Abstract
Second-order forms for the material response functions of an elastic heat conductor are derived by approximating the response functions by polynomials in the appropriate invariants. Solutions based upon these forms of the response functions are exact for special materials and approximate for general materials. The second-order dependence on temperature of isothermal elasticity solutions is found, and the results are shown to agree well with experimental data taken on rubber. Within the second-order theory for incompressible and isotropic bodies, the problems of biaxial stretching of a plate with transverse heat flow and the simultaneous extension and shear of a cylindrical annulus with radial heat flow are solved.
Résumé
Les termes du deuxième ordre des fonctions de réponse d'un conducteur de chaleur élastique sont dérivés dans une approximation basée sur le développement en polynomes d'invariants appropriés de ces fonctions. Les solutions qui en résultent sont exactes pour certains matériaux et approchées dans le cas général. Une dépendance du second ordre en température de l'élasticité isotherme est établie et il est montré que, dans le cas du caoutchouc, les résultats sont en bon accord avec les données expérimentales. Les problèmes de l'état de tension bidimensionnel d'une plaque soumise à un flux de chaleur transversal et de l'allongement et du cisaillement simultanés d'un anneau cylindrique parcouru par un flux radial sont résolus dans le cadre de la théorie du second ordre pour les corps incompressibles et isotropes.
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Martin, S.E., Carlson, D.E. The behavior of elastic heat conductors with second-order response functions. Journal of Applied Mathematics and Physics (ZAMP) 28, 311–329 (1977). https://doi.org/10.1007/BF01595598
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DOI: https://doi.org/10.1007/BF01595598