Generalized shear of a bilayer

• A bilayer problem under generalized shear is studied.
• The shear displacement takes the form of the product of sine and hyperbolic sine function.
• Elastic inhomogeneity can influence the second-order stresses and interfacial displacement.
• A generalized Poynting effect, associated with an out-of-plane shear stress, is predicted.
• Experimental results of agar-gelatin bilayers show reasonable agreement with theory.

A bilayer block with dissimilar elastic constants under generalized shear is studied. The shear displacement is not constrained a priori to be a function of the vertical coordinate. Using second-order isotropic elasticity and under a prescribed shear displacement on the top face, the shear displacement takes the form of the product of sine and hyperbolic sine functions. There exist first- and second-order shear stresses, as well as second-order normal stresses corresponding to the Poynting effect. The shear moduli inhomogeneity between the layers has an “intrinsic” influence on the second-order normal stresses, meaning that this influence persists even if both shear moduli approach zero. Generally, the elastic inhomogeneity has a strong influence on the sign, magnitude and functional variation of the stresses and displacements. A generalized Poynting effect, associated with a sinusoidal shear stress, is also predicted in which the sheared block distorts not only in plane but also tends to distort out of plane. Experimental results on the deformed lateral profiles of agar–gelatin bilayers show reasonable agreement with theory.