ROMANIAN JOURNAL OF INFORMATION SCIENCE AND
Volume 2, Number 3, 1999, 249 - 258
Systematised Theory for Micromechanics
on Crystalline Materials
Mihaela Ilie, Eugen Vasile
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.