Smooth solutions for nonlinear elastic waves with softening

Harold Berjamin (1) , Stéphane Junca (2, 3) , Bruno Lombard (4)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Inria-SIC [Sophia Antipolis]
4 O&I - Ondes et Imagerie

A new hyperbolic softening model has been proposed for wave propagation in damaged solids [2]. The linear elasticity becomes nonlinear through an additional internal variable. This thermodynamically relevant model yields a dissipative energy. The 3×3 nonlinear hyperbolic system so-obtained is totally linearly degenerate like the well-known Kerr-Debye system. Existence of global smooth solutions is studied here thanks to the Kawashima condition. Moreover, shocks never appear with smooth initial data.

Mots clés: Finite-volume method; Nonlinear balance law; Damaged solids; Nonlinear elasticity; Linearly degenerate flux; Nonlinear balance laws; Internal variable; Conservation law

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique [physics]

Harold Berjamin, Stéphane Junca, Bruno Lombard. Smooth solutions for nonlinear elastic waves with softening. HYP2018 - 17th International Conference on Hyperbolic PDEs, Alberto BRESSAN, Marha Lewicka, Dehua Wang, Yuxi Zheng, Jun 2018, College Park, United States. pp.304-3011. ⟨hal-01994898v2⟩