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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]

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]

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 reflection/transmission of seismoelectric waves propagating through a sandwiched structure are studied. • A new fractional order viscoelastic model with two attenuation peaks at seismic and sonic frequencies is established. • The seismoelectric effects have noticeable influences on EM wave while negligible influences on seismic waves. • The porosity and the viscoelasticity of solid frame have evident influences on both elastic waves and EM waves The seismoelectric waves generated in a fluid-saturated porous interlayer and the reflection/transmission characteristics at the interfaces of sandwiched structure are studied in this paper. Aiming to describe the strong attenuation and dispersion simultaneously at seismic and sonic frequencies, a new fractional viscoelastic model for the solid skeleton is introduced to the Pride's seismoelectric coupling theory. Using the interfacial continuity of stress, displacements, magnetic and electric fields, the reflection/transmission coefficients are determined. The numerical results are provided and shown graphically. The effects of seismoelectric coupling and the viscoelastic characteristics of solid skeleton on the reflection and transmission of seismoelectric waves are mainly studied. It is observed that the thickness, porosity and the viscoelastic characteristics of solid skeleton have evident effects not only on the electromagnetic waves but also on the seismic waves. [ABSTRACT FROM AUTHOR]

We study the numerical approximation by space-time finite element methods of a coupled hyperbolic-parabolic system modeling, for instance, poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in time and inf-sup stable pairs of finite element spaces for the spatial variables are investigated. Optimal order error estimates are proved for the first-order energy of the system's variables. An important ingredient of the estimates is the control of the coupling terms by a tailored testing strategy. The techniques developed here can be generalized to other families of space-time finite element discretizations and related models. The error estimates are confirmed by numerical experiments, also for higher order piecewise polynomials in space and time. The latter lead to algebraic systems with complex block structure and put a facet of challenge on the design of iterative solvers. An efficient solution technique is referenced. [ABSTRACT FROM AUTHOR]

We present a finite element discretization to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of displacement and total traction, as well as no-flux for the fluid phase. Our formulation of the poroelasticity equations incorporates displacement, fluid pressure, and total pressure, while the elasticity equations adopt a displacement-pressure formulation. Notably, the transmission conditions at the interface are enforced without the need for Lagrange multipliers. We demonstrate the stability and convergence of the divergence-conforming finite element method across various polynomial degrees. The a priori error bounds remain robust, even when considering large variations in intricate model parameters such as Lamé constants, permeability, and storativity coefficient. To enhance computational efficiency and reliability, we develop residual-based a posteriori error estimators that are independent of the aforementioned coefficients. Additionally, we devise parameter-robust and optimal block diagonal preconditioners. Through numerical examples, including adaptive scenarios, we illustrate the scheme's properties such as convergence and parameter robustness. [ABSTRACT FROM AUTHOR]

The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in fluid-saturated solids and frequency-dependent phenomena in porous media. Therefore, the development of an efficient numerical method for the equation is of both theoretical and practical importance. Recently, local randomized neural networks with discontinuous Galerkin (LRNN-DG) methods have been introduced in [21] to solve elliptic and parabolic equations. Numerical examples suggest that LRNN-DG can achieve high accuracy, and can handle time-dependent problems naturally and efficiently by using a space-time framework. In this paper, we develop LRNN-DG methods for solving the diffusive-viscous wave equation and present numerical experiments with several cases. The numerical results show that the proposed methods can solve the diffusive-viscous wave equation more accurately with less computing costs than traditional methods. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of a double poro-elastic medium derived by the homogenization of a two-component periodically heterogeneous Biot continuum characterized by strong heterogeneities in the permeability and poroelastic coefficients of mesoscopic structure. A new scaling of the mesoscopic material parameters with respect to the small parameter which is involved in the asymptotic analysis is introduced to capture this high contrast quality of the mesoscopic model. It is shown that such a scaling ansatz of the mesoscopic material parameters can be justified using different micromodels associated with the two mesoscopic components. While the "matrix" is a little permeable stiff phase, the "conductive channels" are made of a very soft fibrous structure equivalently represented by an network of helical springs. The unfolding method of the homogenization is employed to derive the macroscopic model involving the frequency-dependent effective parameters. Semipermeable interfaces between hard dual porosity and soft primary porosity are considered. The wave dispersion of two shear wave modes S 1 , S 2 , and two pressure wave modes P 1 , P 2 , is illustrated in an numerical example and validated, in a part, using the reference dispersion analysis based on the Bloch wave decomposition. • A new type high-contrast double porosity Biot medium is introduced by material parameters related to scale. • The effective medium model is derived by the periodic homogenization for the scaling ansatz. • Frequency-dependent homogenized coefficients induce remarkable wave dispersion. • The scaling relevant in the soft matter is justified by homogenization of fibrous microstructures. • The wave response of the homogenized medium is compared with results of the Bloch wave analysis. [ABSTRACT FROM AUTHOR]

• A novel time-domain 3D artificial boundary for poroelastic medium. • Capability to model boundaries with general geometries. • Capability to consider planar physical interfaces extending to infinity. • Seamless coupling with poroelastic finite-element codes based on Biot's theory. In this paper, we introduce a novel direct time-domain artificial boundary condition, called the scaled boundary perfectly matched layer, for wave problems in 3D unbounded fluid-saturated poroelastic medium. The poroelastic medium is conceptualized as a two-phase medium composed of a solid skeleton and an interstitial fluid based on the u- p formulation of Biot's theory. The scaled boundary perfectly matched layer proposed in this work originates from an extension of a recently developed perfectly matched layer for wave problems in a single-phase solid medium. The dependence of the conventional perfectly matched layer on the global coordinate system is overcome in the present method. As a result, this method permits the utilization of an artificial boundary with general geometry (not necessarily convex) and can consider planar physical surfaces and interfaces extending to infinity. The proposed method is formulated by a mixed unsplit-field form, which includes both the mixed displacement-stress field and pore pressure-relative displacement field. The resulting scaled boundary perfectly matched layer formulation can be directly described by a system of third-order ordinary differential equations in time, which can be easily integrated into the standard finite-element framework of poroelastic theory. Finally, numerical benchmark examples are presented to demonstrate the accuracy and robustness of the proposed scaled boundary perfectly matched layer, as well as the versatility in practical engineering problems. [ABSTRACT FROM AUTHOR]

