Basic Mathematics for Physically Correct Mechanical Properties from Indentations

Abstract

This book dealt with basic mathematics for physically correct mechanical properties from indentations. The iteration-free physical description of pyramidal indentations with closed mathematical equations is  comprehensively described and extended for creating new insights in this important field of research and applications. The book also stated the force vs depth loading curves of conical, pyramidal, wedged and for spherical indentations on a strict mathematical basis by explicit use of the indenter geometries rather than on still world-wide used iterated “contact depths” with elastic theory and violation of the energy law. The book also specified physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossible. This book contains various materials suitable for students, researchers and academicians.