Search

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (| W |), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building. [ABSTRACT FROM AUTHOR]

We derive, for the first time , the transient response (or Green's function, GF) induced by a general point dislocation in a transversely isotropic and layered poroelastic half-space where the contributions from the fluid dislocation and fluid-phase coupling effect are considered. The GF is expressed in terms of the powerful Fourier-Bessel series system of vector functions recently introduced (with the expansion coefficients being the novel dislocation Love numbers). The corresponding source functions, i.e. discontinuities across the source level, are derived, which show that 1) the fluid-phase creates a new type of source functions called fluid dislocation, and 2) it further contributes directly to the traditional solid horizontal tensile dislocation (or tensile-fracture) via the Biot effective stress coefficient. While the dual-variable and position (DVP) method is applied to take care of multilayers, the Talbot's method is employed to carry out the inverse Laplace transform, both showing excellent numerical stability, efficiency, and accuracy. Key features of these GFs are analyzed numerically. It is shown that 1) the poroelastic process is featured by some transient statuses, including drained and undrained limits; 2) while these two limits are sharply different when the dislocation source is a vertical strike-slip or horizontal tensile-fracture, they are the same when a vertical dip-slip or vertical tensile-fracture is in a homogeneous half-space; 3) in all the cases, there are temporal poroelastic deformations which are significantly different from these two limits; and 4) the fluid dislocation alone could significantly contribute to the poroelastic deformation at the earlier time history. These GFs provide the kernel functions in the corresponding boundary element formulation and the method of fundamental solutions, with potential applications in geomechanics and biomedical engineering. [ABSTRACT FROM AUTHOR]

• The initially stressed porous hyperelasticity (ISPH) is established based on the multiplicative decomposition. • The in-plane elastic coefficients increase with the increase of initial stress. • The ISPH reflects the impact of porosity and initial stress compared with existing constitutive models. • Analytical solutions to the axisymmetric problem under confining pressures are derived. • Results show that initial stresses both affect the pore size variation and the distribution of stress. Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale samples, the parameters in the constitutive equation are determined. Then, the explicit equations of in-plane elastic coefficients are proposed by linearizing the finite deformation formulation. The influences brought by the coexistence of initial stresses and porosity on these coefficients are revealed. Later, comparative analyses of the linearized equations between the present model, the initially-stressed models without pores, the Biot poroelasticity, and the porous hyperelastic model without initial stress are conducted to illustrate the performances of the two ingredients. As a specific example, we investigate the variation of pore sizes under external pressures and initial stresses since changes in pore sizes during deformation are crucial for understanding the accumulation and migration of shale oil and gas. The newly proposed model provides the first initially stressed porous hyperelasticity (ISPH), which is suitable for describing the finite deformation behavior of solid materials with large porosity and significant initial stress simultaneously. [ABSTRACT FROM AUTHOR]

• Transversely isotropic (TI) parameter expression of geogrid reinforced subgrade is set up. • Governing equations of poroelastic reinforced subgrade are established in the wavenumber domain. • The fractional Zener viscoelastic model is introduced to considere the viscosity of subgrade. • The extended precise integration method is employed to obtain the solution in the spatial domain. • Sensitivity analysis for relaxation time, permeability, reinforcement ratio and load velocity are conducted. This paper conducts the dynamic analysis of fractional poroviscoelastic reinforced subgrade under moving loading. Based on the Biot theory and transversely isotropic (TI) parameter expression of the geogrid reinforced subgrade, the governing equations of the poroelastic reinforced subgrade are established in the wavenumber domain by the double Fourier transform. Considering the viscosity of the soil skeleton and the flow-dependent viscosity between the soil skeleton and pore water, the governing equations are extended to the fractional poroviscoelastic medium by introducing the Zener viscoelastic model, fractional calculus theory and the dynamic elastic-viscoelastic correspondence principle. Combining boundary conditions and interlayer continuity conditions, the extended precise integration method (PIM) and double Fourier integral transform are employed to obtain the solution of fractional poroviscoelastic reinforced subgrade in the spatial domain. After the numerical validation, a sensitivity analysis of the relaxation time, permeability, reinforcement ratio and the load velocity are conducted. [ABSTRACT FROM AUTHOR]

• The form of Green's function is first given as a simple explicit function for fluid-saturated multilayered transversely isotropic formation. • The anisotropy and stratified characteristic of formation simultaneously are considered in this study. • The influences of multiple parameters are evaluated to predict the stability of the soil structure. According to the potential theory and mirror image method, the three-dimensional (3D) Green's functions of a fluid-saturated transversely isotropic multilayer formation with different thicknesses were first obtained. The exact 3D explicit closed analytical forms of the pressure increment and stress fields were expressed by simple functions which can be used to accurately calculate the full-field distribution under a fluid source. The numerical results reveal that the method had good convergence, high accuracy, and high stability. Based on this method, the effects of the modulus ratio, stratified characteristic, medium thickness, and medium stacking sequence on the 3D hydraulic coupling response of the medium were examined. Numerical results indicated that these parameters affected the behavior of the formation in different degrees. The main contributions of this study are as follows: (1) the anisotropy and stratified characteristic of the formation material are simultaneously considered; (2) the Green's functions are given as a simple explicit function for fluid-saturated multilayer transversely isotropic formation; and (3) the Green's function is a potential function that can be calculated as a boundary element to improve the calculation accuracy. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, the dynamic responses of a plate on layered transversely isotropic (TI) poroelastic subgrade under moving thermo-mechanical loads are investigated. Based on the thermodynamics, poroelastic mechanics and the Kirchhoff's thin plate theory, the governing equations of the plate and layered TI saturated subgrade are derived in the wavenumber domain. Then, by introducing the flexibility coefficient of the layered TI poroelastic subgrade and the plate-subgrade interface condition, the solution of the plate-subgrade dynamic interaction is obtained through the extended precise integration method. After the presented method is validated, parametric studies are carried out to confirm the influences of the thermal load, plate-subgrade modulus ratio, plate thickness, and the speed of moving load. Parametric analysis shows that the effect of the thermal load cannot be ignored when considering the plate-subgrade dynamic interaction. In addition, the plate-subgrade modulus ratio, plate thickness, and the speed of moving load have a significant effect on the plate-subgrade dynamic interaction. [ABSTRACT FROM AUTHOR]

