Torsion and bending of micron-scaled structures

Abstract

Typical microelectromechanical systems (MEMS) devices and packages are composed of micron-scaled structures. Experimental investigations on the effect of size on the deformation behavior of simple structures have shown that the deformation behavior of metals and polymers is size dependent. The size dependence in small structures is attributed to the contribution of nonnegligible strain gradients. In this work, torsion and bending of micron-sized rods and plates were analyzed by using a two-parameter model of strain-gradient plasticity. Microrod torsion and microplate bending experimental data were analyzed to determine the magnitude of the strain-gradient material parameters. The parametric analyses showed that conventional analysis is applicable only when the size of the structure is significantly larger than the material parameters, which are typically in the micron range. Strain-gradient analysis of micron-sized rod revealed that the presence of strain gradient increased the torque by three to nine times at the same twist. For MEMS structures with micron-sized features, conventional structural analysis without strain gradient is potentially inadequate, and strain-gradient analysis must be conducted to determine the elastoplastic behavior in the micron scale.

Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory

“…In such applications, size effects were experimentally observed [4][5][6]. The size effect can be captured using sizedependent continuum theories.…”

A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

“…This parameter can be determined from torsion tests of slim cylinders [4] or bending tests of thin beams [11]. Substituting Eq.…”

“…Recently, the application of FGMs has broadly been spread in micro-and nano-scale devices and systems such as thin films [1], atomic force microscopes [2], micro-and nano-electro-mechanical systems (MEMS and NEMS) [3]. In such applications, size effects or small scale effects are experimentally observed [4][5][6]. Conventional plate models based on classical continuum theories do not account for such size effects due to the lack of a material length scale parameter.…”

Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory

“…Multiple recent experimental results have shown that as the size of the structures reduces to micro/nanoscale, the influences of atomic forces and small scale play a significant role in mechanical properties of these nano-structures (Chong et al, 2001;Fleck et al, 1994;Ma and Clarke, 1995). Thus, neglecting these effects in some cases may results in completely incorrect solutions and hence wrong designs.…”