Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

Gaël Pierson,Pierre Bravetti,M’Barek Taghite,Richard Kouitat Njiwa

doi:10.3390/applmech2030033

Abstract

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.

Highlights

Depth sensing indentation is commonly adopted for the determination of local elastic and plastic properties of small size samples
It has been shown that, in the small strain deformation regime, the useful relation between the material depression and the radius of the contact area remains valid in the plastic regime [3]
The method called Local point interpolation-boundary element method has been initiated by Kouitat [16] in the context of anisotropic materials

Summary

Introduction

Depth sensing indentation is commonly adopted for the determination of local elastic and plastic properties of small size samples. There is the so-called micromorphic medium of Eringen [4] which is widely accepted as the most successful phenomenological top-down approach In this theory, the impact of the microstructure of the medium is expressed at the macroscopic scale through an incompatible microdeformation tensor. The method called Local point interpolation-boundary element method has been initiated by Kouitat [16] in the context of anisotropic materials. It has since proved efficient for various fields including micropolar materials (see [17,18,19]).

Governing Equations

Solution Method

Numerical Results

Influence of the Coupling Number

Influence of the Characteristic Length in Torsion and the Polar Ratio

Conclusions