Diffusion-induced bending of viscoelastic beams

The contribution of local volumetric change due to the diffusion/migration of solute atoms to viscoelastic deformation is incorporated in the theory of linear viscoelasticity, following the elastic theory of diffusion-induced stress. Three-dimensional constitutive relationship in differential form for diffusion-induced stress in linear viscoelastic materials is proposed. Using the correspondence principle between linear viscoelasticity and linear elasticity and the results from the diffusion-induced bending of elastic beams, the radii of curvature of the centroidal plane of viscoelastic beams of single layer and bilayer with top layer being viscoelastic in the transform domain are obtained. For viscoelastic beams of single layer, closed-form solution of the radius of curvature of the centroidal plane is derived, and the radius of curvature is inversely proportional to the diffusion moment created by non-uniform distribution of solute atoms. For the condition of constant concentration on free surface, there is overshoot behavior; for the condition of constant flux on free surface, there is no overshoot behavior. For viscoelastic beams of bilayer with top layer being the Maxwell-type standard material, the numerical results show the presence of the overshoot behavior for a very compliant elastic layer under the condition of constant concentration on free surface, and there is no overshoot behavior under the condition of constant flux on free surface.