Crystal Elasticity

Introduction

The first part of this book focuses on the description of crystal elasticity. This field became fully established at the beginning of the 20th century. Its ancestral branches can be referred to as “crystallosapiens” and “elastosapiens”.

The ancestor of the first branch can be considered the mineralogist René Just Haüy, the father of geometric crystallography in the 18th century, who observed the features of the cleavage of crystals such as calcite and deduced that they were made up of small orderly stacks, which he named integrant molecules. The concept of atomic lattice dates back to the 19th century, when it was introduced by Gabriel Delafosse, one of Haüy’s disciples. Shortly afterwards, Auguste Bravais formulated the hypothesis of a lattice structure of crystals based on the principles of geometry, according to which he listed 14 different types of crystal lattices that accounted for crystal anisotropy and symmetry properties. Finally, at the beginning of the 20th century, Max von Laue used X-ray diffraction to experimentally confirm Bravais’ works.

As for the second branch, its forerunner is beyond any doubt Robert Hooke, who in the 17th century established the linear relation between force and displacement in a loaded spring. Then, the notions of stress and deformation were formulated by Thomas Young at the beginning of the 19th century. Soon afterwards, Augustin-Louis Cauchy established the 3D formalism for the generalized Hooke’s law using the notion of ...