Size effect in micro-scale cantilever beam bending

Abstract

When the thickness of metallic cantilever beams reduces to the order of micron, a strong size effect of mechanical behavior has been found. In order to explain the size effect in a micro-cantilever beam, the couple-stress theory (Fleck and Hutchinson, J Mech Phys Solids 41:1825-1857, 1993) and the C-W strain gradient theory (Chen and Wang, Acta Mater 48:3997-4005, 2000) are used with the help of the BernoulliEuler beam model. The cantilever beam is considered as the linear elastic and rigid-plastic one, respectively. Analytical results of the cantilever beam deflection under strain gradient effects by applying these two kinds of theories are obtained, from which we find an explicit relationship between the intrinsic lengths introduced in the two kinds of theories. The theoretical results are further used to analyze the experimental observations, and predictions by both theories are further compared. The results in the present paper should be useful for the design of micro-cantilever beams in MEMS and NEMS.

Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory

“…Roque et al [27] studied the mechanical behavior of a laminated Timoshenko microbeam by using the meshless method. Chen and Feng [28] compared couple stress theory and strain gradient theory to examine the model of a microcantilever beam bending subject to different loading forms with various material characteristics. Asghari et al [29] used strain gradient theory to develop a geometrically nonlinear elastic size-dependent Timoshenko beam formulation.…”

Creep and Fatigue Failure in Single- and Double Hot Arm MEMS Thermal Actuators

“…Material properties of MEMS materials are mostly process dependent [19]. Thermal conductivity and the thermal expansion coefficient of polysilicon are temperature dependent and given in Table 1.…”

“…There have also been a number of fatigue studies on micropolysilicon samples and devices under electrostatic loading (Brown et al [12] and Muhlstein et al [13]) and electromechanical loading (Conant and Muller [4], Comtois et al [14], Kapels et al [15], Que et al [16] Chen et al [17,18], Hocheng et al [19], and Kung and Chen [20]). Some of these research works were related to the flexural thermal actuators [2,4,14,15,20].…”

A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory

“…Since the classical continuum mechanics has failed to predict or interpret the experimentally observed size-dependent behaviors in small-scale structures [8][9][10][11], some nonclassical continuum theories such as the nonlocal, strain gradient and couple stress theories have been introduced, developed and utilized for analyzing this type of structures [12][13][14][15][16][17]. In the two latter nonclassical theories, there are some higher-order stress components beside the classical stresses.…”