Wave curves for the Riemann problem of plane waves in isotropic elastic solids

DOI10.1016/0020-7225(87)90014-0zbMath0637.73020OpenAlexW2052312859MaRDI QIDQ1098666

Zhijing Tang, Ting, T. C. T.

Publication date: 1987

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(87)90014-0

zbMATH Keywords

plane wavesquasilinear differential equationsshock waveumbilic pointinitial and boundary conditionssimple wavessystem of hyperbolic conservation lawsmodified Riemann problemSecond-order hyperelastic materialstwo-wave-speed systemWave curves

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Bulk waves in solid mechanics (74J10) Shock waves and blast waves in fluid mechanics (76L05) Wave equation (35L05) Hyperbolic conservation laws (35L65)

Related Items (17)

Hyperbolicity singularities in rarefaction waves ⋮ Numerical modeling of elastoplastic flows by the Godunov method on moving Eulerian grids ⋮ The Riemann problem for 2\(\times 2\) systems of hyperbolic conservation laws with case I quadratic nonlinearities ⋮ An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics. ⋮ Classification of \(2\times{} 2\) non-strictly hyperbolic systems for plane waves in isotropic elastic solids ⋮ Wave curves with the presence of an umbilic point and an umbilic line for plane waves in isotropic elastic solids ⋮ Solution of a Riemann problem for elasticity ⋮ Topological resolution of Riemann problems for pairs of conservation laws ⋮ The quasilinear wave equation for antiplane shearing of nonlinearly elastic bodies ⋮ The Riemann problem for fluid flow of real materials ⋮ A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids. ⋮ Riemann solutions for spacetime discontinuous Galerkin methods ⋮ The small anisotropy formulation of elastic deformation ⋮ A generalized Goursat-Riemann problem for plane waves in isotropic elastic solids ⋮ Two-dimensional stress wave analysis in incompressible elastic solids ⋮ Global existence to the Cauchy problem for hyperbolic conservation laws with an isolated umbilic point ⋮ A second-order Godunov algorithm for two-dimensional solid mechanics

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• The classification of 2 × 2 systems of non-strictly hyperbolic conservation laws, with application to oil recovery
• On wave propagation problems in which 𝑐_{𝑓}=𝑐_{𝑠}=𝑐₂ occurs
• ONE-DIMENSIONAL NON-LINEAR WAVE PROPAGATION IN INCOMPRESSIBLE ELASTIC MATERIALS
• THE PROPAGATION AND INTERACTION OF ONE-DIMENSIONAL NON-LINEAR WAVES IN AN INCOMPRESSIBLE ISOTROPIC ELASTIC HALF-SPACE
• Plane Waves Due to Combined Compressive and Shear Stresses in a Half Space
• FINITE SIMPLE WAVES IN A COMPRESSIBLE TRANSVERSELY ISOTROPIC ELASTIC SOLID
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