APPLIED MODEL OF AXIAL COMPRESSION OF TRANSVERSELY ISOTROPIC POROUS CYLINDER WITH END FRICTION

Abstract

In the context of the linear Cowin – Nunziato micro-dilatation theory, the contact problem of axial compression of a finite transversely isotropic porous cylinder placed between two rigid plates moving towards each other is addressed. To account for the effect of friction, an effective integral parameter is introduced as the ratio of the equivalent tangential force to the normal force. Using physically justified approximations (linear radial variation of the radial displacement, no radial dependence of the axial displacement and micro-dilatation) together with the first-order Kantorovich method and the Lagrange variational principle, the three-dimensional boundary value problem is reduced to a system of three ordinary differential equations. The analytical solution is obtained as a sum of a rod-type solution describing the fundamental stress-strain state in the central part of the cylinder and exponentially decaying boundary-layer terms generated by the combined action of micro-dilatation phenomena and contact friction. Using cortical bone as an example, a parametric study is carried out to reveal the influence of the friction coefficient and porosity characteristics on axial distributions of displacements, stresses, and micro-dilatation. The analysis reveals that end friction restricts transverse expansion, causing “barreling” (bulging of the lateral surface), and leads to a concentration of compressive radial and tangential stresses near the ends. Friction also enhances volumetric compression in the end region, which stimulates micro-dilatation through coupling parameters. Additionally, the presence of porosity increases the overall compliance of the material. The derived relationships enable the accurate interpretation of laboratory compression tests, the correction of experimental data, and the identification of contact properties and porous characteristics of anisotropic biomaterials.