Role of material microstructure in plate stiffness with relevance to microcantilever sensors

This work examines the effect of microstructure upon microcantilever bending stiffness. An existing beam theory model, based upon an isotropic Hooke's law constitutive relationship, is compared to a model based upon a micropolar elasticity constitutive model. The micropolar approach introduces a bending stiffness relation which is a function of any two independent elastic constants of the Hooke's law model (e.g., the elastic modulus and the Poisson's ratio), and an additional material constant (called γ). A consequence of the additional material constant is the prediction of an increased bending stiffness as the cantilever thickness decreases—a stiffening due to the material microstructure which becomes…