Volume 2, Number 3, 1999, 249 - 258


Systematised Theory for Micromechanics on Crystalline Materials

Mihaela Ilie, Eugen Vasile
IMT-Bucharest, Romania

The aim of this paper was to systematise the mathematical relations of the elasticity theory, in an appropriate form dedicated to the engineering design of micromechanical structures made of crystalline materials with diamond type lattice (Si, Ge). Starting from the generalised Hooke's law (in its tensorial form for a continuous medium) the stress vector and the strain vector are put into evidence and the reduced matrix form of the law is written. The case of cubic symmetry is analysed. The necessary matrix transformations are determined in order to calculate the compliances ?s? of a 3-D planar microstructure taking into account its orientation with respect to the orthonormal basis of the crystal. Torsion and bending are studied. Anisotropy diagrams for the elasticity moduli (G and E) are deduced enabling the calculus of stiffnesses k. The obtained results permit a rapid computer aided extraction of the elasticity constants necessary for simulation dedicated programs.