On the splay deformation mode of a polar linearly elastic bar stretched by its own weight

Abstract

This communication considers the fundamental linear elasticity problem of a prismatic bar, or plate, stretched by its own weight and examines the impact of its classical solution in the regime of isotropic and anisotropic polar material elasticity. Accordingly, the existing non-polar elasticity solution of such a self-stretched isotropic bar is initially extended to embrace appropriate classes of non-polar material anisotropy. This extension verifies that, in non-polar transverse isotropy and special orthotropy, the attained solution is exclusively dominated by splay-type features of deformation. Attention then focuses on the influence that the observed fiber-splay deformation mode, as well as its fiber-bending deformation counterpart, exert on the formulation and potential solution of corresponding boundary value problems met in polar linear elasticity. It is seen that, regardless of the isotropic or anisotropic material symmetries considered, the outlined process may lead to solution of relevant boundary value problems that are slightly different to their non-polar elasticity counterparts. This conclusion reinforces the role that a polar material version of the theorem of minimum potential energy, and relevant energy minimization approaches, can play in the search for full solution of boundary value problems met polar material elasticity.