• Poroelastic vibration analysis of three-layered shells in thermal atmospheres is carried out. • Three types of shells namely cylindrical, spherical, and doubly-curved are investigated. • The FG porous core of the shells is saturated by fluid. • The composite patches are reinforced by GNPs that their amount and dispersion patterns are considered. • A Fourier series-based analytical solution is used to obtain the natural frequencies. Porous and nanocomposite materials are widely used in various engineering structures due to their exceptional thermos-mechanical properties. In this work, the poro-thermoelastic frequency analysis of three-layer functionally graded saturated porous (FGSP) lightweight shells covered with two graphene nanoplatelets (GNPs)-reinforced composite surfaces is explored. Both the volume fraction and the diffusion types of GNPs reinforcement in the patches are investigated and moreover, the effect of pressure exerted by the fluids in the openings is considered and the different pore arrangements are compared. Based on the first-order shear deformation theory (FSDT) combined with Hamilton's principle, the equations of motion are derived and then solved analytically. After confirming the accuracy of the results, the frequencies are presented for different types of shells, including cylindrical, spherical, and doubly-curved shells. These types of shells are widely used in various industries, so the results of this work can be useful for these industries. In addition, this is the first comprehensive frequency analysis for different types of shells, and the results can serve as a benchmark for future studies. [ABSTRACT FROM AUTHOR]

In this work, a locking-free nonconforming virtual element method for the three-field Biot's model (the displacements, Darcy velocity and pore pressure) is developed and analyzed. We solve the model as: nonconforming VEM for the displacements, RT-like VEM for Darcy velocity and pressure. We show the well-posedness and the optimal error estimates of the discrete schemes. The numerical experiments support the convergence analysis of our method and illustrate it can be used to avoid Poisson locking and nonphysical pressure oscillations. [ABSTRACT FROM AUTHOR]

The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches the physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering. Poroelasticity drives the functional mechanics of articular cartilage (load bearing and lubrication). In this work we develop the design rationale and approach to produce a poroelastic material, known as a fiber reinforced hydrated network (FiHy™), that begins to approach the native performance of articular cartilage. This is the first engineered material system capable of exceeding isotropic linear poroelastic theory. The framework developed here enables fundamental studies of poroelasticity and the development of translational materials for cartilage repair. [Display omitted] [ABSTRACT FROM AUTHOR]

We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes–Biot problem. Of particular interest is that the discrete velocities and displacement are H (div) -conforming and satisfy the compressibility equations pointwise on the elements. Furthermore, in the incompressible limit, the discretization is strongly conservative. We prove well-posedness of the discretization and, after combining the HDG method with backward Euler time stepping, present a priori error estimates that demonstrate that the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence in the L 2 -norm for all unknowns and that the discretization is locking-free. [ABSTRACT FROM AUTHOR]

In this paper, we develop a weak Galerkin (WG) finite element method for a linear poroelasticity model where weak divergence and weak gradient operators defined over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete H 1 norm for the displacement and in H 1 and L 2 norms for the pressure. Finally, we present some numerical experiments on different kinds of meshes to illustrate the theoretical error estimates, and furthermore verify the locking-free property of our proposed method. [ABSTRACT FROM AUTHOR]

Cell transitions between the epithelial and mesenchymal phenotypes provide the regulated morphogenesis and regeneration throughout the ontogenesis. The tissue mechanics and mechanotransduction play an essential role in these processes. Cell spheroids reproduce the cell density of native tissues and represent simple building blocks for the tissue engineering purposes. The mechanical properties of mesenchymal and epithelial cells have been extensively studied in 2D monolayer cultures, but have not been sufficiently compared in spheroids. Here, we have simultaneously applied several techniques to assess the mechanical parameters of such spheroids. The local surface mechanical properties were measured by AFM, and the bulk properties were analyzed with parallel-plate compression, as well as by observing cut opening after microdissection. The comparison of the collected data allowed us to apply the model of a solid body with surface tension, and estimate the parameters of this model. We found an expectedly higher surface tension in mesenchymal spheroids, as well as a higher bulk modulus and relaxation time. The two latter parameters agree with the bulk poroelastic behavior of spheroids, and with the higher cell density and extracellular matrix content in mesenchymal spheroids. The higher tension of the surface layer cells in mesenchymal cell spheroids was also confirmed by the viscoelastic AFM characterization. The cell phenotype affected the self-organization during the spheroid formation, as well as the structure, biomechanical properties, and spreading of spheroids. The obtained results will contribute to a more detailed description of spheroid and tissue biomechanics, and will help in controlling the tissue regeneration and morphogenesis. Spheroids are widely used as building blocks for scaffold-based and scaffold-free strategies in tissue engineering. In most studies, either the concept of a solid body or a liquid with surface tension was used to describe the biomechanical behavior of spheroids. Here, we have used a model which combines both aspects, a solid body with surface tension. The "solid" aspect was described as a visco-poroelastic material, affected by the liquid redistribution through the cells and ECM at the scale of the whole spheroid. A higher surface tension was found for mesenchymal spheroids than that for epithelial spheroids, observed as a higher stiffness of the spheroid surface, as well as a larger spontaneous opening of the cut edges after microdissection. [Display omitted] [ABSTRACT FROM AUTHOR]

