The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media.

*(English)*Zbl 0617.73008(Authors’ summary.) The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints are investigated for classes of constraints broad enough to encompass all those encountered in practice. Attention is focussed on principal waves, and results are presented for the growth of the amplitudes of such waves first for fronts of arbitrary curvature, and subsequently by specialisation for plane, cylindrical and spherical waves travelling in material which has undergone one-dimensional plane deformation, cylindrically symmetric and spherically symmetric deformation, respectively.

Reviewer: G.Warnecke

##### MSC:

74F05 | Thermal effects in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |

74A15 | Thermodynamics in solid mechanics |

##### Keywords:

homothermal waves; constrained media; acceleration waves; isotropic heat- conducting elastic media; arbitrary sets of constraints; principal waves; growth of the amplitudes; fronts of arbitrary curvature; plane, cylindrical and spherical waves; one-dimensional plane deformation; cylindrically symmetric; spherically symmetric deformation
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\textit{G. P. Bleach} and \textit{B. D. Reddy}, Arch. Ration. Mech. Anal. 98, 31--64 (1987; Zbl 0617.73008)

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##### References:

[1] | Bailey, P. B., & Chen, P. J. (1971) On the local and global behavior of acceleration waves. Arch. Rational Mech. Anal., 41, 121–131. Addendum: Asymptotic behavior. 44, 213–216. · Zbl 0228.73038 |

[2] | Borejko, P., & Chadwick, P. (1980) Energy relations for acceleration waves in elastic materials. Wave Motion, 2, 361–374. · Zbl 0459.73018 |

[3] | Bowen, R. M., & Chen, P. J. (1972) Some comments on the behavior of acceleration waves of arbitrary shape. J. Math. Phys., 13, 948–950. · Zbl 0253.73028 |

[4] | Bowen, R. M., & Wang, C. C. (1970) Acceleration waves in inhomogeneous isotropic elastic bodies. Arch. Rational Mech. Anal. 38, 13–45; Corrigendum, Arch. Rational Mech. Anal. 40, 403. · Zbl 0206.54004 |

[5] | Bowen, R. M., & Wang, C. C. (1971) Thermodynamic influences on acceleration waves in inhomogeneous isotropic elastic bodies with internal state variables. Arch. Rational Mech. Anal. 41, 287–318. · Zbl 0325.73009 |

[6] | Bowen, R. M., & Wang, C. C. (1972) Acceleration waves in orthotropic elastic materials. Arch. Rational Mech. Anal. 47, 149–170. · Zbl 0249.73032 |

[7] | Carlson, D. E. (1972) Linear Thermoelasticity. In Handbuch der Physik VIa/2 (ed. C. Truesdell). Springer (Berlin). |

[8] | Chadwick, P., & Currie, P. K. (1972) The propagation and growth of acceleration waves in heat-conducting elastic materials. Arch. Rational Mech. Anal. 49, 137–158. · Zbl 0251.73023 |

[9] | Chadwick, P., & Ogden, R. W. (1971) On the definition of elastic moduli. Arch. Rational Mech. Anal. 44, 41–53. · Zbl 0229.73007 |

[10] | Chadwick, P., & Ogden, R. W. (1971) A theorem of tensor calculus and its application to isotropic elasticity. Arch. Rational Mech. Anal. 44, 54–68. · Zbl 0229.73008 |

[11] | Chen, P. J. (1968) Growth of acceleration waves in isotropic elastic materials. J. Acoust. Soc. of Am. 43, 982–987. |

[12] | Chen, P. J. (1968) The growth of acceleration waves of arbitrary form in homogeneously deformed elastic materials. Arch. Rational Mech. Anal. 30, 81–89. · Zbl 0165.28301 |

[13] | Chen, P. J. (1968) Thermodynamic influences on the propagation and the growth of acceleration waves in elastic materials. Arch. Rational Mech. Anal. 31, 228–254. Corrigendum 32, 400–401. · Zbl 0198.58201 |

