One-dimensional shock waves in simple materials with memory

DOI10.1098/rspa.1990.0047zbMath0725.73024OpenAlexW2061812845MaRDI QIDQ5203755

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Publication date: 1990

Published in: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1990.0047

zbMATH Keywords

approximation methodnonlinear viscoelastic materialsmodulated simple wave theoryhigher-order discontinuitiesasymptotic evolution lawscombination of singular surface theory and perturbation methodsplane dilatational shock wavesshock- fitting methodsystem of two coupled first-order ordinary differential equations

Mathematics Subject Classification ID

Bulk waves in solid mechanics (74J10) Impact in solid mechanics (74M20) Nonlinear constitutive equations for materials with memory (74D10) Waves in solid mechanics (74J99) Dynamical problems in solid mechanics (74Hxx)

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Shear shock formation in incompressible viscoelastic solids ⋮ Jordan-Cattaneo waves: analogues of compressible flow ⋮ Acoustic black hole in a hyperelastic rod ⋮ Singular travelling waves in soft viscoelastic solids of rate type ⋮ Analytical study of acceleration waves on a nonlinear, externally damped string ⋮ IMPLODING CYLINDRICAL AND SPHERICAL SHOCK WAVES IN A NON-IDEAL MEDIUM ⋮ Growth, decay and bifurcation of shock amplitudes under the type-II flux law ⋮ Methods for solving one-dimensional boundary value problems in a nonlinear elastic medium ⋮ Kinematics of a shock wave of arbitrary strength in a non-ideal gas ⋮ Propagation of simple waves and shock waves in a rod of slowly varying cross-sectional area

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