A mechanics model of hard-magnetic soft rod with deformable cross-section under three-dimensional large deformation

•Rigid cross-section assumption is replaced with a planar areal change assumption.•Incompressible neo-Hookean material model is used.•An explicit load-deformation relation of the soft beam is presented.•The equilibrium equations and the finite element formulation of the HMS beam are obtained.•Several numerical benchmark examples and experiments are presented.