A size-dependent bilayered microbeam model based on strain gradient elasticity theory

A size-dependent model for bilayered microbeams is developed based on the strain gradient elasticity theory. The governing equations and boundary conditions are derived by using the variational principle. To illustrate the new model, the bending problem of a bilayered cantilever microbeam subjected to a moment at the free end is solved. Numerical results reveal that the deflection and total axial stress decrease remarkably compared with the classical deflection and axial stress, and the neutral axis and zero-stress axis deviate significantly from the conventional positions, when the height of beam is comparable to the material length scale parameters. The size effects, however, are almost diminishing as the height of the beam is far greater than the material length scale parameters. In addition, the neutral axis and zero-stress axis no longer coincide with each other, and the results of bilayered beam gradually approach to that of monolayer beam as the height of one layer is becoming much greater than that of the other layer.