Recent clinical applications of mRNA vaccines highlight the critical role of drug delivery, especially when using lipid nanoparticles (LNPs) as the carrier for genetic payloads. However, kinetic and transport mechanisms for locally injected LNPs, such as lymphatic or cellular uptake and drug release, remain poorly understood. Herein, we developed a bottom-up multiphysics computational model to simulate the injection and absorption processes of LNPs in muscular tissues. Our purpose was to seek underlying connections between formulation attributes and local exposure kinetics of LNPs and the delivered drug. We were also interested in modeling the absorption kinetics from the local injection site to the systemic circulation. In our model, the tissue was treated as the homogeneous, poroelastic medium in which vascular and lymphatic vessel densities are considered. Tissue deformation and interstitial fluid flow (modeled using Darcy's Law) were also implemented. Transport of LNPs was described based on diffusion and advection; local disintegration and cellular uptake were also integrated. Sensitivity analyses of LNP and drug properties and tissue attributes were conducted using the simulation model. It was found that intrinsic tissue porosity and lymphatic vessel density affect the local transport kinetics; diffusivity, lymphatic permeability, and intracellular update kinetics also play critical roles. Simulated results were commensurate with experimental observations. This study could shed light on the development of LNP formulations and enable further development of whole-body pharmacokinetic models. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper presents an original algorithm to simulate quasi-static loading of fluid-saturated porous material for numerical upscaling of the complex fluid-saturated fractured-porous media. The resulting model is anisotropic viscoelastic which means that it is defined by a complex-valued frequency-dependent stiffness tensor that can be recomputed into the frequency-dependent phase velocities and attenuation of seismic waves. Numerical upscaling requires a solution of parabolic approximation of the Biot poroelastic equation for anisotropic media in frequency space for a series of frequencies and multiple right-hand sides. The approach is based on the finite-difference approximation of the quasi-static formulation of the Biot equation with the use of a direct solver to resolve the obtained system of linear algebraic equations. The direct solver allows for efficiently treating multiple right-hand sides which is an essential statement of the upscaling problem. The presented realization of the algorithm allows solving the problems of the size of up to 2000 points in each spatial direction using a single machine, which allows dealing with representative fractured-porous models. To illustrate the applicability of the algorithm we provide several series of experiments illustrating the effects of fracture connectivity and anisotropy of fracture-filling material on seismic waves dispersion and attenuation if propagating in complex fluid-saturated fractured-porous media. • We present a new finite-difference algorithm to upscale fluid-saturated poroelastic media. • The solver allows solving quasi-static Biot equation for hundreds of time frequencies on a single-node machine. • Use of finite differences allows dealing with fractured porous media of almost arbitrary complexity. [ABSTRACT FROM AUTHOR]

In this paper, a semi-decoupled marker and cell (MAC) scheme is proposed for the Stokes-Biot system, in which the displacement of structure is split from the whole system using the time-lagging scheme, then the rest system composed by the velocity and pressure is treated in a similar way as the Stokes-Darcy coupling problem. It keeps the desirable qualities such as the mass conservation. The backward Euler scheme is used for the time discretization. We derive the stability and the error estimates for the fully discrete scheme, obtain the second order superconvergence for the discrete L 2 norm for velocity, pressure and displacement and some terms of the H 1 norm for displacement and velocity. Numerical experiments confirm well the theoretical analysis results and the robustness of parameters. [ABSTRACT FROM AUTHOR]

We propose and analyze an H(div) conforming discontinuous galerkin (CDG) method for the three-field Biot's consolidation model with the displacement reconstruction technique. The displacement is discretized by the k th-order Brezzi-Douglas-Marini (BDM) element, and the fluid flux and pore pressure are approximated by the k-1 th-order Raviart-Thomas-Nedelec element pairs. The H(div) CDG method is derived from the H(div) conforming formulation by replacing the classical gradient operator with a weak gradient operator, where the weak one is locally computed by the k th-order Raviart-Thomas (RT) element. We prove optimal a-priori error estimates for both semi-discrete scheme and fully-discrete scheme with the backward Euler discretization in time. The implicit constants in the error estimates are robust for the arbitrarily large Lamé coefficient and the arbitrarily small constrained specific storage coefficient. Our method has no stabilizers, which simplifies the finite element formulations. Meanwhile, it can also overcome the poroelasticity locking mathematically and preserve the pointwise mass conservation on the discrete level. The validity and accuracy of the proposed method are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

• The pattern formation of morphogens is studied in geometrically-confined microtissues during early embryogenesis. • The microtissue consisted of human stem cells is modeled as a piece of biphasic poroelastic material. • The active contractility is fully-coupled with the reaction-diffusion of the morphogens through the poroelasticity. • Linear stability analysis is performed to determine ranges of parameters that leads to diffusion-induced instability. • A comprehensive parameter study, including the sizes and geometries of the tissues, is carried out in the paper. The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Mechanical cues, such as the cellular stresses and strains, have been found to dictate the pattern formation in human stem cell differentiation. As a result, the traditional reaction-diffusion models are modified by adding mechanically related terms to consider the role played by the mechanical cues during the very early stage of embryogenesis. However, these models either do not consider the activeness of the cellular tissues or neglect their poroelastic nature that biological tissues are made by both cells and interstitial fluid. Here we propose a modified reaction-diffusion model that couples with the active contraction of cellular tissues. The cellular tissue is modelled as a piece of biphasic poroelastic material, where mechanical forces naturally regulate the transport of chemical cues. Such chemical cues direct cell fate and hence yield certain types of pattern formations observed in previous experiments. [ABSTRACT FROM AUTHOR]

