Boudilmi, Aissa2019-06-122019-06-122016-08http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/14247In this study, firstly we introduced general mathematical concepts related to the geometrical form of ellipse and ellipsoid. Secondly, the hardness was calculated when we used an indenter having a geometrical shape of an oblate spheroid; the mathematical expressions of static hardness were determined as functions of the applied load, the radius or the depth of the imprint area. The general static hardness formula was expressed considering the projected and the real area imprint of the oblate spheroid indenter. Thirdly mathematical assumptions were introduced in order to simplify the mirohardness and nanohardness formulas when we used the real imprint area. Finally we did a comparative study between the oblate spheroid and the spherical indenters.Hardness measurement Mechanical characterization Indenter Geometrical modeling Mathematical formulasArticle