A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory

Micro scale experiments demonstrated that the material deformation behaviors of some metals and polymers deformed elasticity are size dependence, and the modified couple stress theory (MCST), which introduce an additional material length scale parameter, could capture the size dependences. The article reviews the available size-dependent models of micro-beam and micro-plate based on the MCST. For the representative micro-beams and micro-plates, the relevant mechanical models of micro-structures for static bending, vibration, buckling and pull-in instability, have been established based on the MCST, and the analytical and numerical solutions have been obtained. The results show that the size effects on the mechanical properties of the micro-structures are obvious and significant. Further possible researches on the size-dependent behaviors of the micro-structures are proposed.

Automated summary

The article discusses the size-dependent material deformation behaviors of certain metals and polymers at micro scale experiments and how the modified couple stress theory (MCST) can capture these size dependences. It reviews available size-dependent models for micro-beam and micro-plate based on MCST, and establishes relevant mechanical models and solutions for static bending, vibration, buckling, and pull-in instability of representative micro-structures. The results indicate significant size effects on the mechanical properties of micro-structures, suggesting potential further research on size-dependent behaviors.