• Novel mathematical model for deriving semi-analytical Green's function solutions. • First time on the coupled horizontal and rocking vibrations in poroelasticity. • Anisotropic and layered poroelastic half-space via Biot's poroelastodynamic theory. • Handling layering via the powerful and stable dual variable and position method. • Soil-structure interaction (SSI) via a novel integral least-square approach. The coupled horizontal and rocking vibrations of a rigid circular disc resting on a transversely isotropic (TI) and layered poroelastic half-space is solved by a newly developed semi-analytical method for the first time. The poroelastic medium is modelled via Biot's poroelastodynamic theory. The Green's function corresponding to the horizontal uniform and vertical linearly changing patch loads on the surface of the layered half-space are first derived by virtue of the cylindrical system of vector functions and dual variable and position method. To solve the dynamic interaction, the influence function by the ring load is then introduced and calculated via the method of superposition. Together with the mixed boundary-value conditions, the dynamic horizontal, rocking, and coupling compliances are finally solved by a novel discretization scheme and an integral least-square approach. The developed fundamental solutions are verified by comparing with existing solutions in the purely elastic and poroelastic media. Numerical examples are presented to investigate the influence of poroelastic properties on the coupled vibration characteristics, which could be useful to the dynamic design of foundation on the saturated soil. It should be emphasized that the effect of the coupling compliance must be considered since its contribution can be as large as 26%, compared to the diagonal compliances. [ABSTRACT FROM AUTHOR]

Viable Enhanced Geothermal Systems (EGS) require (1) access to large reservoir volumes at high temperatures and (2) sufficient permeability for large production flow rates. However, working fluid injection might quickly decrease the recoverable heat energy. Thermal destressing increases fracture transmissivity and reduces the production temperature. Large fracture openings cause the injection fluid to localize in a single fracture, or a few dominant fractures, and leads to thermal short-circuiting within the EGS hydraulic network. This work provides novel numerical simulations of a multi-fracture EGS that models the fracture aperture from initially closed to mechanically open. Fractures are modeled as discontinuities within a three dimensional thermo-poroelastic rock mass. We derived weak-form equations of mass balance, energy balance, and mechanical contact for fractures and wells and coupled those equations to the Comsol Multiphysics base package. The simulations investigate the full reservoir behavior through coupling of fluid flow through wellbores and fractures with the surrounding rock. Results show that large in-situ stresses contribute to a uniform fluid flow distribution in the fracture network because high compressive contact stresses decrease fracture compressibility and prevent large fracture openings. Initial or late large fracture openings cause thermal short-circuiting and are more likely to arise in locations with low initial stress and compliant fractures. Geometrical and operational properties of the EGS hydraulic network can minimize the severity of thermal short-circuiting including wellbore diameter, fracture spacing, injector/producer lateral spacing, EGS doublet orientation, and number of transmissive fractures. Thermo-mechanical interference between fracture stages causes (1) larger fracture opening displacements and (2) thermal short-circuiting earlier in time. Distinct initial fracture geometries and compliance causes the EGS hydraulic network to flow a non-uniform distribution of the injection fluid from the beginning and tends to decrease heat recovery. [Display omitted] • Initially large hydraulic apertures or late re-opening decreases heat recovery. • Fractures with high compliance tend to short-circuit. • EGS hydraulic network design can minimize the severity of short-circuiting. • Thermo-mechanical fracture interaction greatly decreases heat recovery. • Heat recovery benefits from homogeneous fracture aperture and high initial stress. [ABSTRACT FROM AUTHOR]

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation). [Display omitted] [ABSTRACT FROM AUTHOR]

This work focuses on the numerical solution of the dynamics of a poroelastic material in the frequency domain. We provide a detailed stability analysis based on the application of the Fredholm alternative in the continuous case, considering a total pressure formulation of the Biot's equations. In the discrete setting, we propose a stabilized equal order finite element method complemented by an additional pressure stabilization to enhance the robustness of the numerical scheme with respect to the fluid permeability. Utilizing the Fredholm alternative, we extend the well-posedness results to the discrete setting, obtaining theoretical optimal convergence for the case of linear finite elements. We present different numerical experiments to validate the proposed method. First, we consider model problems with known analytic solutions in two and three dimensions. As next, we show that the method is robust for a wide range of permeabilities, including the case of discontinuous coefficients. Lastly, we show the application for the simulation of brain elastography on a realistic brain geometry obtained from medical imaging. [ABSTRACT FROM AUTHOR]

We consider Biot's equations of poroelasticity where the development of viscous boundary layers in the pores is allowed for by using a dynamic permeability convolution operator in the time domain. This system with memory effects is also referred to as the dynamic Biot–Allard model. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in the time domain in a coupled system without convolution integrals, which is also suitable for designing efficient numerical approximation schemes. The main result here is the well-posedness of the system, rewritten in evolutionary form, which is proved by an abstract theory for evolutionary problems. [ABSTRACT FROM AUTHOR]