A recent study published in Blood Weekly discusses a new method for characterizing the mechanical properties of soft tissues and hydrogels. The study introduces a semi-analytical model that allows for the isolation of poroelastic and viscoelastic effects in these materials. By applying this model to microscale indentation data, the researchers were able to identify distinct differences in the mechanical properties of porcine heart and liver tissues, as well as collagen and GelMA hydrogels. This approach offers advantages in terms of speed, computational efficiency, and practicality, and has implications for tissue engineering applications. However, it is important to note that this study has not yet undergone peer review. [Extracted from the article]

This work establishes a novel direct time-domain artificial boundary method for acoustic wave problems. The proposed method, called scaled boundary perfectly matched layer (SBPML), is more generalized and flexible than the conventional perfectly matched layer (PML). This work originates from an extension of recently proposed SBPMLs for wave problems in solid medium and fluid-saturated poroelastic media. The acoustic SBPML is constructed by combining the scaled boundary coordinates transformation inspired by the scaled boundary finite element method (SBFEM) with the complex coordinate stretching technology from the PML. This method directly constructs the complex coordinate stretching function in the scaled boundary coordinates, eliminating the reliance of existing PMLs on the global coordinate system. As a result, this method can accommodate artificial boundaries with general geometries and consider planar physical surfaces and interfaces that may exist in infinite acoustic domains. Moreover, it also can be described as a second-order mixed unsplit-field form of the acoustic pressure-velocity field in time, which can be seamlessly coupled with the finite-element equations of the bounded domains. Numerical examples are presented to demonstrate the accuracy and potential of the proposed method in dealing with the interaction problems in infinite acoustic domains. [ABSTRACT FROM AUTHOR]

This paper explores a complete set of impedance functions including vertical, torsional, horizontal, rocking, and coupling impedances for a surface rigid rectangular foundation bonded on a multilayered transversely isotropic half-space composed of alternatively elastic and poroelastic layers with the use of boundary element method. The slow convergence issue of Green's functions in numerical evaluation is remedied by a simple asymptotic approach presented in this paper. To evaluate the impedances accurately and efficiently, new finite elements namely exponentially-gradient elements are employed to consider the singular behavior of tractions that happens at the edges and corners of the foundation. The validity and accuracy of the solutions are verified by comparing the results with some simpler existing cases. The impedance functions are presented for different aspect ratios of the foundation to be applicable for a variety of structures. The effects of anisotropy, inhomogeneity, layer thickness, underground water level, and soil damping are assessed. [ABSTRACT FROM AUTHOR]

A new indirect boundary integral equation method (IBIEM) is developed to solve the seismic wave scattering problem in a three-dimensional fluid-saturated layered half-space. Based on Biot's theory, the Green's functions of inclined circular loads in porous elastic layered half-space are firstly deduced. According to the single-layer potential theory, when establishing the scattered wave field, the uniform surface loads and fluid sources are located directly on the boundary surfaces of the scatterers, so as to avoid determining the optimal location of fictitious wave sources surface. At the same time, the radiation condition of wave in semi-infinite layered media can be accurately realized by using the dynamic Green's function of concentrated load, and the computational memory can be greatly reduced. The scattering of seismic waves by a canyon topography in saturated layered half-space is examined in detail. The numerical results indicate that with the increase of the porosity of the overlying soil, the amplitude of surface displacement can be amplified by 1∼6 times, and the amplification effect is more significant near the corner of the canyon, which can be attributed to the superposition of wave diffraction effect and resonance amplification effect of saturated soil layer. [ABSTRACT FROM AUTHOR]

• A poro-visco-VIB is developed to simulate the time-dependent porous rock. • Porosity- and stress-dependent permeability of the porous rock and fracture are considered. • Stress reorientation near wellbore in production is studied. • Hydraulic refracture by plugging treatment is studied. The refracture is a promising restimulation technique in the unconventional reservoir during production. It can be realized due to the stress reorientation. To study the mechanism of stress reorientation and refracturing behaviors, a new poro-visco-VIB (virtual internal bond) method is developed in this paper. In the framework of Boit's theory, the visco-VIB is used to describe the skeleton instead of the conventional continuum constitutive model. Through this poro-visco-VIB, both the time- and stress-dependent behaviors of the porous rock can be well simulated. The simulation results of stress reorientation show that the smaller in-situ stress difference can result in a larger stress reorientation scope. To include the fractures into the numerical model, the element partition method (EPM) is adopted. By this VIB/EPM method, the refracture by plugging is studied. The results indicate the plugging position significantly impacts the reorientation distance of refracture. The reorientation distance by plugging fracture end is much larger than by plugging fracture mouth. Thus, it is critically important to control the plugging position in refracture treatment. These findings provide valuable references for the refracture design. It also provides an efficient approach to hydraulic fracture simulation with consideration of the porosity and the time-dependency effect. [ABSTRACT FROM AUTHOR]

