Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Carroll, Michael Mary

  • James CaseyEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_293-1

Michael Mary Carroll (December 8, 1936, Thurles, County Tipperary, Ireland; †January 17, 2016, Houston, Texas, USA) was a mathematical physicist who worked on continuum mechanics and a professor of engineering. His research in the areas of nonlinear elasticity and porous media is especially significant. (This entry is based largely on Casey (2011), pp. 453–466, where a fuller account of Carroll’s life and work may be found.)

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  1. Bhatt JJ, Carroll MM, Schatz JF (1975) A spherical model calculation for volumetric response of porous rocks. J Appl Mech 42:363–368Google Scholar
  2. Carroll MM (1967a) On circularly-polarized nonlinear electromagnetic waves. Quart Appl Math 25:319–323Google Scholar
  3. Carroll MM (1967b) Controllable deformations of incompressible simple materials. Int J Eng Sci 5:515–525CrossRefGoogle Scholar
  4. Carroll MM (1967c) Some results on finite amplitude elastic waves. Acta Mech 3:167–181CrossRefGoogle Scholar
  5. Carroll MM (1968) Finite deformations of incompressible simple solids I. Isotropic solids. Quart J Mech Appl Math 21:147–170CrossRefGoogle Scholar
  6. Carroll MM (1974) Oscillatory shearing of nonlinearly elastic solids. J Appl Math Phys (ZAMP) 25:83–88CrossRefGoogle Scholar
  7. Carroll MM (1977a) Plane elastic standing waves of finite amplitude. J Elast 7:411–424CrossRefGoogle Scholar
  8. Carroll MM (1977b) Plane circular shearing of incompressible fluids and solids. Quart J Mech Appl Math 30:223–234MathSciNetCrossRefGoogle Scholar
  9. Carroll MM (1978) Finite amplitude standing waves in compressible elastic solids. J Elast 8:323–328MathSciNetCrossRefGoogle Scholar
  10. Carroll MM (1979) An effective stress law for anisotropic elastic deformation. J Geophys Res 84:7510–7512CrossRefGoogle Scholar
  11. Carroll MM (1980) Mechanical response of fluid-saturated porous materials. In: Rimrott FPJ, Tabarrok B (eds) Proceedings of the 15th international congress of theoretical and applied mechanics. North-Holland Publishing Co., Amsterdam, pp 251–262Google Scholar
  12. Carroll MM (1987a) Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders. Quart Appl Math 45:141–154Google Scholar
  13. Carroll MM (1987b) A rate-independent constitutive theory for finite inelastic deformation. J Appl Mech 54:15–21CrossRefGoogle Scholar
  14. Carroll MM (1988) Finite strain solutions in compressible isotropic elasticity. J Elast 20:65–92MathSciNetCrossRefGoogle Scholar
  15. Carroll MM (1991a) Controllable deformations for special classes of compressible elastic solids. Stability Appl Anal Contin Media 1:309–323Google Scholar
  16. Carroll MM (1991b) Controllable deformations in compressible finite elasticity. Stability Appl Anal Contin Media 1:373–384Google Scholar
  17. Carroll MM (1995) On obtaining closed form solutions for compressible nonlinearly elastic materials. J Appl Math Phys (ZAMP) 46 (Special Issue):S126–S145MathSciNetzbMATHGoogle Scholar
  18. Carroll MM (2009) Must elastic materials be hyperelastic? Math Mech Solids 14:369–376CrossRefGoogle Scholar
  19. Carroll MM (2011) A strain energy function for vulcanized rubbers. J Elast 103:173–187MathSciNetCrossRefGoogle Scholar
  20. Carroll MM (2019) Molecular chain networks and strain energy functions in rubber elasticity. Phil Trans R Soc A377:20180067CrossRefGoogle Scholar
  21. Carroll MM, Chien CF (1977) Decay of reverberant sound in a spherical enclosure. J Acoust Soc Am 22:1442–1446CrossRefGoogle Scholar
  22. Carroll MM, Hayes MA (2006) In memory of Ronald S. Rivlin. Math Mech Solids 11:103–112MathSciNetCrossRefGoogle Scholar
  23. Carroll MM, Holt AC (1972a) Suggested modification of the P-α model for porous materials. J Appl Phys 43:759–761CrossRefGoogle Scholar
  24. Carroll MM, Holt AC (1972b) Static and dynamic pore-collapse relations for ductile porous materials. J Appl Phys 43:1626–1636CrossRefGoogle Scholar
  25. Carroll MM, Horgan CO (1990) Finite strain solutions for a compressible elastic solid. Quart Appl Math 48:767–780Google Scholar
  26. Carroll MM, Kim KT (1984) Pressure-density equations for porous metals and metal powders. Powder Metall 27:153–159CrossRefGoogle Scholar
  27. Carroll MM, Miles RN (1978) Steady-state sound in an enclosure with diffusely reflecting boundary. J Acoust Soc Am 64:1424–1428CrossRefGoogle Scholar
  28. Carroll MM, Rivlin RS (1966) Transverse electric and magnetic effects. Quart Appl Math 23:365–368Google Scholar
  29. Carroll MM, Rivlin RS (1967) Electro-optical effects, I. J Math Physics 8:2088–2091CrossRefGoogle Scholar
  30. Carroll MM, Rooney FJ (2005) Implications of Shield’s inverse deformation theorem for compressible finite elasticity. J Appl Math Phys (ZAMP) 56:1048–1060MathSciNetCrossRefGoogle Scholar
  31. Casey J (2005) A remark on Cauchy-elasticity. Int J Nonlin Mech 40:331–339CrossRefGoogle Scholar
  32. Casey J (ed) (2011) Contributions to nonlinear and linear elasticity, and continuum mechanics. Math Mech Solids 16:453–790Google Scholar
  33. Curran JH, Carroll MM (1979) Shear stress enhancement of void compaction. J Geophys Res 84:1105–1112CrossRefGoogle Scholar
  34. Katsube N, Carroll MM (1987a) The modified mixture theory for fluid-filled porous media: theory. J Appl Mech 54:35–40CrossRefGoogle Scholar
  35. Katsube N, Carroll MM (1987b) The modified mixture theory for fluid-filled porous media: applications. J Appl Mech 54:41–46CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

Section editors and affiliations

  • Holm Altenbach
    • 1
  1. 1.Fakultät für Maschinenbau, Institut für MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany