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In this paper, wave propagation in a poroelastic thick-walled hollow cylinder is investigated in the framework of Biot’s extension theory. Biot’s theory of poroelasticity is valid for isotropic porous solids saturated with non-viscous fluid. The bulk and shear viscosities are not considered in the classical Biot’s theory. Biot’s extension theory takes all these into an account. Biot’s extension theory is applied here to investigate the radial vibrations in thick-walled hollow poroelastic cylinder. The paper aims to discuss these issues.

By considering the stress-free boundaries, the frequency equation is obtained in the presence of dissipation. Limiting case when the ratio between thickness and inner radius is very small is investigated numerically. In the limiting case, the asymptotic expansions of Bessel functions are employed so that frequency equation is separated into two parts which gives attenuation coefficient and phase velocity. If the shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory.

For the numerical purpose, the solids Berea sandstone and bone are used. The results are presented graphically.

Radial vibrations of thick-walled hollow poroelastic cylinder are investigated in the framework of Biot’s extension theory. Due to the mathematical complexity, limiting case is considered. The complex valued frequency equation is discussed numerically which gives the attenuation coefficient and phase velocity. If shear viscosity is neglected, then the problem reduces to that of the classical Biot’s theory. The comparison has been made between the current results and that of classical results.

The purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.

Torsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.

Phase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.

Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

A three‐dimensional dynamic analysis program for saturated porous‐rocks and soils (MPDAP‐3D) is developed in this study. The theoretical formulations incorporated in the proposed computer program are the extension of Biot’s two‐phase theory to non‐linear region. The generalized Hoek and Brown model is used to represent the skeleton constitutive relation. A three‐dimensional elasto‐plastic matrix for the generalized Hoek and Brown model is derived by extending two‐dimensional formulation. Numerical study for typical verification problems is carried out to show the validation of the computational algorithms of the computer program.

The paper aims to propose a rate‐dependent model of structural concrete in combination with the kinematics of condensed water.

First, the paper proposes the coupling model of water versus cracked concrete with a mathematical completeness of equilibrium and deformational compatibility. The proposed model deals with anisotropy of structural performance and of permeability, which is a particular issue of concrete caused by cracks. The governing equation for saturated concrete in this study is based on Biot's theory that deals with particle assembly as a two‐phase composite. Second, the paper shows the possible reduction of the fatigue life of real‐scale bridge RC decks owing to the water residing in structural cracks under moving wheel‐type loading.

The paper shows that the existence of water possibly has an influence on the rate‐dependency of structural performance. The comparison of transition of pore pressure and principal strain indicates that damage to the concrete skeleton is accelerated by internal stress caused by high pore pressure. It suggests that the existence of water can reduce the fatigue life of bridge decks, especially when the upper layer is saturated.

This paper clarifies the effect of pore water on structural concrete by using numerical model considering kinematics of water.

This paper presents a mathematical model for the analysis of cohesive fracture propagation through a non‐homogeneous porous medium. Governing equations are stated within the frame of Biot's theory, accounting for the flow through the solid skeleton, along the fracture and across its sides toward the surrounding medium. The numerical solution is obtained in a 2D context, exploiting the capabilities of an efficient mesh generator, and requires continuous updating of the domain as the fractures enucleate and propagate. It results that fracture paths and their velocity of propagation, usually assumed as known, are supplied directly by the model without introducing any simplifying assumption.

A finite element solution to the rolling of two‐phase materials is presented and applied to the rolling of prepared sugar cane. The generalized Biot theory is extended and modified to suit the present problem and the velocity of the solid skeleton and the pore pressure are taken as the primary unknowns. The finite element approach is applied to the governing equations for spatial discretization, followed by time domain discretization by standard difference methods. A constitutive relation evaluated from a finite element simulation of experiments performed on a constrained compression test cell is employed. The computational model of the rolling of prepared cane with two rolls is presented. The material parameters of prepared cane are described and their variation during the rolling process are derived and discussed. Numerical results are presented to illustrate the performance and capability of the model and solution procedures.

Presents a fully coupled numerical model to simulate the slow transient phenomena involving heat and mass transfer in deforming partially saturated porous materials. Makes use of the modified effective stress concept together with the capillary pressure relationship. Examines phase changes (evaporation‐condensation(, heat transfer through conduction and convection, as well as latent heat transfer. The governing equations in terms of gas pressure, capillary pressure, temperature and displacements are coupled non‐linear differential equations and are discretized by the finite element method in space and by finite differences in the time domain. The model is further validated with respect to a documented experiment on partially saturated soil behaviour, and the effects of two‐phase flow, as compared to the one‐phase flow solution, are analysed. Two other examples involving drying of a concrete wall and thermoelastic consolidation of partially saturated clay demonstrate the importance of proper physical modelling and of appropriate choice of the boundary conditions.

This paper aims to study photothermal excitation process in an initially stressed semi-infinite double porous thermoelastic semiconductor with voids subjected to Eringen’s nonlocal elasticity theory under the fractional order triple-phase-lag thermoelasticity theory. The considered substrate is governed by the mechanical and thermal loads at the free surface.

The normal mode technique is used to carry out the investigation of photothermal transportation. By virtue of the MATHEMATICA software, each distribution is exhibited graphically.

The expressions of the displacements, temperature, volume fractions of both kinds of voids, carrier density and stresses are determined analytically. With the help of the numerical data for silicon (Si) material, graphical implementations are presented on the basis of initial stress, fractional order, nonlocality and thermoelectric coupling parameters.

The present study fabricates the association of Eringen’s nonlocal theory and the stress analysis in a semiconducting double porous thermoelastic material with voids, which significantly implies the originality of the conducted work.

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 propagation of circular crested waves in a fluid saturated incompressible porous plate is analyzed. The frequency equations, for symmetric and anti‐symmetric waves, connecting the phase velocity with wave number are derived. At short wave length limits the frequency equations for symmetric and antisymmetric waves in a stress free plate reduce to Rayleigh type surface wave frequency equation and the finite thickness plate appears as a semi‐infinite medium. The results at various steps are compared with the corresponding results of classical theory and finally the variations of phase velocity, attenuation coefficient with wave number and displacements amplitudes with distance from the boundary of the plate is presented graphically and discussed.