R. K. N. D. Rajapakse

On a plane crack in piezoelectric solids

A new analytical solution for a piezoelectric plane with an elliptical void is derived by removing the commonly held assumptions that the void boundary is impermeable and a void axis is perpendicular to the poling direction. The approach of Lekhnitskiis complex potential functions is used in the derivation. Applicability of the common practice of reducing a void solution to a crack solution is examined. It is shown that a recently reported solution for exact electric boundary conditions is actually the well known solution for a permeable crack. A unified formulation for plane cracks containing air or vacuum is then developed to account for different electric boundary conditions. Crack closure is taken into consideration in the analysis. The influence of electric boundary conditions and crack orientation on fracture parameters is discussed.

On singularities in composite piezoelectric wedges and junctions

Abstract The plane problems of piezoelectric wedges and multi-material wedges/junctions involving piezoelectrics are studied in this paper. The study is focused on the singular behaviour of electroelastic fields at the corner of wedges and junctions. The polarization orientation of the piezoelectric medium may be arbitrary. The problem is formulated by extending Lekhnitskii’s complex potential functions. In the homogeneous piezoelectric cases of a half plane and a semi-infinite crack, it is shown that the singularity is invariant with respect to the direction of polarization and explicit solutions are derived for homogeneous boundary condition combinations. In general cases involving multi-material systems, the order of singularity is determined by solving a transcendental characteristic equation derived on the basis of boundary conditions and geometry. The accuracy of the numerical algorithm is verified by comparing with the existing results for pure elastic wedges. Numerical results of homogeneous piezoelectric wedges indicate that electric boundary conditions have a significant effect on the order of singularities. A selected set of practically useful wedges and junctions involving piezoelectrics are studied to examine the influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the order of singularity of electroelastic fields.

A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration

Abstract A coupled thermoporoelastic model accounting for compressibility and thermal expansion of constituents, convective heat flow and changing porosity and related properties of a saturated soil is presented. The model also considers thermodynamically coupled water and heat flow (thermal-filtration and thermo-osmosis that are analogous to Soret and Dufour effects in solutions) . These coupling effects are reported to be significant in the case of semi-impermeable clay barriers used in waste repositories. The governing equations derived in terms of displacements, temperature and pore water pressure are non-linear. A mixed finite element formulation is presented to obtain numerical solutions. An exact analytical solution for a 1-D soil column is presented for a simplified linear case that includes thermodynamic coupling. Selected numerical solutions for soil columns and radially symmetric plane strain problems are presented to demonstrate the principle features of the coupled model and the significance of thermodynamic coupling.

Vertical vibrations of a rigid disk embedded in a poroelastic medium

This paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a finite depth below the free surface of a poroelastic medium. Biots elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic fields are obtained by using Hankel integral transforms. Analytical solutions for influence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the influence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully flexible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for different depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils. Copyright

Coupled consolidation of a porous medium with a cylindrical or a spherical cavity

This paper presents a theoretical approach to analyse coupled, linear thermoporoelastic fields in a saturated porous medium under radial and spherical symmetry. The governing equations account for compressibility and thermal expansion of constituents, heat sink due to thermal dilatation of water and thermal expansion of the medium, and thermodynamically coupled heat–water flow. It has been reported in the literature that thermodynamically coupled heat–water flows known as thermo-osmosis and thermal filtration have the potential to significantly alter the flow fields in clay-rich barriers in the near field of a underground waste containment scheme. This study presents a mathematical model and examines the effects of thermo-osmosis and thermal-filtration on coupled consolidation fields in a porous medium with a cavity. Analytical solutions of the governing equations are presented in the Laplace transform space. A numerical inversion scheme is used to obtain the time-domain solutions for a cylindrical cavity in a homogeneous or a non-homogeneous medium. A closed form time-domain solution is presented for a spherical cavity in a homogeneous medium. Selected numerical solutions for homogeneous and non-homogeneous media show a significant increase in pore pressure and displacements due to the presence of thermodynamically coupled flows and a negligible influence on temperature.

Coupled fields in a deformable unsaturated medium

Abstract This paper considers several problems involving coupled heat–moisture–air flow indeformable unsaturated media. A set of coupled non-linear governing equations expressed in terms of displacements, capillary pressure, air pressure and temperature are used in the analysis. The mathematical model accounts for fully coupled heat and moisture flow, volume strain effects on water-air-heat flow, stress and temperature dependence of the water retention curve, heat sink due to thermal expansion, phase change between liquid water and vapour water, and compressibility of liquid water. Numerical solutions are obtained by using the finite element method. Comparisons with existing analytical and experimental results for problems involving infiltration, drying–rewetting (hysteresis effects) and heating confirm the general validity of the present mathematical model. Coupled fields in a confined clay cylinder are also examined. It is found that consideration of absorbed liquid flow due to thermal gradients (thermo-osmosis effect) results in increased drying and shrinkage near the heated boundary. The case of a confined clay cylinder under combined heating and infiltration is also studied. Important features of coupled fields are discussed.

Axisymmetric fundamental solutions for a completely saturated porous elastic solid

Abstract This paper is concerned with the derivation of axisymmetric fundamental solutions that are required in the application of boundary integral equation method to solve complicated boundaryvalue problems involving poroelastic semi-infinite and infinite domains. General solutions for a fully saturated poroelastic solid derived through the application of Laplace and Hankel integral transforms with respect to time and radial coordinates are utilized in the analysis. The derivation of complete fundamental solutions requires the consideration of three boundary-value problems involving unit buried ring loads acting in the vertical and radial directions and a unit buried ring flow source. These boundary-value problems are solved for both half space and full space regions. Explicit solutions for Laplace transform of displacements, tractions, pore fluid pressure and fluid flow are presented. Solutions corresponding to a buried vertical point load and a point source in a poroelastic half space are also deduced from ring load and source solutions. Thereafter, solutions are presented for buried distributed normal load, radial shear load and a flow source with intensity specified by a polynomial of arbitrary degree. Selected numerical results corresponding to buried uniform and non-uniform distributed vertical loads are presented to illustrate computational procedure.

A boundary integral equation formulation for coupled heat-moisture transfer in porous media

Abstract A boundary integral equation formulation based on a reciprocal relation established in this article is developed for coupled heat-moisture transfer in porous media in the fully three-dimensional setting, including the internal sources of heat and mass, and the body forces. The fundamental solutions corresponding to singular sources of heat and mass respectively, necessary to develop the boundary integral equation scheme, are constructed. Selected numerical results are presented to demonstrate the features of temperature and moisture content distributions induced by the singular sources. The Laplace transforms of the boundary integral equations and the fundamental solutions are included and these provide a computationally efficient alternative to a direct time domain analysis.