Double restabilization and design of force–displacement response of the extensible elastica with movable constraints

Elastic solids under frictionless rigid contact and configurational force

“…In conclusion, the presence of the configurational force F c 1 at the sliding sleeve exit so far obtained for rod models [1,5,23,28,35,37] is confirmed from a solid mechanics point of view.…”

“…The introduced theoretical framework, disclosing the development of configurational sliding forces at the (sharp or rounded) corner of a frictionless, rigid, and flat surface acting on an elastic body, is now used to throw light on the akin problem of elastic rods partially constrained with a sliding sleeve. The presence of configurational forces at the end of a sliding sleeve was disclosed by analyzing one-dimensional flexible structures through a variational approach [1,5,28] or by imposing jump conditions in the material momentum balance law [23,35,37]. This result is confirmed here through the application of the framework developed in the previous Sections to an elastic solid of rectangular shape in its undeformed configuration B 0 , as defined by eqn (60), in contact with two frictionless rigid surfaces realizing a sliding sleeve constraint.…”

“…However, a number of elastic structures with variable length has been recently investigated to show that a special class of configurational forces are Newtonian forces and, as such, can even be determined experimentally. These structures include a rod with one end sliding inside a frictionless sleeve (in both quasi-static [5,29] and dynamic [1,28,44] settings), a rod subjected to torsion [6] and a rod moving inside a frictionless, rigid and curved channel [15]. Remarkably, a common feature of these structures is the possibility of a free movement in a certain direction, to which the configurational force becomes energetically conjugate.…”