On nonmaterial surfaces with structure

Pfenning, Nancy M.; Williams, W. O.

doi:10.1090/qam/1233530

Authors: Nancy M. Pfenning and W. O. Williams
Journal: Quart. Appl. Math. 51 (1993), 559-576
MSC: Primary 73B99; Secondary 73B30
DOI: https://doi.org/10.1090/qam/1233530
MathSciNet review: MR1233530
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G. Capriz, Continua with microstructure, Springer Tracts in Natural Philosophy, vol. 35, Springer-Verlag, New York, 1989. MR 985585
J. Fernandez-Diaz and W. O. Williams, A generalized Stefan condition, Z. Angew. Math. Phys. 30 (1979), no. 5, 749–755 (English, with German summary). MR 553277, DOI https://doi.org/10.1007/BF01590684
George M. C. Fisher and Marshall J. Leitman, On continuum thermodynamics with surfaces, Arch. Rational Mech. Anal. 30 (1968), 225–262. MR 229428, DOI https://doi.org/10.1007/BF00253875
Morton E. Gurtin, On thermomechanical laws for the motion of a phase interface, Z. Angew. Math. Phys. 42 (1991), no. 3, 370–388 (English, with German summary). MR 1115197, DOI https://doi.org/10.1007/BF00945710
Morton E. Gurtin and Luiz C. Martins, Cauchy’s theorem in classical physics, Arch. Rational Mech. Anal. 60 (1975/76), no. 4, 305–324. MR 408377, DOI https://doi.org/10.1007/BF00248882

M. E. Gurtin and A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 50, 291–323 (1974)

A. E. Green and R. S. Rivlin, Simple force and stress multipoles, Arch. Rational Mech. Anal. 16 (1964), 325–353. MR 182191, DOI https://doi.org/10.1007/BF00281725
Morton E. Gurtin and Allan Struthers, Multiphase thermomechanics with interfacial structure. III. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. 112 (1990), no. 2, 97–160. MR 1073827, DOI https://doi.org/10.1007/BF00375667
Morton E. Gurtin, Allan Struthers, and William O. Williams, A transport theorem for moving interfaces, Quart. Appl. Math. 47 (1989), no. 4, 773–777. MR 1031691, DOI https://doi.org/10.1090/qam/1031691
Morton E. Gurtin and William O. Williams, An axiomatic foundation for continuum thermodynamics, Arch. Rational Mech. Anal. 26 (1967), 83–117. MR 214335, DOI https://doi.org/10.1007/BF00285676
Morton E. Gurtin, William O. Williams, and William P. Ziemer, Geometric measure theory and the axioms of continuum thermodynamics, Arch. Rational Mech. Anal. 92 (1986), no. 1, 1–22. MR 816619, DOI https://doi.org/10.1007/BF00250730
G. P. Moeckel, Thermodynamics of an interface, Arch. Rational Mech. Anal. 57 (1975), 255–280. MR 366245, DOI https://doi.org/10.1007/BF00280158
Walter Noll, The foundations of classical mechanics in the light of recent advances in continuum mechanics, The axiomatic method. With special reference to geometry and physics. Proceedings of an International Symposium held at the Univ. of Calif., Berkeley, Dec. 26, 1957-Jan. 4, 1958 (edited by L. Henkin, P. Suppes and A. Tarski), Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam, 1959, pp. 266–281. MR 0108036

W. Noll, La mechanique classique, basée sur un axiome d’objetivitie, La Methode Axiomatique dans les Mecaniques Classiques et Nouvelles, Gauthier-Villars, Paris, 1963, pp. 47–56

N. M. Pfenning, Theory of non-material surfaces with energy concentration, Ph.D. Thesis, Carnegie Mellon Univ., 1984

Miroslav Šilhavý, The existence of the flux vector and the divergence theorem for general Cauchy fluxes, Arch. Rational Mech. Anal. 90 (1985), no. 3, 195–212. MR 803773, DOI https://doi.org/10.1007/BF00251730

M. Šilhavý, Cauchy’s stress theorem and tensor fields with divergences in $L^{p}$, Arch. Rational Mech. Anal. 116, 223–255 (1991)

William O. Williams, Axioms for work and energy in general continua. II. Surfaces of discontinuity, Arch. Rational Mech. Anal. 49 (1972/73), 225–240. MR 339645, DOI https://doi.org/10.1007/BF00255667