Simple effective shear modulus approximation for single crystal Si torsional bars

Torsion stiffness of elastic suspensions made of anisotropic single crystal silicon cannot be calculated by formulas derived for isotropic materials. We introduce a simple expression for an effective shear modulus, which depends on the aspect ratio (AR) of the torsional bar cross section. The approximation allows torsion stiffness evaluation of prismatic bars oriented in the most common 1 1 0 and 1 0 0 crystal directions, and can be directly used in an isotropic formula and is applicable within an entire range of the bar cross section AR. Our numerical and experimental results show that the approach can be conveniently used as a design tool for tilting micro devices.