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The propagation and growth of acceleration waves in constrained thermoelastic materials. (English) Zbl 0573.73032
For thermoelastic materials subjected to arbitrary thermo-kinematic constraints the propagation conditions are derived. For plane homothermal waves, the equations governing the growth of acceleration amplitude are also deduced and are shown to be similar to the corresponding equations for unconstrained materials.
Reviewer: N.Sandru

MSC:
74J99 Waves in solid mechanics
74F05 Thermal effects in solid mechanics
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[1] Alts, T. A simple method for the consideration of thermo-kinematic constraints in the thermodynamics of elastic bodies. Zeit. Ang. Math. Mech. (ZAMM), 58 (1978) T191-T192. · Zbl 0389.73003
[2] Andreussi, F. and Podio Guidugli, P. Thermomechanical constraints in simple materials. Bull. Acad. Pol. Sci., S?r. Sci. Tech. 21 (1973) 199-205. · Zbl 0278.73004
[3] Bertram, A. and Haupt, P. A note on Andreussi-Guidugli’s theory of thermomechanical constraints in simple materials. Bull. Acad. Pol. Sci., S?r. Sci. Tech. 24 (1976) 47-51. · Zbl 0352.73005
[4] Chadwick, P. and Ogden, R.W. On the definition of elastic moduli. Arch. Rat. Mech. Anal. 44 (1971) 41-53. · Zbl 0229.73007
[5] Chadwick, P. and Currie, P.K. The propagation and growthof acceleration waves in heat-conducting elastic materials. Arch. Rat. Mech. Anal. 49 (1972) 137-158. · Zbl 0251.73023
[6] Chadwick, P. and Seet, L.T.C. Second order thermoelasticity for isotropic and transversely isotropic materials. In Trends in Elasticity and Thermoelasticity (Nowacki Anniversary Volume) Wolters-Noordhoff (Groningen) (1971) 29-57. · Zbl 0229.73045
[7] Chen, P.J. Thermodynamic influences on the propagation and the growth of acceleration waves in elastic materials. Arch. Rat. Mech. Anal. 31 (1968) 228-254. · Zbl 0198.58201
[8] Chen, P.J. Corrigendum to Chen (1968), Arch. Rat. Mech. Anal. 32 (1969) 400-401.
[9] Chen, P.J. and Gurtin, M.E. On wave propagation in inextensible elastic bodies. Int. J. Solids. Structs. 10 (1974) 275-282. · Zbl 0269.73034
[10] Chen, P.J. and Nunziato, J.W. On wave propagation in perfectly heat-conducting inextensible elastic bodies. J. Elast. 5 (1975) 155-160. · Zbl 0332.73033
[11] Cohen, H. and Epstein, M. Acceleration waves in constrained elastic rods. Arch. Rat. Mech. Anal. 72 (1979) 141-154. · Zbl 0426.73052
[12] Coleman, B.D. and Gurtin, M.E. Waves in materials with memory III. Thermodynamic influences on the growth and decay of acceleration waves. Arch. Rat. Mech. Anal. 19 (1965) 266-298. · Zbl 0244.73018
[13] Green, A.E. and Lindsay, K.A. Thermoelasticity. J. Elast. 2 (1972) 1-7. · Zbl 0775.73063
[14] Green, A.E., Naghdi, P.M. and Trapp, J.A. Thermodynamics of a continuum with internal constraints. Int. J. Eng. Sci. 8 (1970) 891-908. · Zbl 0218.73006
[15] Gurtin, M.E. and Podio Guidugli, P. The thermodynamics of constrained materials. Arch. Rat. Mech. Anal. 51 (1973) 192-208. · Zbl 0263.73004
[16] Lindsay, K.A. and Straughan, B. Propagation of mechanical and temperature acceleration waves in thermoelastic materials. Zeit. Ang. Math. Phys. (ZAAMP) 30 (1979) 477-490. · Zbl 0405.73087
[17] Ogden, R.W. Growth and decay of acceleration waves in incompressible elastic solids. Quart. J. Mech. Appl. Math. 27 (1974) 451-464. · Zbl 0335.73009
[18] Scott, N.H. Acceleration waves in constrained elastic materials. Arch. Rat. Mech. Anal. 58 (1975) 57-75. · Zbl 0339.73006
[19] Scott, N.H. Acceleration waves in incompressible solids. Quart. J. Mech. Appl. Math. 29 (1976) 295-310. · Zbl 0363.73026
[20] Trapp, J.A. Reinforced materials with thermomechanical constraints. Int. J. Eng. Sci. 9 (1971) 757-773. · Zbl 0231.73004
[21] Truesdell, C. General and exact theory of waves in finite elastic strain. Arch. Rat. Mech. Anal. 8 (1961) 263-296. · Zbl 0111.37703
[22] Truesdell, C. Rational Thermodynamics, McGraw-Hill (New York) 1969.
[23] Truesdell, C. and Noll, W. The nonlinear field theories of mechanics. Handbuch der Physik III/3 (ed. S. Flugge). Springer (Berlin) 1965). · Zbl 0779.73004
[24] Wang, C.C. and Truesdell, C. Introduction to Rational Elasticity. Nordhoff (Leiden) 1973. · Zbl 0308.73001
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