Nonuniform bending theory of hyperelastic beams in finite elasticity

This paper deals with the equilibrium problem of slender beams inflexed under variable curvature in framework fully nonlinear elasticity. For specific case uniform flexion, authors have recently proposed a mathematical model. In that analysis, complete three-dimensional kinematics beam is taken into account and both deformations displacements are considered large. present paper, aforementioned model has been reformulated taking curvature. Subsequently, focusing on local determination curvature, new conditions cross sections introduced formulation. The governing equations take form coupled system three integral form, which solved numerically through an iterative procedure. Therefore, for generic class hyperelastic isotropic materials, explicit formulae displacement field, stretches stresses every point beam, following Lagrangian Eulerian descriptions, derived. analysis allows studying very wide problems different restraint subject to external load systems. By way example, Euler obtained specialized neoprene rubber material, constitutive constants determined experimentally. shapes assumed by as multiplier increases shown some graphs. distributions Cauchy plotted most stressed section. Some comparisons made using FE code. addition, accuracy solution estimated evaluating posteriori locally satisfied. • Nonuniform bending formulated context finite formulation accounts anticlastic sections. deformation along longitudinal axis. A material obeying compressible Mooney–Rivlin stored energy function considered. Owing nonuniform bending, further condition respect layout found.