A novel model is put forward to characterize the seismic response excited by vertical P-waves in a transversely isotropic and layered nonlocal poroelastic seabed. The proposed model integrates nonlocal parameter, anisotropy, and stratification to accurately examine wave propagation behavior. The fundamental equations for the underlying seabed are formulated using Biot's poroelastodynamic theory and Eringen's nonlocal theory. The wave equation for the overlying water is expressed in terms of the velocity potential. General solutions in both the poroelastic seabed and water layer are derived by solving the involved ordinary differential equations. Employing the newly devised and unconditionally stable propagator matrix scheme, semi-analytical solutions are derived for the time-harmonic response in a layered poroelastic seabed subjected to vertical P-wave excitation within the frequency domain. The validity of the proposed solutions is confirmed through rigorous comparison with the previously established analytical solutions. The influence of key material properties of seabed on the velocities of P-waves and free-field response in the poroelastic seabed is estimated in detail, along with the free-field response in a nonhomogeneous poroelastic seabed. • A semi-analytical dynamic seabed model by vertical P-waves is presented. • 1D rigorous nonlocal Biot theory is proposed. • Dual-variable and position (DVP) method is utilized for solving layered seabed. • Effect of nonlocal parameters and anisotropy on wave propagation is analyzed. • Free-field response in a nonhomogeneous poroelastic seabed is estimated. [ABSTRACT FROM AUTHOR]

The stress-strain state of the saturated porous media determines the behavior of fracturing, which defines the efficiency of developing tight oil, shale, coalbed, and thermal energy fields. Therefore, reliable hydromechanical coupled simulations with destruction reconstruction are critical. The proposed innovative simulator has a strong interrelation between fluid flow and rock deformation of porous media and realizes a fully coupled pseudo-transient numerical method by high-performance computing (HPC) tools. To increase the detail of the results in the problem, a finite difference numerical algorithm was implemented in the axisymmetric cylindrical domain, which reduces from three to two dimensions without loss of precision. Highly efficient parallelization using CUDA on the GPU computes meshes of up to one billion cells, allowing the simulation of a total core sample to sub-micrometer resolution in an appropriate time. The algorithm has been validated to find the exact solution to the cylinder problem. The proposed model accounts for cracks propagation with their coalescence within a single computational static grid, which keeps timing close to the continuous model. This comprehensive implementation enables solving industrial problems, such as modeling core sample damage during rapid decompression. High-resolution simulations help reconstruct fracture propagation, analyze the initial stress state, and identify critical damage factors. The comparison with the exact solution to the cylinder problem confirmed the reliability of the algorithm. The calculation results show a strong dependence of decompression failure on the coalescence and elongation of cracks, influenced significantly by the rock's cohesion. Microcracks length and distribution play a decisive role in the decompressive destruction behavior of the rock sample. For the first time, the simulations demonstrated the decompressive destruction of a core sample during an uncontrolled, rapid core retrieval operation. • The article describes the hydromechanical coupling algorithm based on the pseudo-transient numerical method. • The method considers the dynamic fracturing model and coalescence using a pseudo-continuous approach and cellular automata principles. • For the first time, simulations confirmed the failure of a shale core sample during a rapid decompression driven by an uncontrollable fast core retrieval operation. • Microfractures' characteristics determine the tendency of decompression failure. • During the process of decompression, the primary type of failure that occurs is shear failure. [ABSTRACT FROM AUTHOR]

Fluid flow in subsurface tight reservoirs containing pores, microcracks and macrocracks is notably influenced by the characteristics of macro/micro-cracks. A novel hybrid multiscale model is proposed to address the response of macrocracks and pores/microcracks in different spatial scales. Specifically, an equivalent macroscopic model (EMM) deduced from locally periodic representative element volume (REV) is developed using the asymptotic homogenization method to represent the poroelastic behavior of porous medium with microcracks. Simultaneously, the macrocracks are modeled explicitly using the discrete fracture model (DFM), where the hydraulic properties of cracks influenced by fluid pressure gradient is represented by the nonlinear opening/closure behavior. The obtained hybrid model takes into account the heterogeneous nature of fractured rock masses containing pores, micro/macro-cracks, which is fundamental to describe fluid flow behavior in fracture-matrix system. Specialized finite elements, regular meshing technique and adaptive time stepping algorithm are adopted to improve the computational efficiency. The hybrid multiscale model is firstly validated step by step to demonstrate the accuracy and then used to simulate fluid flow in fractured rock reservoir, shedding light on the underlying mechanisms of the enhanced flow capacity resulting from microcrack distribution, connectivity, and macrocrack stimulation. • A novel hybrid multiscale framework is developed to describe fluid flow in naturally fractured rock reservoir containing pores and multiscale cracks. • The equivalent macroscopic model deducing from asymptotic homogenization method is employed to represent the poroelastic behavior of porous medium with microcracks. • Fluid flow in fractured reservoir is shown to be influenced by both the microcrack distribution and connectivity, as well as stimulated macrocracks. [ABSTRACT FROM AUTHOR]

We present a poroelastic fluid–structure interaction δ -SPH model for simulating biofilm deformation and sloughing in microfluidic channels. Based on the mixture theory, this model accurately handles large deformations of solid structures and simultaneously simulates seepage flow within the porous biofilm and external flow. A key advantage of the model is its reliance on the solid phase material properties rather than the averaged properties of the biofilm, enabling the modeling of changes in porosity and biofilm material properties induced by loads. Model verification is achieved through two benchmark problems, followed by application to biofilm deformation and sloughing studies. The Young's modulus of biofilms is a key parameter of interest in many studies. Calibration of the biofilm's solid material elasticity modulus by using the presented model yields a value of 200 Pa, aligning with previous reports in literature. Additionally, the model is capable of simulating the sloughing process by evaluating local von Mises equivalent stress, reproducing different detachment patterns corresponding to various material strengths. This δ -SPH model offers an efficient numerical tool for biofilm analysis and is extendable to simulate other fluid–structure interaction problems involving porous media with large deformations, such as soil, debris flow, and biological tissues. [ABSTRACT FROM AUTHOR]