We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf–sup stable finite elements have been found suitable to avoid spurious pressure oscillations in the initial phase of the evolution. In this paper, we first clarify the role of the inf–sup condition for the well-posedness of the continuous problem and discuss the choice of appropriate initial conditions. We then develop an abstract error analysis that allows us to analyse some approximation schemes discussed in the literature in a unified manner. In addition, we propose and analyse the high-order time discretization by a scheme that can be interpreted as a variant of continuous-Galerkin or particular Runge–Kutta methods applied to a modified system. The scheme is designed to preserve both, the underlying differential–algebraic structure and the energy-dissipation property of the problem. In summary, we obtain high-order Galerkin approximations with respect to space and time and derive order-optimal convergence rates. The numerical analysis is carried out in detail for the discretization of the two-field formulation by Taylor–Hood elements and a variant of a Runge–Kutta time discretization. [ABSTRACT FROM AUTHOR]

A recent study conducted by researchers at the University of Chile explores the application of fully nonlinear inverse poroelasticity in the field of applied mechanics and engineering. The study focuses on the computation of stress-free geometry in computational biomedicine, which is often based on images that do not account for external forces or transient states. The researchers propose a computational strategy using Anderson acceleration to speed up the convergence of the problem. The findings are supported by numerical simulations in both idealized and realistic scenarios. The study has been peer-reviewed and published in Computer Methods in Applied Mechanics and Engineering. [Extracted from the article]

In this study, we aim at investigating the coupling between poroelasticity (including the fluid flow) and gradient damage phenomena in saturated porous media. To this end, we first extend the thermodynamics-based Biot–Coussy theory of poroelasticity in order to incorporate gradient damage processes. Taking advantage of this framework, we establish a variational formulation for the proposed model, expressed as a four-field incremental minimization problem of a total energy functional which includes poroelastic energy as well as dissipated energy related to damage growth together with Darcy-like fluid flow. Moreover, after a careful analysis of the so-called kinetic porosity in each increment, the incremental minimization is reduced to that of three fields, namely, the displacement and damage fields of the skeleton phase of the porous media as well as the pore fluid pressure. Subsequently, we proceed to the numerical implementation of the variational problem via a semi-staggered optimization algorithm and apply it to a first benchmark modeling for which corresponding solution as well as numerical results for hydraulic fracturing are available. Finally, we perform an application of the proposed model for the evaluation of an Excavation Damage Zone (EDZ) around an underground waste storage gallery. The model is shown to be able to deliver sufficiently reliable predictions. [ABSTRACT FROM AUTHOR]

A recent study conducted by researchers at Polytechnic University Torino in Turin, Italy, focuses on the growth of malignant brain tumors and their impact on surrounding healthy brain tissue. The study proposes a mechanical model that quantifies deformations and solid stresses caused by the expanding tumor mass and incorporates anisotropic growth influenced by brain fibers. The researchers use patient-specific imaging data to create realistic three-dimensional brain geometries and evaluate how the growing mass may compress and deform the cerebral ventricles. The model also allows for the simulation of therapeutic protocols, aiding in the evaluation of treatment efficacy and the development of personalized therapies for individual patients. Overall, this research provides a deeper analysis of the complex interactions between brain tumors and their environment, with a particular focus on ventricular compression and therapeutic treatment. [Extracted from the article]

A recent study conducted at the University of Calgary in Canada explored the influence of changing material properties on cartilage mechanics in osteoarthritis. The study used three-dimensional finite element models to simulate the knee joint in different stages of osteoarthritis. The findings revealed that in the early stage of osteoarthritis, the cartilage demonstrated stiffer behavior due to swelling, while in the late stage, decreased cartilage thickness led to increased knee deformation. The study also highlighted the impact of increased permeability on fluid exudation and pressure within the cartilage. Understanding these material property changes may contribute to a better understanding of cartilage mechanics during disease progression. [Extracted from the article]

The spectral boundary integral (SBI) method has been widely employed in the study of fractures and friction within elastic and elastodynamic media, given its natural applicability to thin or infinitesimal interfaces. Many such interfaces and layers are also prevalent in porous, fluid-filled media. In this work, we introduce analytical SBI equations for cracks and thin layers in a 3D medium, with a particular focus on fluid presence within these interfaces or layers. We present three distinct solutions, each based on different assumptions: arbitrary pressure boundary conditions, arbitrary flux boundary conditions, or a bi-linear pressure profile within the layer. The bi-linear pressure solution models the flux through a thin, potentially pressurized, leaky layer. We highlight conditions under which the bi-linear SBI equations simplify to either the arbitrary flux or arbitrary pressure SBI equations, contingent on a specific non-dimensional parameter. We then delve into the in-plane pressure effects arising from a shear crack in a poroelastic solid. While such pressurization has been suggested to influence frictional strength in various ways and only occurs in mode II sliding, our findings indicate that a significant portion of the crack face is affected in 3D scenarios. Additionally, we investigate non-dimensional timescales governing the potential migration of this pressurization beyond the crack tip, which could induce strength alterations beyond the initially ruptured area. [ABSTRACT FROM AUTHOR]

Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially different sizes dissolved in fluid and are transported through pores of different sizes. The stress tensor, the main force leading to the material deformation, is taken not only in the standard linear form but also with an additional nonlinear part. The model is constructed in 1D space and consists of five nonlinear equations. It is shown that the governing equations are integrable in stationary case, therefore all steady-state solutions are constructed. The obtained solutions are used in an example for healthy and tumour tissue, in particular, tissue displacements are calculated and compared for parameters taken from experimental data in cases of the linear and nonlinear stress tensors. Since the governing equations are non-integrable in non-stationary case, the Lie symmetry analysis is used in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with non-trivial Lie symmetries are identified. As a result, multiparameter families of exact solutions are constructed including those in terms of special functions(hypergeometric and Bessel functions). A possible application of the solutions obtained is demonstrated. • A new mathematical model for solute transport in a poroelastic material is suggested. • All possible steady-state solutions are constructed and used in a realistic example. • Lie symmetry analysis is applied for constructing time-dependent exact solutions. • An example is presented for application of the time-dependent exact solutions. [ABSTRACT FROM AUTHOR]

