Mechanics of contact between bi-material elastic solids perturbed by a flexible interface

Abstract

This paper generalizes the classical result of R.D. Mindlin for the axisymmetric problem related to the action of a concentrated force at the interior of an isotropic elastic half-space to include a bi-material region that is perturbed by an interface exhibiting flexural behaviour. The flexural behaviour of the interface is described by a Germain-Poisson-Kirchhoff thin plate theory. A Hankel integral transform technique is used to obtain an explicit result for the deflection of the flexural interface. The reduction of the solution to conventional results associated with both half-space problems and infinite space problems is indicated. Formal results are also presented for the case where the flexural behaviour of the plate is modelled by the plate theory proposed by E. Reissner.

Poromechanical behaviour of a surficial geological barrier during fluid injection into an underlying poroelastic storage formation

“…The stiffening action of the caprock diffuses the spatial distribution of heave. These effects have also been observed in the purely elastic modelling of caprock-storage horizon interaction [5][6][7]12], the surface heave becomes flattened and localized to the region of the injection region for the case when the caprock is not present [24]. It was also found that the ratio of the surface heave to the steady-state displacement was larger when a caprock was present.…”

“…The boundary conditions are prescribed in such a way that the injection rates are dimensionally consistent. The specification of the total volume rate of injection over the circular region of radius a also makes it possible to compare the results of this study with the point injection studies, such as the nuclei of fluid influx, that have been developed for both infinite and semiinfinite domains [5,6,12]. We note that the assumption of injection over a circular disc-shaped region enables the convenient formulation of the initial boundary value problem.…”

“…The objective of the study was to determine the stress state in the caprock during the injection process. If injection is modelled as the rise and maintenance of the pressure in a specified region in the storage formation [11], then the state of stress in the caprock can be examined using an elastostatic model of the storage formation where the caprock is idealized as a structural element with a response that can be modelled as either a Poisson-Kirchhoff thin plate [5,6] or as a Mindlin-Reissner thick plate [12]. The elastostatic model can also provide quantitative estimates for the deflections of the caprock in the long term.…”

Response of bimaterials with interfacial tension subjected to axisymmetric body force

“…The mechanics of bimaterial models are useful to provide reliable first approximations to the performances of many composite structures, e.g. reinforced concrete, soil foundation, and geological barriers systems [37,38]. On the other hand, from the theoretical perspective of mathematical elasticity, the static response of bimaterial systems is also the analytical core for the issue of singularity extraction in the relevant dynamic problems of multilayered structures [39].…”

“…However, the analytical treatment pertaining to bimaterials with interfacial reinforcement, which are analogous to interfacial effects under the context of surface elasticity, are quite limited. Our literature review indicates that only two recent papers by Selvadurai [37] and Ahmadi and Samea [56], for the problems of bimaterials reinforced, respectively, by thin plate and extensible thin film, are available in the open literature in English. This situation thus motivates the present study.…”