Internal solitary waves (ISWs) are a frequently observed phenomenon in the ocean and significantly affect sediment soil dynamics and transportation. This study entailed the use of the poroelastic theory to investigate ISW-induced soil responses. To validate this theory, the solution for pore pressure was compared with a set of laboratory measurements. The theoretical results agree well with the experimental data, indicating that the poroelastic solution can be used to study ISW-induced soil dynamics. The Dubriel–Jacotin–Long (DJL) model was used to examine the flows and pressure induced by a large ISW observed in the northern South China Sea, and the wave–driven pressure at the water–seabed interface was obtained. The validated analytical solution was then used to analyze the ISW-induced soil dynamics for sandy silt and clayey silt. The results indicate that the effective stresses are relatively small under the observed ISW, and the stress angle inside the clayey silt is larger than that inside the sandy silt owing to the smaller penetrated depth. According to the Mohr-Coulomb criterion, shear failure is difficult to happen under the observed ISW conditions and seabed properties. Moreover, the effects of the water density profile and shear modulus on the shear failure potential of the soil were analyzed. The results show that the ISW-induced soil dynamics are sensitive to the shear modulus of soil and the density profile of water. In the event of substantial density variations in the pycnocline, shear failure may occur within the seabed in regions with a large shear modulus. • Soil dynamics significantly affected by internal solitary waves. • Shear failure can be caused by internal solitary waves within the seabed. • Shear failure happens before the occurrence of liquefaction. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the full-waveform inversion (FWI) for recovering three media parameters of the poroelastic wave equations as training a neural network. We recast the poroelastic wave simulation in the time domain by the staggered-grid schemes into a process of recurrent neural networks (RNNs). Furthermore, the parameters of RNNs coincide with the inverted parameters in FWI. The algorithm of FWI with a stochastic gradient optimizer named Adam is proposed. The gradients of the objective function with respect to the media parameters are computed by the automatic differentiation. FWI is implemented numerically for three media parameters, i.e., solid density, Lamé parameter of of saturated matrix and shear modulus of dry porous matrix. The numerical computations with two designed models show the good imaging ability of the described method in this paper. It can be applied to invert more media parameters of the poroelastic wave equations. • We firstly investigate the poroelastic FWI with Adam by our knowledge. • Both variations and interface positions of parameters are inverted very well. • The inherent relationship between time-domain FWI and RNNs is expounded. • The automatic differentiation technique is applied to compute gradient. • The stochastic optimizer can help iterations escape from improper local minimum. [ABSTRACT FROM AUTHOR]

The Callovo-Oxfordian (COx) claystone is selected as the host rock in the French project for geological disposal of radioactive waste. In its initial state, the host rock is fully saturated. Due to the low permeability, the pore fluid pressure can locally evolve in a quasi undrained condition due to subsequent mechanical and thermal loading, and then significantly affects deformation and cracking process of geological barrier. Most previous studies were carried out in quasi drained conditions or with constant pore pressure. Poromechanical behavior of COx claystone in undrained condition has been so far rarely investigated. In the present work, we carry out a new series of laboratory tests. Two representative loading paths are considered: triaxial compression with constant confining pressure and triaxial extension with constant mean stress. The variations of strain and pore pressure are measured during the tests. It is found that the poromechanical behavior of the claystone is clearly affected by loading path. The failure strength is higher in triaxial compression than in extension. The evolution of pore fluid pressure is correlated with volumetric strain. Compared with the results obtained in drained tests, it seems that the Terzaghi effective stress can be used for the description of pore fluid pressure effect on failure strength. [ABSTRACT FROM AUTHOR]

We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem of linear poroelasticity with high contrast. Firstly, dominant basis functions generated by the CEM-GMsFEM approach are used to capture important degrees of freedom and it is known to give contrast-independent convergence that scales with the mesh size. In typical situation, one has very few degrees of freedom in dominant basis functions. This part is treated implicitly. Secondly, we design and introduce an additional space in the complement space and these degrees are treated explicitly. We also investigate the CFL-type stability restriction for this problem, and the restriction for the time step is contrast independent. [ABSTRACT FROM AUTHOR]

Geothermal reservoir operations can lead to seismic activity, for instance, due to increased pore pressure, but some observations are difficult to explain by pressure changes alone. Such observations include unexpected, induced events after injection well shut-in when pore pressures are thought to decrease. Here, we analyze induced seismicity up to M L 1.5 and surface deformation in Blue Mountain, Nevada using seismic, geodetic, and hydraulic data between 2016 and 2020. This period is characterized by long-term surface subsidence of up to 1 cm/yr above the reservoir. The long-term deformation is associated with modest seismic activity but also short-lived seismicity spikes during rapid maintenance shutdowns in 2017 and 2018. The seismicity is concentrated within the geothermal reservoir at 0.5 - 2.5 km depth, similar to injection operations. We present a numerical model of abrupt seismicity rate changes during the two shutdowns that explains the observation through short-term poroelastic effects leading to increased Coulomb stressing rates. In contrast, the long-term surface subsidence can be modeled statically by superimposing localized fault slip, and thermal contraction of the reservoir. Our findings demonstrate that poroelastic coupling drives the abrupt increase in seismic activity following well shutdown, while aseismic fault slip and thermal contraction dictate the long-term static deformation. [ABSTRACT FROM AUTHOR]