A recent study conducted at the University of Rochester aimed to understand the factors that contribute to the vulnerability of chondrocytes, the cells responsible for the health of articular cartilage, to mechanical injury or death. The researchers found that tissue deformation, rather than load magnitude, drives chondrocyte death. They also developed a method to calculate poroelastic material properties of cartilage based on time-dependent cell death measurements. This study provides valuable insights into the biomechanics of cartilage and could have practical applications in the field of bioengineering. [Extracted from the article]

A recent study conducted at Purdue University in West Lafayette, Indiana, focused on the mechanical characterization of subcutaneous tissue for drug delivery systems. The researchers used porcine subcutaneous samples and gelatin hydrogels to test the tissue under confined compression. They developed a constitutive model and implemented it into an isogeometric analysis framework to study subcutaneous injection. The study found that the model accurately captured the response of the tissue and showed that the implementation of isogeometric analysis enables predictive simulations of drug delivery. This research has been peer-reviewed and published in the Annals of Biomedical Engineering. [Extracted from the article]

A fully coupled dynamic model is presented in this paper by considering the effect of matric suction, varying parameters in connection with saturation, stratification and transverse isotropy. This model can describe separate flows of two immiscible fluids in layered transversely isotropic unsaturated poroelastic media subjected to harmonically dynamic loads. The ordinary differential matrix equations of this model are derived based on Hankel integral transform and a series of algebraic manipulations. Then the final solution is obtained by conducting the extended precise integration method, and further verified against the existing solution. Numerical examples are carried out to demonstrate the effects of saturation, transversely isotropic parameters, angular frequency and soil thickness on dynamic behavior of unsaturated porous media. [ABSTRACT FROM AUTHOR]

The Shaikan Field is a large producing oil field in the Kurdistan region of Iraq. It consists of multiple fractured reservoirs consisting of limestones, calcareous sandstones and mudstones. The surrounding tectonic terrane is situated in the seismically active Zagros–Taurus orogenic zone, where present-day stresses are high. The regional stresses are found to impose conditions that satisfy failure along reservoir-bound fractures, suggesting that a significant proportion of fractures are likely to be critically stressed. The in situ maximum principal stress magnitudes are estimated using three methods, namely, the tensile and compressive strengths of reservoir rock, and leak-off test (LOT) data. Stress-field orientations are determined from wellbore image log data, which are used to interpret wellbore breakouts and the associated induced tensile fractures. Reservoir pressure has declined since production started and poroelastic responses have been assessed and used to estimate the present-day stress-state and the criticality of those fractures that are most likely to fail or slip. Although a conventional approach has been used the present authors argue that a new approach to stress response with changing pore pressure should be taken. Unlike the previous theory of criticality in which a reduction in pore pressure is considered to lead to a stabilization of the fracture network, the present study suggests that a system may remain critically stressed regardless of pressure decline. Thematic collection: This article is part of the The Geology of Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/the-geology-of-fractured-reservoirs [ABSTRACT FROM AUTHOR]

In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction–diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters on brain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; the Young's modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influence on the tissue deformation and the developing speed of brain swelling. [ABSTRACT FROM AUTHOR]

Fundamental solution for the time-harmonic vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space is developed using a semi-analytical method. First, based on the Green's function of the time-harmonic vertical circular load embedded in the layered half-space, function of the corresponding annular ring load is determined via the method of superposition. Then the disc-medium contact area is discretized into annular ring elements with unknown densities which are determined via an integral least-square approach. Finally, the dynamic vertical compliance is derived by virtue of the equilibrium between the applied load on the disc and the resultant contact stress. Based on the derived fundamental solution, selected numerical examples on the dynamic vertical compliance are presented to investigate the influence of the surface hydraulic condition, fluid saturation, embedment depth of the disc, material anisotropy, material layering, and input frequency. [ABSTRACT FROM AUTHOR]

This paper attempts to develop a novel hybrid method to address the dynamic impedance functions of a rigid strip-foundation resting on a non-homogeneous poroelastic soil profile. The rigid footing is perfectly bonded to the soil profile and is subjected to time-harmonic loadings. The soil profile under consideration comprises several horizontal layers with different thicknesses and an underlying half-space or fixed base (layered stratum); these aspects are governed by Biot's theory of poroelastodynamics combined with a simplified approach to consider the saturation effect. The dynamic interaction problem is solved by employing a hybrid formulation combining the Boundary Element Method (BEM), the Thin Layer Method (TLM) and the Perfectly Matched Layer technique (PML), which allows the calculation of Green's functions for the multi-layered poroelastic half-space. Comparisons with the existing results were made to verify the formulation; these are special cases of the more general problems that have been addressed. Select numerical solutions are presented to demonstrate the impact of the boundary conditions at the bottom of the soil profile, geotechnical properties (such as the saturation degree, uniformity coefficient, angle of internal friction, etc.) and non-homogeneity effects on the dynamic impedance functions. [ABSTRACT FROM AUTHOR]

The purpose of hydraulic fracturing or acid fracturing is to use artificial fractures to connect the caves and establish high-conductivity oil and gas flow channels between the caves and the wellbore, the essence of the process is the interaction of a hydraulic fracture with a hole in poroelasticity medium. While the interaction mechanism between hydraulic fracture and hole in the poroelasticity medium remains unclear. In order to clarify the process, a seepage-free flow-mechanical coupling extended finite element method (XFEM) model was established. In the numerical study, the curved beam fracture propagation path with holes and initial preset fracture was calculated, and fracture connecting holes under triaxial stress was simulated. The results showed that the fracture path deflection degree was reduced by fluid pressure in the holes. Under triaxial stress, hydraulic fractures tend to extend toward the direction of the maximum horizontal principal stress. When the angle between the perforation direction and the maximum horizontal principal stress was 30°, the hydraulic fracture was deflected quickly in the direction of the maximum horizontal principal stress. As the angle was increased, the hydraulic fracture took more time to deflect toward the direction of the maximum horizontal principal stress. [ABSTRACT FROM AUTHOR]

