Propagation and interaction of weakly nonlinear plane waves in transversely isotropic elastic materials

DOI10.1007/S10665-021-10093-8zbMath1497.35456OpenAlexW3134906642MaRDI QIDQ2060982

Yanyan Li

Publication date: 13 December 2021

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10665-021-10093-8

zbMATH Keywords

transverse isotropyhyperelasticityquasilinear hyperbolic systemself-interaction coefficientsweakly nonlinear plane waves

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Nonlinear waves in solid mechanics (74J30) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• The complex Burgers equation as a model for collinear interactions of weakly nonlinear shear plane waves in anisotropic elastic materials
• Tensile instabilities and ellipticity in fiber-reinforced compressible non-linearly elastic solids
• Propagation and interaction of weakly nonlinear elastic plane waves in a cubic crystal
• Convexity conditions and existence theorems in nonlinear elasticity
• Instabilities and loss of ellipticity in fiber-reinforced compressible nonlinearly elastic solids under plane deformation.
• Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions.
• Wave propagation in transversely isotropic elastic media - I. Homogeneous plane waves
• On Finite Element Implementation of Polyconvex Incompressible Hyperelasticity: Theory, Coding and Applications
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