Nonlinear Shear Waves in Compressible Media: Occurrence of Strong Shocks

Bratov, Vladimir; Kuznetsov, Sergey V.

Abstract

Apparently for the first time, shear shock wave fronts (shear shocks) are observed in a hyperfoam at the propagation of shear waves. The hyperfoam is modelled by the Ogden compressible hyperelastic potential. A possible appearance of the shear shocks may explain the kinetic and strain energy attenuation along with heat release at the propagation of shear waves in hyperfoams. The analysis is based on the Cauchy formalism for equations of motion, equations of energy balance, and FE analysis for solutions of the constructed nonlinear hyperbolic equation.

Citation

Bratov, V., & Kuznetsov, S. V. (2025). Nonlinear Shear Waves in Compressible Media: Occurrence of Strong Shocks. Mathematics, 13(12), Article 1991. https://doi.org/10.3390/math13121991

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2025
• Online Publication Date: Jun 17, 2025
• Publication Date: 2025
• Deposit Date: Jul 7, 2025
• Publicly Available Date: Jul 7, 2025
• Journal: Mathematics
• Electronic ISSN: 2227-7390
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 12
• Article Number: 1991
• DOI: https://doi.org/10.3390/math13121991
• Keywords: shear shock wave front; hyperfoam; hyperelasticity; Ogden potential; energy attenuation