This paper presents a boundary meshless method, singular boundary method (SBM), in conjunction with the exponential window method (EWM) to simulate the dynamic response of the 2D partially saturated poroelastic media. The problem is firstly solved in the frequency-domain resulted from the time-domain governing equations via the Fourier transformation. Then the SBM approximates the solutions with a linear combination of fundamental solutions with respect to the source points on the physical boundary. To successfully apply the SBM, two issues are addressed. Firstly, the kernel functions, namely the fundamental solutions of frequency-domain governing equations, are derived based on the eigen-analysis. Secondly, the source singularities of the fundamental solutions are desingularized with analytical formulas. After obtaining the SBM formulation, the time-domain solutions can be obtained by the EWM, where the frequency domain windowing technique is introduced to stabilize the oscillations caused by damping parameters. Four numerical examples are carried out to show the validity and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, we have derived a theoretical solution for the poroelastic axisymmetric Boussinesq problem when an indenter with arbitrary profiles is subjected to step displacement loading. The analysis is conducted within the framework of Biot's theory, employing the McNamee–Gibson displacement function method. We explore two distinct scenarios for surface drainage boundary conditions: one where the surface allows full permeability and another where it is fully impermeable. The formulation of the mechanical boundary condition at the surface relies on an equation that establishes the relationship between the depth of indentation and the contact radius. Our solution encompasses two aspects: force asymptotes at the undrained and drained limits, and a normalized force relaxation that accounts for transient responses. Specific findings are presented for three indenter shapes: paraboloidal, conical, and cylindrical. Of particular significance, we demonstrate that for these specific indenter shapes, the normalized force relaxation at ω = 0 can be expressed in closed form in the Laplace domain. In addition to this analytical breakthrough, we conducted numerical simulations employing actual indenters. Remarkably, the normalized force relaxation curves from actual indenters show negligible dependence on material properties and closely align with our closed-form solution at ω = 0. This finding suggests that the closed-form solution could act as a universal master curve capable of characterizing the normalized force relaxation response in instances of a real indenter, irrespective of material properties. [ABSTRACT FROM AUTHOR]

New research from Purdue University has developed a model called MPET2 that combines the multi-network poroelastic theory with solute transport equations to predict material deformation, fluid dynamics, and solute transport in different compartments of a deformable multiple-porosity medium. The model has a wide range of applications, including studying rock formations, soil mechanics, and subsurface reservoirs, as well as investigating biological tissues and modeling groundwater flow. The researchers propose a stabilized formulation of the MPET2 model and conduct simulations of subcutaneous injection of monoclonal antibodies to demonstrate its effectiveness. The study also explores the effects of different injection conditions on drug absorption, suggesting potential for optimizing injection strategies in the future. [Extracted from the article]

• Fluid pressure can be generated in a poroelastic cylinder subjected to a sudden twist when finite deformations are considered. • Dissipation of fluid pressure taking place after the sudden twist is applied to the cylinder results in the initial increase of the cylinder's diameter and the decrease of the diameter in the long-term. The paper examines the torsion of a solid cylinder composed of a fluid-saturated porous medium with a hyperelastic porous skeleton. The general formulation of the problem is followed with applications to special cases where the strain energy function for the skeletal behavior is described by either a neoHookean or an Ogden-type hyperelastic behavior. The analytical developments involve the numerical solution of the governing equations followed by a computational treatment of the problems using the ABAQUS™ finite element code. The time-dependent mechanics of the twisted cylinder is examined for the instantaneous short-term behavior as well as the long-term behavior when the excess fluid pressures generated during the application of a finite twist have dissipated. [ABSTRACT FROM AUTHOR]

Using the indirect boundary element method (IBEM) and Biot's theory, surface displacement associated with the field scattered by a 3-D inclusion in a two-phase poroelastic half space under plane SV waves has been studied. According to single-layered potential theory, scattering waves are constructed by the introduction of uniform loads and fluid sources distributed over the surface of the half space and on the interface between the inclusion and the half space. The magnitudes of these loads and sources are obtained by establishing a boundary integral equation based on continuity boundary conditions. The accuracy of this method is verified by comparing the results of degradation with existing results of cavities in elastic media. The scattering of plane waves due to a 3-D inclusion is investigated from several aspects. Numerical results show that the dynamic coupling effect between the solid frame and pore water and the permeability condition of the poroelastic soil boundary result in a generally larger surface displacement amplitude for dry soil than poroelastic soil when the porosity is n = 0.3. By contrast, the surface displacement amplitude of poroelastic soil is larger than that of dry soil when the porosity is n = 0.36. As the depth of burial decreases and as the inclusion becomes wider and thicker, the scattering effect increases. The peak value of the displacement spectrum curve usually appears near the incident frequency η = 1. [ABSTRACT FROM AUTHOR]

Slow slip events on tectonic faults, sliding instabilities that never accelerate to inertially limited ruptures or earthquakes, are one of the most enigmatic phenomena in frictional sliding. While observations of slow slip events continue to mount, a plausible mechanism that permits instability while simultaneously limiting slip speed remains elusive. Rate-and-state friction has been successful in describing most aspects of rock friction, faulting, and earthquakes; current explanations of slow slip events appeal to rate-weakening friction to induce instabilities, which are then stalled by additional stabilizing processes like dilatancy or a transition to rate-strengthening friction at high slip rates. However, the temperatures and/or clay-rich compositions at slow slip locations are almost ubiquitously associated with rate-strengthening friction. In this study, we propose a fundamentally different instability mechanism that may reconcile this contradiction, demonstrating how slow slip events can nucleate with mildly rate-strengthening friction. We identify two destabilizing mechanisms, both reducing frictional shear strength through reductions in effective normal stress, that counteract the stabilizing effects of rate-strengthening friction. The instability develops into slow slip pulses. We quantify parameter controls on pulse length, propagation speed, and other characteristics, and demonstrate broad consistency with observations of tectonic slow slip events as well as laboratory tribology experiments. [ABSTRACT FROM AUTHOR]

