NUMERICAL STUDY ON SIZE EFFECTS OF THE MICROSTRUCTURES BASED ON STRAIN GRADIENT ELASTICITY

Strain gradient theory can be classified into couple-stress theory and stretch-rotation gradient theory according to the difference in second-order gradients of the displacements. Compared with couple-stress theory, the stretch-rotation gradient theory involves the stretch gradients besides the rotation gradients; therefore, size effects predicted by stretch-rotation gradient theory are stronger than those predicted by couple-stress theory. Based on strain gradient elasticity C¹ natural element method, size effects on microgripper and microspeciem are studied. For the microgripper, S-shaped spring structure adopted to link the electrostatic comb drive arm and the anchor reduces the bending stiffness and increases the gripping force; when the width of spring is close to the material characteristic length scales, the normalized bending stiffness is very large, which implies strong size effects in this case. For the microspeciem, size effects are obviously strong when the radius of circular perforation and the long axis of elliptical perforation are close to the material characteristic length scales. For the U-shaped notch, with the increase of notch radius, size effects become weak obviously; with the increase of the length of notch, size effects become weak slightly. Numerical results for all cases demonstrate that size effects in the stretch-rotation gradient theory are stronger than those in couple-stress theory, which agrees well with the theoretical predictions.