The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due to piezoelectric segments embedded in the microstructure and locally actuated by voltage waves. The homogenization is employed to derive a macroscopic model of the poroelastic medium with effective parameters modified by piezoelectric properties of the skeleton. To capture the peristaltic pumping, the nonlinearity associated with deforming configuration must be respected. In the macroscopic model, this nonlinearity is introduced through homogenized coefficients depending on the deforming micro-configurations. For this, linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to deformation induced by the macroscopic quantities are employed. This enables to avoid the two-scale tight coupling of the macro- and microproblems otherwise needed in nonlinear problems. The derived reduced-order model is implemented and verified using direct numerical simulations of the periodic heterogeneous medium. Numerical results demonstrate the peristaltic driven fluid propulsion in response to the electric actuation and the efficiency of the proposed treatment of the nonlinearity. The paper shows new perspectives in homogenization-based computationally efficient modelling of weakly nonlinear problems where continuum microstructures are perturbed by coupled fields. • Derived a two-scale model of peristaltic pumping of fluid in elastic skeleton with piezoelectric controlable actuators. • The quasistatic fluid-structure interaction problem in periodic structures is upscaled by the homogenization method. • Nonlinearity due to deformation dependent microconfigurations is respected by solution-dependent effective model parameters. • The continuum model is new and also the modelling approach with the linearization based on the sensitivity analysis. • The paper shows new perspectives in homogenization-based computationally efficient modelling of weakly nonlinear problems. [ABSTRACT FROM AUTHOR]

We reveal that inertial flow can introduce additional pressure perturbations which accelerate the instability of critically stressed faults. We integrate a poroelastic spring-slider model with rate-and-state friction (RSF), a nonlinear flow model characterized by the improved Izbash equation, and a universal visco-inertial permeability model. The effect of inertial flow depends on the fracture network properties, proximity to faults, and injection parameters. Significant inertial flow results in higher pressure magnitudes and pressurization rates, causing notable differences in predictions between linear and nonlinear flow models, as well as aging and slip laws. The impact of inertial flow is particularly pronounced within a specific permeability range and is enhanced by high-rate injections. The fault reactivation is delayed due to fault strengthening with RSF in response to increased pressurization rates. Conversely, the presence of inertial flow enhances fault reactivation and promotes unstable slip behaviors. Furthermore, the results demonstrate that cyclic injection increases the critical stiffness of faults without an adequate release of pore pressure in each cycle. The time interval of the cyclic injection is prolonged as inertial flow generates higher pressure levels. This study highlights the importance of inertial flow in the stability analysis of critically stressed faults. [ABSTRACT FROM AUTHOR]

In this paper, we shall present a weak virtual element method for the standard three field poroelasticity problem on polytopal meshes. The flux velocity and pressure are approximated by the low order H (div) virtual element and the piecewise constant, while the elastic displacement is discretized by the H (div) virtual element with some tangential polynomials on element boundaries. A fully discrete scheme is then given by choosing the backward Euler for the time discretization. With some assumptions on the exact solutions, we prove that the convergence order is of order 1 with respect to the meshsize and the time step, and the hidden constants are independent of the parameters of the problems. Some numerical experiments are given to verify the results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-level multiphysics finite element method for a nonlinear poroelasticity model. To clearly reveal the multiphysics processes and overcome the "locking phenomenon", we reformulate the original fluid-solid coupled problem into a fluid-fluid coupled problem–a generalized nonlinear Stokes problem coupled with a diffusion problem. To reduce the cost of computation, we propose two fully discrete coupling and decoupling two-level multiphysics finite element methods and use the backward Euler method for time variable of the reformulated nonlinear poroelasticity model. In computation, the generalized nonlinear poroelasticity (Stokes in Algorithm 2) problem is solved by using the Newton iterative method on a coarse mesh, then a linearized poroelasticity problem is solved on a fine mesh by using the solution of the coarse mesh. Then, we give the stability analysis and error estimates of the proposed methods. Finally, we show some numerical examples to verify the theoretical results–overcoming "locking phenomenon" and reducing the computational cost. • It is the first time to propose a two-level multiphysics finite element method for the nonlinear poroelasticity model. • The optimal order error estimate of the proposed two-level method is given. • To reduce the cost of computation, a poroelasticity problem is solved by using the Newton method on a coarse mesh. [ABSTRACT FROM AUTHOR]

• Dynamic responses of eccentrically loaded rigid strip foundation are solved analytically. • Extended precise integration method is employed to solve layered poroelastic media. • Contact interface stresses on rigid strip are modelled by bessel series expansions. • Linear equations can be developed and solved for obtaining explicit contact stresses. • Effects of stratification, transverse isotropy and permeability of media are investigated. This paper presents an analytical method for analyzing vertical and rocking motions of a rigid strip foundation on layered transversely isotropic poroelastic media. The extended precise integration method is employed to obtain the plain strain dynamic responses of layered poroelastic media due to the reaction force from the rigid strip. Then, the contact stresses for dynamic soil-structure interactions (SSI) are modelled by the Bessel series expansions, and a set of linear equations can be developed from the dual integral equations of mixed boundary value problems. The explicit expressions for the contact stresses are further obtained by solving these linear equations. Finally, the presented method is verified, and numerical examples are provided to demonstrate the effects of stratifications, transverse isotropy and permeability of media on the dynamic responses of eccentrically loaded rigid strip foundation. [ABSTRACT FROM AUTHOR]

