Curvature Analysis in a Bi-layered Non-linear Elastic Bar under Uniform Heating

The present theoretical paper is concerned with analysis of the curvature in a bi-layered bar of rectangular cross-section. The bar is subjected to uniform heating. The two layers of the bar have different thickness and material properties. Besides, the layers exhibit non-linear elastic mechanical behaviour that is treated by applying a power-law stress-strain constitutive relationship. The bi-layered bar curvature is studied analytically. For this purpose, the mechanical response of the bar to uniform heating is investigated. The strains in the two layers due to heating are analyzed. An equation is compiled by using the fact that the prolongations of the bar layers are equal. Two equations are worked out by considering the equilibrium of the layers. The analysis of the curvature presented in this paper is checked-up by comparing with a known solution for the curvature in a bi-layered linear-elastic bar under uniform heating. The uniform heating induced curvature in a bi-layered bar whose layers are continuously inhomogeneous in longitudinal direction is also studied.