Analysis of contact of elastic rods subject to large displacements

Pierre Béal , Rachid Touzani (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We present a mathematical model for describing motion of two elastic rods in contact. The model allows for large displacements and is essentially based on {\sc Cosserat}'s modeling of rods. Existence of a static solution is proved in the case of a unique rod using a penalty technique. The contact modeling involves unilateral constraints on the central lines of the rods. Existence is also proved for this contact problem.

Mots clés: Elastic rods; Large displacements; Penalized energy formulation; Frictionless constant; Lower semi-continuous

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Béal, Rachid Touzani. Analysis of contact of elastic rods subject to large displacements. Applied Mathematics Letters, 2003, 16, pp.619-625. ⟨10.1016/S0893-9659(03)80121-0⟩. ⟨hal-00087488⟩