A magnetoelastic theory for Kirchhoff rods having uniformly distributed paramagnetic inclusions and its buckling. (January 2022)

• Record Type: Journal Article
• Authors: Barreto, Darius Diogo; Saxena, Shashank; Kumar, Ajeet
• Is Part Of: International journal of solids and structures. Volume 234/235(2022)
• Publication Date: 2022-01
• Subjects: Nonlinear magnetoelasticity -- Kirchhoff rod -- Stability -- Buckling -- Soft continuum robots; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2021.111147
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: We present a theory for finite and spatial elastic deformation of rods under the influence of arbitrary magnetic field and boundary condition. The rod is modeled as a Kirchhoff rod and is assumed to have uniformly distributed array of uniaxial spheroidal paramagnetic inclusions embedded in it all pointing in the same direction in the undeformed state. The governing equations of the magnetoelastic rod are derived which are further non-dimensionalized and linearized to investigate buckling in such rods. Analytical expressions for the onset of buckling from the rod's trivial state are obtained in terms of loading parameters (applied magnetic field, axial load, torque) as well as geometric (inclusion orientation in the undeformed state) and material (ratio of bending and torsional stiffnesses) parameters for different combinations of boundary conditions. The buckled shape of the rod at the onset of buckling is also examined. The presented work can be useful in simulation and design of magnetic soft continuum robots.