[14] | Chen, P. J., & Gurtin, M. E. (1974) On wave propagation in inextensible elastic bodies. Int. J. Solids. Structs. 10, 275–282. · Zbl 0269.73034 |

[15] | Chen, P. J., & Nunziato, J. W. (1975) On wave propagation in perfectly heat-conducting inextensible elastic bodies. J. Elast. 5, 155–160. · Zbl 0332.73033 |

[16] | Doria, M. L., & Bowen, R. M. (1970) Growth and decay of curved acceleration waves in chemically reacting fluids. Phys. of Fluids 13, 867–876. · Zbl 0198.29901 |

[17] | Durban, D. (1978) On the differentiation of tensor functions. Math. Proc. Camb. Phil. Soc. 83, 289–297. · Zbl 0376.73001 |

[18] | Eringen, A. C., & Suhubi, E. S. (1975) Elastodynamics, Volume I. Academic Press (New York). · Zbl 0344.73036 |

[19] | Gurtin, M. E., & Podio-Guidugli, P. (1973) The thermodynamics of constrained materials. Arch. Rational Mech. Anal. 51, 192–208. · Zbl 0263.73004 |

[20] | Marsden, J. E., & Hughes, T. J. R. (1983) Mathematical Foundations of Elasticity. Prentice-Hall (Englewood Cliffs, N.J.). · Zbl 0545.73031 |

[21] | Ogden, R. W. (1974) Growth and decay of acceleration waves in incompressible elastic solids. Quart. J. Mech. Appl. Math. 27, 451–464. · Zbl 0335.73009 |

[22] | Reddy, B. D. (1984) The propagation and growth of acceleration waves in constrained thermoelastic materials. J. Elast. 14, 387–402. · Zbl 0573.73032 |

[23] | Reddy, B. D. (1985) Acceleration waves in isotropic constrained thermoelastic materials. In Wave Phenomena: Modern Theory and Applications (North-Holland Mathematics Studies, vol. 97) (ed. C. Rodgers & T. Bryant Moodie). Elsevier (Amsterdam). · Zbl 0573.73033 |

[24] | Smith, G. F. (1970) On a fundamental error in two papers of C. C. Wang ”On representations for isotropic functions, parts I and II”. Arch. Rational Mech. Anal. 36, 161–165. · Zbl 0327.15029 |

[25] | Scott, N. H. (1975) Acceleration waves in constrained elastic materials. Arch. Rational Mech. Anal. 58, 57–75. · Zbl 0339.73006 |

[26] | Scott, N. H. (1976) Acceleration waves in incompressible solids. Quart. J. Mech. Appl. Math. 29, 295–310. · Zbl 0363.73026 |

[27] | Spencer, A. J. M. (1972) Deformations of Fibre-Reinforced Materials. Oxford University Press. · Zbl 0238.73001 |

[28] | Wang, C. C, & Truesdell, C. (1973) Introduction to Rational Elasticity. Noordhoff (Leiden). · Zbl 0308.73001 |

[29] | Wang, C. C. (1969) On representations for isotropic functions, Parts I and II. Arch. Rational Mech. Anal. 33, 249–267; 268–287. · Zbl 0332.15012 |

[30] | Wang, C. C. (1970) A new representation theorem for isotropic functions: an answer to Professor G. F. Smith’s criticism of my papers on representations for isotropic functions, Parts I and II. Arch. Rational Mech. Anal. 36, 166-197; 198–223. · Zbl 0327.15030 |

[31] | Whitworth, A. (1982) Simple waves in constrained elastic materials. Quart. J. Mech. Appl. Math. 35, 461–484. · Zbl 0514.73017 |

[32] | Whitworth, A., & Chadwick, P. (1984) The effect of inextensibility on elastic surface waves. Wave Motion 6, 289–302. · Zbl 0543.73025 |

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