The piston problem in hyperelasticity with the stored energy in separable form

Serge Ndanou (1) , Nicolas Favrie (1) , Sergey L. Gavrilyuk (1)

1 IUSTI - Institut universitaire des systèmes thermiques industriels

The piston problem for a hyperelastic hyperbolic conservative model where the stored energy is given in separable form is studied. The eigen fields corresponding to the hyperbolic system are of three types : linearly degenerate elds (corresponding to the contact characteristics), the elds which are genuinely nonlinear in the sense of Lax (corresponding to longitudinal waves), and, nally, nonlinear elds which are not genuinely nonlinear (corresponding to transverse waves). Taking the initial state free of stresses, we presented possible auto-similar solutions to the piston problem. In particular, we have shown that the equations admit transverse shock waves having a remarkable property : the solid density is decreasing through such a shock (it is a "rarefaction" shock).

Mots clés: piston problem; non linear elasticity; transverse waves

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Serge Ndanou, Nicolas Favrie, Sergey L. Gavrilyuk. The piston problem in hyperelasticity with the stored energy in separable form. Mathematics and Mechanics of Solids, 2015, ⟨10.1177/1081286514566707⟩. ⟨hal-00917961⟩