Modeling thermal and buckling behavior in electrothermal bimorphs

Buckling is a structural phenomenon that can induce significant motion with minimal input variation. Electrothermal bimorphs, with their simple input and compact design, can leverage out-of-plane buckling motion for a broad range of applications. This paper presents the development of analytical electrothermal and structural models for such bimorphs. The electrothermal model calculates the temperature distribution within the bimorph caused by electrothermal heating, providing a 2D explicit analytical expression for estimating temperature along the bimorph’s length and cross-section. Nonhomogeneous heating leads to varying strains, which induce axial forces and moments along the bimorph’s neutral plane, varying with thermal expansion. The structural model derives the governing equation of deformation for the bimorph by analyzing internal strains and stresses resulting from deformation, electrothermal heating, and residual stresses. An analytical solution for deflection is obtained, incorporating infinite sums of heating and buckling modes, with closed-form equivalent expressions when possible. The bimorph’s behavior under different scenarios of residual stresses and electrothermal heating is elucidated based on the analytical model. Comparisons with finite element simulations demonstrated excellent agreement, highlighting the high accuracy of the proposed models.