changes are in the form of permeability increases, but sometimes decreases; the changes can be either permanent or transient. These observations are relatively well documented but the physical processes behind these changes are not well understood. By combining solid‐earth and barometric tidal groundwater level responses in a borehole in a coherent poroelastic theoretical framework, and a bi‐layer hydrogeological model, we recover a 15 years‐long time series evolution of aquifer transmissivity and shear modulus. This study showcases the full potential of the tidal analysis method, coupling pore pressure diffusion and rock deformation, at the frontier of hydrogeology and rock physics. This unprecedented measurement of permeability and shear modulus evolution by tidal analysis reveals, during interseismic period, high sensitivity of this shallow aquifer to effective stress, and thus to pore pressure. Thanks to additional finite element simulation of seismic wave propagation, we explore the different mechanisms affecting permeability and shear modulus in the studied fractured andesite aquifer. This study confirms the predominant role of seismic dynamic stresses, and more precisely of dynamic shear stresses, in the change of permeability following an earthquake. Plain Language Summary: Tidal oscillations of groundwater level, observable in boreholes all around the world, are information‐rich signals for hydrogeologist to infer the properties of surrounding aquifers, and how they evolve over time. Most importantly, it allows to monitor aquifer permeability and how it evolves under the influence of earthquakes, especially through static stresses changes or seismic wave propagation. Here we push the limits of what tidal analysis can reveal by also retrieving the shear modulus of the studied aquifer. This new observable, combined with the computation of regional earthquakes stresses, allows us to understand better how aquifer properties are modified by earthquakes. The analysis reveals first that dynamic shear stresses are the most probable cause of permeability changes, and second that the sensitivity of our fractured aquifer permeability to pore pressure is high. Key Points: The 15‐years' time series of permeability and shear modulus of the aquifer is deduced from the analysis of solid earth and barometric tidesCo‐seismic irreversible changes of fractured aquifer permeability are induced by earthquakes dynamic shear stressesInterseismic permeability variations of the aquifer are controlled by pore pressure, that is, the hydraulic head [ABSTRACT FROM AUTHOR]