The fast multi-pole indirect boundary element method (FM-IBEM) is proposed to efficiently solve the high-frequency and large-scale two-dimensional (2-D) elastic wave scattering in a fluid-saturated poroelastic heterogeneous medium. The diffracted wave fields are constructed by applying virtual distributed loads and fluid sources on the boundaries according to the single-layer potential theory, and the multi-pole moment and local expansion coefficients of 2-D Green's function are deduced based on Graf addition theorem. Numerical results illustrated that the proposed method can essentially reduce the calculation CPU time and the memory requirement. The 2-D scattering of elastic waves by a canyon and a group of cracks in a fluid-saturated poroelastic half-space is further investigated. It shows that the scattering characteristics are closely related to the incident frequency, porosity of the medium and special topography. There is a significant ground motion amplification effect around the canyon, while a group of cracks produce an isolation effect on the half-space surface motion. [ABSTRACT FROM AUTHOR]

Abstract The problems of quasi-static poroelasticity for a cavity and a crack in an isotropic homogeneous medium are considered. The cavity (crack) surface is subjected to pressure of fluid injected inside by external sources. Using simple and double layer potentials of poroelasticity the problems are reduced to 2D-integral equations on the cavity and crack surfaces. The case of spherical cavity is considered in detail. It is shown that the 2D-integral equations of the crack problem contain operators with various time-asymptotics at infinity. Neglecting operators rapidly vanishing with time results in an approximate formulation of the crack problem. For numerical solution, the integral equations are discretized using Gaussian approximating functions. For planar cracks, an efficient numerical method based on the fast Fourier transform technique is proposed. Numerical solution for a penny shaped crack is presented. [ABSTRACT FROM AUTHOR]

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

Abstract The Lamina Cribrosa is a part of the optic nerve head acting as a scaffold for collecting the retinal ganglion cell axons. It can be modeled as a poroelastic material where the saturated porosity stands for the capillary network running inside the collagen beams. Our aim is to study the interaction between tissue porosity, deformation and hemodynamics. To this end we first focus on the derivation of a poroelastic model in a rather general case, using as a prototype a model of species diffusion in an elastic material. Then we outline the clinical significance of the mechanical behavior of the Lamina Cribrosa and show, through numerical simulations, how an increased intraocular pressure results in a deformation affecting porosity and blood perfusion. We emphasize how the model behavior relies on the free energy expression. [ABSTRACT FROM AUTHOR]

Researchers at Purdue University have developed a new model, called MPET2, to predict the absorption of monoclonal antibodies (mAbs) during and after subcutaneous injection. The model is based on principles of tissue biomechanics and fluid dynamics and describes tissue deformation, fluid flow, and the transport of mAbs in different compartments of the subcutaneous tissue. The researchers used the model to simulate the injection of mAbs and found that it accurately predicted long-term drug absorption. This research has implications for the pharmaceutical industry and could improve the understanding and development of subcutaneous drug delivery methods. [Extracted from the article]

Earlier modeling approaches in the field of mixtures assumed the solid phase of the mixture was the predominant constituent and simplified the constitutive laws for the fluid phase. In the field of mixtures, it has been argued that methods such as the theory of poroelasticity are incapable of accurately capturing mass exchange between phases and stress and strain fields. Mass exchange between phases and accurate stress and strain variations of each phase are indispensable to many fields of study, such as bone remodeling, fault movement in rocks, and shock waves in soils. This study presents an alternative method for capturing the stress and strain fields of mixtures, focusing on the advection term in the balance of linear momentum and mass exchange for each phase. In addition, this extended theory has the potential for measuring the shear stress field of a viscous fluid component, considering complex boundary conditions, and modeling chemical reactions between mixture phases. The capability of the model has been evaluated by analyzing 2D and 3D examples, including a realistic bone remodeling scenario. Calculations have shown a maximum difference of 20% in the displacement fields. Thus, results clearly demonstrate the importance of considering the advection term and mass exchange between phases, as its application causes significant variations in the displacement and stress fields of the mixture. The developed model of this study can be considered as a general theory, which yields the classic poroelastic model with certain manipulations. [ABSTRACT FROM AUTHOR]

Slime molds are composed of simple units that aggregate into networks that exhibit sophisticated emergent responses. These networks operate as smart biological materials, and strongly rely on mechanical interactions to adapt dynamically to the environment. While the microscale features are well understood, emergent intelligence at the macroscale remains a challenge. In this paper, we present a novel computational model, validated with experiments, to elucidate the nonlinear mechanical interactions underlying the synchronized morphological response of the slime mold Physarum polycephalum. We model the growth and reshaping of the network with an integrated phase-field approach and the internal flow as a diffusion–advection process through a poroelastic cytoplasm. The internal flow redistributes nutrients and free Ca2＋, which interacts with the synchronized pulsation of the network. Our study demonstrates that this nonlinear interplay – between the mechanics of the cytoplasm, the pulsation amplitude, and flow velocity – is responsible for the adaptive patterns observed in experiments. Our model reproduces the consolidation of optimized vein structures from amorphous layers, captures optimized redistribution morphologies, and explains inter- and intraspecies behaviors observed in the laboratory. Our results indicate a path for developing active soft materials that exhibit decentralized intelligence and superior adaptivity to the medium. [ABSTRACT FROM AUTHOR]

