Analytic Solution for the Indentation of a Transversely Isotropic Elastic Layer Bonded to a Rigid Foundation
نویسندگان
چکیده
The analytical solution for a transversely isotropic linear elastic layer bonded to a rigid foundation and indented by a rigid cylinder or sphere was developed. This solution follows procedures used by others to solve contact problems of linear anisotropic materials. The solution can be used to find the stress distribution and the displacement field in anisotropic layers like articular cartilage. The solution was used to compare stresses and displacements in articular cartilage assuming two sets of engineering properties with different degrees of anisotropy. The results may support current research about the relation between impact loading on the articular cartilage and the development of osteoarthrosis.
منابع مشابه
Analytical Solution for a Two-Layer Transversely Isotropic Half-Space Affected by an Arbitrary Shape Dynamic Surface Load
The dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. With the help of displacements and stresses Green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface l...
متن کاملVertical and Rocking Impedances for Surface Rigid Foundation Resting on a Transversely Isotropic Half-Space
The vertical and rocking impedances of a rigid foundation resting on a semi-infinite transversely isotropic medium are obtained in the frequency domain. In the present approach, the contact pressure distribution on the soil foundation-interface is approximated by a linear combination of known pressure patterns. It is shown herein that the approximate solutions of spatial displacement distributi...
متن کاملSimulations of Indentation at Continuum and Atomic Levels
The main goal of this work is to determine values of elastic constants of orthotropic, transversely isotropic and cubic materials through indentation tests on thin layers bonded to rigid substrates. Accordingly, we first use the Stroh formalism to provide an analytical solution for generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and inden...
متن کاملA Method of Function Space for Vertical Impedance Function of a Circular Rigid Foundation on a Transversely Isotropic Ground
This paper is concerned with investigation of vertical impedance function of a surface rigid circular foundation resting on a semi-infinite transversely isotropic alluvium. To this end, the equations of motion in cylindrical coordinate system, which because of axissymmetry are two coupled equations, are converted into one partial differential equation using a method of potential function. The g...
متن کاملRocking Rotation of a Rigid Disk Embedded in a Transversely Isotropic Half-Space
The asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. The rigid disk is assumed to be in frictionless contact with the elastic half-space. By virtue of appropriate Green's functions, the mixed boundary value problem is written as a dual integral equation. Employing further mathematical tec...
متن کامل