Rotational self-friction problem of elastic rods

Mohamed Ali Latrach () and Mourad Chamekh ()
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Mohamed Ali Latrach: University of Tunis El Manar, LAMSIN
Mourad Chamekh: University of Tunis El Manar, LAMSIN

Partial Differential Equations and Applications, 2022, vol. 3, issue 2, 1-17

Abstract: Abstract The aim of this paper is to extend the modeling of a hyperelastic rod undergoing large displacements with tangential self-friction to their modeling with rotational self-friction. The discontinuity of contact force into a contact region not known in advance with taking into account the effects of friction in this problem type leads to serious difficulties in modelization, mathematical and numerical analysis. In this paper, we present an accurate modeling of rotational and tangential self-friction with Coulomb’s law and describe also an augmented Lagrangian method to present a weak variational formulation approach of this problem. We then use the minimization method of the total energy to present an existence result of solution for the nonlinear penalized formulation. Finally, we give the linearization and the finite-element discretization of the weak variational formulation that can be useful for a numerical implementation.

Keywords: Cosserat rods; Contact distance; Self-friction; Augmented Lagrangian method; Finite elements; 7400; 7410 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00166-3

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