Journal of Elasticity

, Volume 133, Issue 1, pp 105–118 | Cite as

Partial Constraint Singularities in Elastic Rods

  • J. A. Hanna
  • H. SinghEmail author
  • E. G. Virga


We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the balance of material momentum and the concept of a driving traction. The theory is generalizable and can be applied to a wide array of contact, adhesion, gripping, and locomotion problems.


Rods Constraints Adhesion Jump conditions 

Mathematics Subject Classification

74A15 74G70 74K10 74M15 



J.A. Hanna and H. Singh were supported by U.S. National Science Foundation grant CMMI-1462501. E.G. Virga acknowledges the kind hospitality of the Oxford Centre for Nonlinear PDE, where part of this work was done while he was visiting the Mathematical Institute at the University of Oxford.


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Authors and Affiliations

  1. 1.Department of Biomedical Engineering and Mechanics, Department of Physics, Center for Soft Matter and Biological PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of Biomedical Engineering and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  3. 3.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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