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An anisotropic modelling of hollow porous cylinders under harmonic axial loading is proposed to simulate the in vivo behavior of structural elements of cortical bone called osteons. The peripheral surface of the medium is supposed to be impermeable, except on possible existing cracks. Numerical tests are performed by analytical and finite element methods based on the Biot poroelastic theory. The influence of microcracks on the fluid flow is numerically investigated. The findings show that the existence of peripheral cracks directly modifies the stimulation of the mechano‐sensitive network of the bone. Thus, this study attempts to propose a likely mechanism by which bone can sense changes of the surrounding mechanical environment.

The purpose of this study is to present a theoretical investigation of the effects of cavitation and couple stress on the squeeze film behavior between an anisotropic poroelastic rigid disc and a sinusoidally oscillating rigid disc.

Based on the microcontinuum theory of Vijay Kumar Stokes and the Elrod–Adam algorithm, the non-Newtonian Reynolds equation coupled with modified Darcy's law for lubricant flow through the porous disc is derived. This numerical study includes the continuity of tangential velocity at the porous–fluid interface and the effects of percolation of the polar additives into the anisotropic porous disc.

The effects of couple stress, oscillating amplitude, percolation additives, permeability and anisotropic permeability on the squeeze film characteristics are discussed. It is found that both the percolation effect of the lubricant additives and the anisotropic structure of the porous surface reduce the flow in the porous disc, resulting in a decrease in pressure. It is also observed that cavitation effects are more pronounced for Newtonian fluids than couple stress fluids.

The results of this study can be used to design a variety of engineering applications such as bearings, wet clutches and non-contact mechanical seals.

The purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely.

Techniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed.

Complex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model.

To the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions.

A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions.

The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature.

In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions.

This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper.

The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM).

The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium.

Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified.

The paper includes implications for the development of fluid dynamics of porous media.

This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.

The present discussed problem deals with the torsional surface wave scattering in an initially stressed inhomogeneous medium. The assumed model consists of tri-mediums resting over a viscoelastic semi-infinite medium and the considered tri-mediums are transversely isotropic, porous, and heterogeneous respectively under the impression of initial stress.

Heterogeneities are associated with density and rigidity in the intermediate layer and considered heterogeneities are of the trigonometric form. Displacement components are derived for mediums by applying separable variables.

Frequency equation is deduced by using suitable boundary conditions, defined at the free surface of the uppermost medium, and on the interfaces between mediums. The derived equation is of the complex form, real and imaginary parts direct the phase/damped velocities respectively. Additional results are considered in particular cases. Numerical examples are adopted for computing frequency equation and drawn consequences are demonstrated graphically to analyze the significant impact of various parameters on the phase velocity as well as on damped velocity of the surface wave sketched against the wavenumber.

This presented research work provides a different view over the analysis of torsional surface waves than the earlier investigations. Previously studied problems on the wave generation were conducted in different models under the various affecting parameters. Study on torsional wave generation in the present model is not carried out till now. This study may find its virtue in the theoretical aspect as well as in the possible practical implications. The outcomes are relevant to geology and allied areas; moreover, the concern applications may be implicated in geological exploration, civil engineering, and prediction of Earthquake etc.

The purpose of this paper is to investigate propagation characteristics of seismic waves at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid.

A theoretical formulation of partially saturated poro-thermoelastic solid is used in this study established by Zhou et al. (2019). The incidence of two primary waves (P and SV) is taken. The incident wave from the elastic solid induces two reflected waves and five refracted waves. Due to viscous pore fluids, partially saturated poro-thermoelastic solid behave dissipative, whereas elastic solid behaves non-dissipative. As a result, both reflected and incident waves are homogeneous. However, all the refracted waves are inhomogeneous. A non-singular system of linear equations is formed by the coefficients of reflection and refraction for a specified incident wave. The energy shares of various reflected and refracted waves are determined by using these reflection and refraction factors. Finally, a sensitivity analysis is performed, and the effect of critical variables on energy partitioning at the interface is observed. The numerical example shows that throughout the process of reflection/refraction, the energy of incidence is conserved at all angles of incidences.

This study demonstrated two refracted (homogeneous) and five refracted (inhomogeneous) waves due to the incident wave from elastic solid. The reflection and refraction coefficients and partitioning of incident energy are acquired as a part of diverse physical parameters of the partially saturated poro-thermoelastic media. The interference energies between unlike pairs of refracted waves have been discovered due to the dissipative behavior of unsaturated poro-thermoelastic solid.

The sensitivity of different energy shares to various aspects of the considered model is graphically analyzed for a specific numerical model. The energy balance is maintained by combining interaction energy and bulk wave energy shares.

The purpose of the present study is to investigate the dispersion and damping behaviors of Love-type waves propagating in an irregular fluid-saturated fissured porous stratum coated by a sandy layer.

Two cases are analyzed in this study. In case-I, the irregular fissured porous stratum is covered by a dry sandy layer, whereas in case-II, the sandy layer is considered to be viscous in nature. The method of separation of variables is incorporated in this study to acquire the displacement components of the considered media.

With the help of the suitable boundary conditions, the complex frequency relation is established in each case leading to two distinct equations. The real and imaginary parts of the complex frequency relation define the dispersion and attenuation properties of Love-type waves, respectively. Using the MATHEMATICA software, several graphical implementations are executed to illustrate the influence of the sandiness parameter, total porosity, volume fraction of fissures, fluctuation parameter, flatness parameters and ratio of widths of layers on the phase velocity and attenuation coefficient. Furthermore, comparison between the two cases is clearly framed through the variation of aforementioned parameters. Some particular cases in the presence and absence of irregular interfaces are also analyzed.

To the best of the authors' knowledge, although many articles regarding the surface wave propagation in different crustal layers have been published, the propagation of Love-type waves in a sandwiched fissured porous stratum with irregular boundaries is still undiscovered. Results accomplished in this analytical study can be employed in different practical areas, such as earthquake engineering, material science, carbon sequestration and seismology.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media..

The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB.

In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix.

The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.