• The coupling effects between solid and fluid portions is considered in the analytical solution. • The surrounding soil can consider the variations of vertical displacements in both horizontal and vertical directions. • The research on floating piles is no longer limited to the assumption of semi-infinite space. • The proposed model can be degenerated to the condition of end-bearing pile. Decades of high-speed railways operation around the world have revealed an increasing number of maintenance issues of pile-supported embankments subjected to long-term dynamic train loads in typical unsaturated soft soil areas. As the physical explanation of vibration characteristics of unsaturated soil piles is a theoretical basis for pile foundation design and pile integrity detection, a developed analytical solution of the vertical dynamic response of a floating pile in homogeneous unsaturated soils is proposed in this work. Based on the fictitious unsaturated soil pile (FUSP) model, the influence of saturation degree on soil shear modulus is considered in governing equations, uncoupled by using potential function and operator decomposition methods. The vertical dynamic response of a floating pile in a frequency domain is derived by employing the pile–soil compatibility conditions and the impedance function transfer method. Time-domain results are obtained by utilizing inverse Fourier transform and the convolution theorem. The correctness of the proposed model is verified by degradation to compare with the two existing solutions. Finally, a parameter study is undertaken to find the most sensitive parameters to the dynamic response of the floating pile in unsaturated soils. [ABSTRACT FROM AUTHOR]

Hydrocarbon reservoirs with low porosity and permeability are usually vulnerable to be contaminated owing to the drilling and completion fluids-induced formation damage, which significantly impedes the efficient production of hydrocarbon. However, most current productivity prediction models introduce the concept of skin factor to capture the near-wellbore contamination, which only considers the change of permeability before and after contamination, whereas neglecting the change of threshold pressure gradient (TPG) affected by the permeability reduction. Also, few works have been done to focus on the influences of contamination, TPG, sensitivity of rock porosity to internal stress, and fluid compressibility simultaneously in the actual production process of the low-permeability reservoir. Therefore, to bridge the knowledge gap, this study presents a new comprehensive productivity model encompassing those multiple influencing factors. Firstly, the seepage area is divided into contaminated zone and uncontaminated zone. Thereafter, the proposed model is established based on non-Darcy seepage theory and continuity principle, comprehensively taking account of the effects of different permeability and TPG between contaminated zone and uncontaminated zone, stress sensitivity based on primary stress in porous media, and the fluid compressibility. Subsequently, the newly proposed model is proved to be reliable through the consistency between the simplified model and the existing models in the literatures. Finally, the sensitivity analysis is employed to investigate the effects of key parameters. Main results show that a) the decreased permeability affected by contamination would result in increased TPG, further lowering the well productivity. b) Contamination, TPG and stress sensitivity will cause additional pressure drop and production loss, which will overestimate the production rate by neglecting them. While the fluid compressibility could boost the well productivity, which will underestimate the production rate by ignoring it. c) The order of productivity influencing factors is contamination > TPG > the fluid compressibility > stress sensitivity. d) Contamination and the TPG are significant influencing factors at stage of high bottomhole pressure. Moreover, the influence degree of contamination, the fluid compressibility and stress sensitivity gradually increase, while the influence degree of the TPG greatly decreases with lower pressure. • Established a new productivity prediction model considering the contamination impact for the low-permeability reservoirs. • The contamination, threshold pressure gradient, stress sensitivity, and fluid compressibility were all considered. • The newly proposed model was validated by compared with the one presented by other scholars. • Main-dominated productivity factors were significantly investigated. [ABSTRACT FROM AUTHOR]

Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass. • Simple benchmark problems may not be sufficient for validating numerical solvers for fluid-poroelastic structure interaction. • The mass conservation is not accurately satisfied in the primal and primal mixed formulations. • To address these issues, we propose modifications to the primal and primal mixed methods by adding a penalization term. [ABSTRACT FROM AUTHOR]

A poroelastic medium is defined as a continuous system in which the mechanical response arises from the interaction between a deformable elastic solid skeleton and a pressurised fluid, fully saturating the interconnected porous network. The coupled theory of Poromechanics is effectively employed to solve a broad class of problems spanning various fields, ranging from its original application in Geomechanics to addressing contemporary challenges in tissue Biomechanics. Besides the seminal theory introduced by Biot, several variational multi-field principles have been proposed, leading to various finite element formulations. Finite Element approaches are mostly based on a two-field discretisation involving the coupled solid displacement and interstitial fluid pressure as primary variables. However, this choice of the two-primary variables leads to a saddle-point problem, posing a challenge in achieving accurate solutions and thus making the use of stabilisation methods rather mandatory. This study proposes a novel variationally consistent Hybrid Equilibrium Element formulation, based on the complementary strain energy function. A two-field minimisation principle is formulated, with total Cauchy stress and interstitial fluid pressure serving as primary variables. The proposed variational principle provides a variationally consistent framework for designing inherently self-equilibrated Hybrid Equilibrium Elements, where the solid displacement field emerges as a Lagrangian variable to enforce a co-diffusivity constraint at element sides. The fulfilment of the inf-sup condition, typically challenging in developing stable and computationally efficient finite element formulations, is no longer required, a minimisation principle having been adopted, rather than the classical saddle-point principle. The proposed Hybrid Equilibrium Element approach offers a statically admissible solution even in the proximity of singularities or high space gradient stress distribution, providing a more comprehensive assessment of stress distributions and concentrations. The convexity of the new variational principle has been established, ensuring solution uniqueness. The formulation is based on a 2-D triangular Hybrid Equilibrium Element employed to solve plane strain problems. The element has been implemented in the Open source Finite Element Analysis Program (FEAP) and its performance evaluated against classical benchmark problems for poroelasticity, with the emphasis on stress accuracy. The numerical results obtained for the quasi-static analysis of poroelastic systems show the advantages of the proposed approach, in which accurate stress distributions are displayed, even adopting quite coarse meshes. Remarkably, in the proposed approach no stabilisation technique is required. [ABSTRACT FROM AUTHOR]