Highlights • Poroelastic chemomechanical theory for analyzing vascular collapse in solid tumors. • Effect of biochemmechanical coupling mechanism and fluid transport on vessel buckling. • Biochemomechanical finite element method for buckling and postbuckling analysis. Abstract The collapse of blood vessels are widely observed in solid tumors, but the mechanisms underpinning this abnormal behavior remain unclear. In this paper, we investigate the stability of blood vessels embedded in a growing solid tumor by using a chemomechanical poroelastic theory. Linear stability analysis is first made to give the critical condition of vascular buckling. Thereby, pattern diagrams are provided to predict the collapsed shape of a blood vessel from the mechanical and geometric parameters of the system. Due to the mechano-chemo-biological coupling effect in tumors which involve both fluid transport and tissue growth, the buckling of blood vessels exhibits distinctly different features from such previously reported tubular tissues as airways and esophagi. We show that interstitial fluid pressure tends to drive blood vessels to buckle with a lower buckling mode, while perivascular cell proliferation favors a higher mode. Furthermore, a nonlinear biochemomechanical finite element method is formulated to track the morphological evolution of blood vessels during postbuckling. It is found that the blood vessels with the second mode of buckling may readily evolve into a crack-like shape. This method can reproduce the essential features of vascular collapse observed in in vivo tumors and provide clues for vascular normalization and stress alleviation in cancer treatments. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract Multiple-porosity models are commonly used to describe the poromechanical behavior of complex porous solids occurring in earth and life sciences. From the characterization standpoint, the poroelastic constants of such materials may be determined from the poroelastic constants of their single-porosity constituents. The uniqueness principle of the poroelastic energy density function is herein used to construct and solve a system of equations between the described sets of poroelastic constants in a multiple-porosity material. The method systematically applies to an arbitrary number of co-existing porosities. The presented energy-based approach resolves the perceived closure problem that was reported for solids with more than two porosity systems. [ABSTRACT FROM AUTHOR]

Low-permeablity materials may be seen as natural geological barriers for radioactive waste repositories. However, to ensure their safe performance, a good understanding of their mechanical properties is required. Although the standard Biot's poroelastic model is widely used to estimate the key properties of these materials, experimental observations differ from this mathematical formulation and suggest that a more complex rock deformation behaviour to include a creep effect is needed. In this study, the Biot's differential equations are modified to include a rheological skeleton. In comparison with other existing models, here we propose a formulation with a minimal parametric uncertainty: we show that with just one additional physically-based parameter, the experimental creep behaviour is properly described. This enhanced model is implemented within a finite element framework and employed in a fitting algorithm to extract the hydro-mechanical properties from experimental data. To illustrate its generality, we analyse laboratory tests performed on three different types of materials: (a) an unlithified lower Oligocene clay from Belgium (Boom Clay), (b) an indurated Jurassic mudrock (Callovo-Oxfordian mudstone) and (c) a Triassic siltstone (Mercia Mudstone Formation). Numerical fits to the data support the validity of this approach and demonstrate its applicability to a range of low-permeability materials regardless of mineralogy or burial history. [ABSTRACT FROM AUTHOR]

Based on a linear poroelastic formulation, we present an asymptotic analysis of the crack tip fields for steady-state crack growth in polymer gels. A finite element method is then developed for numerical analysis. A semi-infinite crack in a long strip specimen subject to plane-strain loading is studied in detail. The crack-tip fields from the numerical analysis agree with the asymptotic analysis with a poroelastic stress intensity factor, which is generally smaller than the stress intensity factor predicted by linear elasticity due to poroelastic shielding. Similarly, the crack-tip energy release rate calculated by a modified J -integral method is smaller than the applied energy release rate. The size of the poroelastic crack-tip field (or K -field) is characterized by a diffusion length scale that is inversely proportional to the crack speed. For relatively fast crack growth, the diffusion length is small compared to the strip thickness (small-scale diffusion), and the poroelastic K -field transitions to an elastic K -field at a distance proportional to the diffusion length. In this case, the crack-tip energy release rate decreases with increasing crack speed under the same loading condition. For relatively slow crack growth, the diffusion length is greater than the strip thickness (large-scale diffusion), and the poroelastic crack-tip field is confined and transitions to a one-dimensional diffusion zone ahead of the crack tip. In this case, the energy release rate increases with increasing crack speed. Both immersed and not-immersed crack face conditions are considered. Under the same loading conditions, the poroelastic stress intensity factor and the modified J -integral are higher for the immersed case than not-immersed, but they approach the same values at the fast and slow crack limits. In general, if the crack-tip energy release rate is taken to be the intrinsic fracture toughness of the gel, the applied energy release rate as the apparent fracture toughness is greater due to energy dissipation associated with solvent diffusion, which is referred to as poroelastic toughening. It is proposed that the modified J -integral can be used to determine the intrinsic fracture toughness of the gel in experiments, which may or may not depend on crack speed. Moreover, the present results are found to be qualitatively consistent with previous experiments on the effects of solvent viscosity and crack-tip soaking. [ABSTRACT FROM AUTHOR]

Self-consistent extension of linear poroelasticity (Biot 1941) to overlapping systems or scales of porosity and permeability within fluid-saturated, elastic materials is presented. An arbitrary number of N porosity systems with linear relations for fluid flow within and in between the porosities is considered. The theory is applied to Cryer's problem of poroelasticity. The problem considers sudden confinement of a spherical sample of porous material while the pore fluid is allowed to drain from the surface boundary. The closed-form solution to Cryer's problem is developed in Laplace transform domain for the general case where N porosity systems with full inter-porosity fluid exchange properties are present in the spherical sample. Numerical results are retrieved in the time domain for a hierarchical class of multiple-porosity models describing the commonly observed porosity systems of organic-rich shale. The stress and pore fluid pressure solutions pertaining to the cases of up to five coexisting porosity systems are demonstrated. [ABSTRACT FROM AUTHOR]

Scattering of longitudinal monochromatic waves on an isolated inclusion in an infinite poroelastic medium is considered. Wave propagation in both medium and inclusion is described by Biot’s equations of poroelasticity. For the material parameters typical for sedimentary rocks, the corresponding system of equations contains a second order differential operator with a small parameter. As the result, the wave field in the medium consists of a slowly changing part and boundary layer functions concentrated near the inclusion interface. Such a specific form of the wave field should be taken into account by the numerical solution of the problem since application of conventional numerical methods can result in substantial errors. In the present paper, the method of matched asymptotic expansions is applied to the solution of the scattering problem for a spherical inclusion. The systems of equations for a slowly changing part of the wave field and for boundary layer functions are derived. The solutions of these systems for the fields in the vicinity of the inclusion and for far wave fields are obtained and analyzed. Comparisons of the results of the straightforward solution and the asymptotic expansion are presented. [ABSTRACT FROM AUTHOR]

A random distribution of cylindrical fluid cavities in a poroelastic matrix obeying Biot’s theory is considered. Using the Conoir–Norris generalization of the Linton–Martin formula to media sustaining both P and SV waves, we examine successively the incidence of fast, slow and shear waves onto the random medium. Analytical expressions are sought for the effective wavenumbers of the coherent waves in the Rayleigh limit. The estimates for the mass density and moduli of the heterogeneous media are presented up to the order of c 2 in concentration. The limiting case of random fluid cavities in an elastic matrix is also discussed. [ABSTRACT FROM AUTHOR]

Wave propagation phenomena occur in reality often in semi-infinite two-phase (porous) regions. It is well known that such problems can be handled well with the poroelastodynamic Boundary Element Method (BEM). But, it is also well known that the BEM with its dense matrices becomes prohibitive with respect to storage and computing time. This is especially true for poroelastodynamics, where in the best case four degrees of freedom per node are required. As well, the fundamental solution of poroelastodynamics is computationally expensive. Here, a fast multipole BEM is proposed to circumvent those points. The Chebyshev interpolation-based FMM significantly reduces the memory consumption of the system matrix and thus allows for larger problem sizes to be treated. As well, it requires fewer evaluations of the fundamental solution. To employ an iterative solver, the use of a transformation of the material data is mandatory. Numerical tests show the expected almost linear complexity of the proposed method. [ABSTRACT FROM AUTHOR]

Growth of biological tissues has been recently treated within the framework of Continuum Mechanics, by adopting heterogeneous poroelastic models where the interaction between soft matrix and interstitial fluid flow is coupled with inelastic effects ad hoc introduced to simulate the macroscopic volumetric growth determined by cells division, cells growth and extracellular matrix changes occurring at the micro-scale level. These continuum models seem to overcome some limitations intrinsically associated to other alternative approaches based on mass balances in multiphase systems, because the crucial role played by residual stresses accompanying growth and nutrients walkway is preserved. Nevertheless, when these strategies are applied to analyze solid tumors, mass growth is usually assigned in a prescribed form that essentially copies the in vitro measured intrinsic growth rates of the cell species. As a consequence, some important cell-cell dynamics governing mass evolution and invasion rates of cancer cells, as well as their coupling with feedback mechanisms associated to in situ stresses, are inevitably lost and thus the spatial distribution and the evolution with time of the growth inside the tumor –which would be results rather than inputs– are forced to enter in the model simply as data. In order to solve this paradox, it is here proposed an enhanced multi-scale poroelastic model undergoing large deformations and embodying inelastic growth, where the net growth terms directly result from the “interspecific” predator-prey (Volterra/Lotka-like) competition occurring at the micro-scale level between healthy and abnormal cell species. In this way, a system of fully-coupled non-linear PDEs is derived to describe how the fight among cell species to grab the available common resources, stress field, pressure gradients, interstitial fluid flows driving nutrients and inhomogeneous growth all simultaneously interact to decide the tumor fate. [ABSTRACT FROM AUTHOR]

We present new results explaining why fracturing in saturated porous media is not smooth and continuous but is a distinct stepwise process concomitant with fluid pressure oscillations. All exact solutions and almost all numerical models yield smooth fracture advancement and fluid pressure evolution, while recent experimental results, mainly from the oil industry, observation from geophysics and a very few numerical results for the quasi-static case indeed reveal the stepwise phenomenon. We summarize first these new experiments and these few numerical solutions for the quasi-static case. Both mechanical loading and pressure driven fractures are considered because their behaviours differ in the direction of the pressure jumps. Then we explore stepwise crack tip advancement and pressure fluctuations in dynamic fracturing with a hydro-mechanical model of porous media based on the Hybrid Mixture Theory. Full dynamic analyses of examples dealing with both hydraulic fracturing and mechanical loading are presented. The stepwise fracture advancement is confirmed in the dynamic setting as well as in the pressure fluctuations, but there are substantial differences in the frequency contents of the pressure waves in the two loading cases. Comparison between the quasi-static and fully dynamic solutions reveals that the dynamic response gives much more information such as the type of pressure oscillations and related frequencies and should be applied whenever there is a doubt about inertia forces playing a role - the case in most fracturing events. In the absence of direct relevant dynamic tests on saturated media some experimental results on dynamic fracture in dry materials, a fast hydraulic fracturing test and observations from geophysics confirm qualitatively the obtained results such as the type of pressure oscillations and the substantial difference in the behaviour under the two loading cases. [ABSTRACT FROM AUTHOR]

We discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all necessary properties of equilibrium equations. In particular, the loss of the ellipticity could be considered as a criterion of a strain localization or material instability. [ABSTRACT FROM AUTHOR]