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Encyclopedia of Continuum Mechanics pp 1–6Cite as

Carroll, Michael Mary

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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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References

  • Bhatt JJ, Carroll MM, Schatz JF (1975) A spherical model calculation for volumetric response of porous rocks. J Appl Mech 42:363–368

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  • Carroll MM (1967a) On circularly-polarized nonlinear electromagnetic waves. Quart Appl Math 25:319–323

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  • Carroll MM (1967b) Controllable deformations of incompressible simple materials. Int J Eng Sci 5:515–525

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  • Carroll MM (1967c) Some results on finite amplitude elastic waves. Acta Mech 3:167–181

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  • Carroll MM (1968) Finite deformations of incompressible simple solids I. Isotropic solids. Quart J Mech Appl Math 21:147–170

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  • Carroll MM (1974) Oscillatory shearing of nonlinearly elastic solids. J Appl Math Phys (ZAMP) 25:83–88

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  • Carroll MM (1977a) Plane elastic standing waves of finite amplitude. J Elast 7:411–424

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  • Carroll MM (1977b) Plane circular shearing of incompressible fluids and solids. Quart J Mech Appl Math 30:223–234

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  • Carroll MM (1978) Finite amplitude standing waves in compressible elastic solids. J Elast 8:323–328

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  • Carroll MM (1979) An effective stress law for anisotropic elastic deformation. J Geophys Res 84:7510–7512

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  • 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 251–262

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  • Carroll MM (1987a) Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders. Quart Appl Math 45:141–154

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  • Carroll MM (1987b) A rate-independent constitutive theory for finite inelastic deformation. J Appl Mech 54:15–21

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  • Carroll MM (1988) Finite strain solutions in compressible isotropic elasticity. J Elast 20:65–92

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  • Carroll MM (1991a) Controllable deformations for special classes of compressible elastic solids. Stability Appl Anal Contin Media 1:309–323

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  • Carroll MM (1991b) Controllable deformations in compressible finite elasticity. Stability Appl Anal Contin Media 1:373–384

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  • Carroll MM (1995) On obtaining closed form solutions for compressible nonlinearly elastic materials. J Appl Math Phys (ZAMP) 46 (Special Issue):S126–S145

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  • Carroll MM (2009) Must elastic materials be hyperelastic? Math Mech Solids 14:369–376

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  • Carroll MM (2011) A strain energy function for vulcanized rubbers. J Elast 103:173–187

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  • Carroll MM (2019) Molecular chain networks and strain energy functions in rubber elasticity. Phil Trans R Soc A377:20180067

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  • Carroll MM, Chien CF (1977) Decay of reverberant sound in a spherical enclosure. J Acoust Soc Am 22:1442–1446

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  • Carroll MM, Hayes MA (2006) In memory of Ronald S. Rivlin. Math Mech Solids 11:103–112

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  • Carroll MM, Holt AC (1972a) Suggested modification of the P-α model for porous materials. J Appl Phys 43:759–761

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  • Carroll MM, Holt AC (1972b) Static and dynamic pore-collapse relations for ductile porous materials. J Appl Phys 43:1626–1636

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  • Carroll MM, Horgan CO (1990) Finite strain solutions for a compressible elastic solid. Quart Appl Math 48:767–780

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  • Carroll MM, Kim KT (1984) Pressure-density equations for porous metals and metal powders. Powder Metall 27:153–159

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  • Carroll MM, Miles RN (1978) Steady-state sound in an enclosure with diffusely reflecting boundary. J Acoust Soc Am 64:1424–1428

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  • Carroll MM, Rivlin RS (1966) Transverse electric and magnetic effects. Quart Appl Math 23:365–368

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  • Carroll MM, Rivlin RS (1967) Electro-optical effects, I. J Math Physics 8:2088–2091

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  • Carroll MM, Rooney FJ (2005) Implications of Shield’s inverse deformation theorem for compressible finite elasticity. J Appl Math Phys (ZAMP) 56:1048–1060

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  • Casey J (2005) A remark on Cauchy-elasticity. Int J Nonlin Mech 40:331–339

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  • Casey J (ed) (2011) Contributions to nonlinear and linear elasticity, and continuum mechanics. Math Mech Solids 16:453–790

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  • Curran JH, Carroll MM (1979) Shear stress enhancement of void compaction. J Geophys Res 84:1105–1112

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  • Katsube N, Carroll MM (1987a) The modified mixture theory for fluid-filled porous media: theory. J Appl Mech 54:35–40

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  • Katsube N, Carroll MM (1987b) The modified mixture theory for fluid-filled porous media: applications. J Appl Mech 54:41–46

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Berkeley, CA, USA

    James Casey

Authors
  1. James Casey
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Corresponding author

Correspondence to James Casey .

Editor information

Editors and Affiliations

  1. Otto-von-Guericke University Magdeburg, Chair of Engineering Mechanics, Institut, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Fakultät für Maschinenbau, Hochschule Esslingen, Esslingen am Neckar, Baden-Württemberg, Germany

    Andreas Öchsner

Section Editor information

  1. Fakultät für Maschinenbau, Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

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Casey, J. (2019). Carroll, Michael Mary. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_293-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_293-1

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  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

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