Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Physical Foundations of Continuum Mechanics
  • Cited by 24
Publisher:
Cambridge University Press
Online publication date:
November 2012
Print publication year:
2012
Online ISBN:
9781139028318
DOI:
https://doi.org/10.1017/CBO9781139028318
Subjects:
Mathematics, Engineering, Fluid Dynamics and Solid Mechanics, Solid Mechanics and Materials
Information

Book description

Ian Murdoch's Physical Foundations of Continuum Mechanics will interest engineers, mathematicians, and physicists who study the macroscopic behaviour of solids and fluids or engage in molecular dynamical simulations. In contrast to standard works on the subject, Murdoch's book examines physical assumptions implicit in continuum modelling from a molecular perspective. In so doing, physical interpretations of concepts and fields are clarified by emphasising both their microscopic origin and sensitivity to scales of length and time. Murdoch expertly applies this approach to theories of mixtures, generalised continua, fluid flow through porous media, and systems whose molecular content changes with time. Elements of statistical mechanics are included, for comparison, and two extensive appendices address relevant mathematical concepts and results. This unique and thorough work is an authoritative reference for both students and experts in the field.

Reviews

'Numerous books have been written on the subject, but this book has unique features that make it somewhat different from the conventional [ones] … the microscale viewpoints of the book are somewhat unique and may cultivate a different view of continuum models in students.'

Majid Molki Source: Heat Transfer Engineering

‘This is a very instructive book … useful for researchers, teachers and graduate students … numerous exercises, examples and additional comments … are very helpful for a better understanding of the nature of the treated subjects.’

Vladimir Cadez Source: Zentralblatt MATH

'The subject is developed carefully and rigorously. Relevant mathematical background is included in appendices. … The volume presents a stimulating and original approach to a fundamental problem in physics and is recommended to all workers in continuum mechanics concerned with how their subject may be consistently and generally grounded in atomic theory.'

Peter Holland Source: Contemporary Physics

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
References
[1] Gurtin, M. E., 1981. An Introduction to Continuum Mechanics. Academic Press, New York.
[2] Truesdell, C., & Noll, W., 1965. The nonlinear field theories of mechanics. In: Handbuch der Physik III/1 (ed. S., Flügge). Springer-Verlag, Berlin.
[3] Chadwick, P., 1976. Continuum Mechanics. Allen & Unwin, London.
[4] Landau, L. D., & Lifschitz, E. M., 1959. Fluid Mechanics. Pergamon Press, London.
[5] Paterson, A. R., 1983. A First Course in Fluid Dynamics. Cambridge University Press, Cambridge, UK.
[6] Brush, S. G., 1986. The Kind of Motion we call Heat. North Holland, Amsterdam.
[7] Goldstein, H., Poole, C., & Safko, J., 2002. Classical Mechanics (3rd ed.). Addison-Wesley, San Francisco.
[8] Truesdell, C., 1977. A First Course in Rational Continuum Mechanics, Vol. 1. Academic Press, New York.
[9] Born, W., & Wolf, E., 1999. Principles of Optics (7th ed.). Cambridge University Press, Cambridge, UK.
[10] Hardy, R. J., 1982. Formulas for determining local properties in molecular-dynamics simulations: Shock waves. J. Chem. Phys. 76, 622–628.
[11] Gurtin, M. E., 1972. The linear theory of elasticity. In: Handbuch der Physik VIa/2 (ed. C., Truesdell). Springer-Verlag, Berlin.
[12] Zadeh, L. A., 1965. Fuzzy sets. Information and Control 8, 338–353.
[13] Bear, J., 1972. Dynamics of Fluids in Porous Media. Elsevier, Amsterdam.
[14] Murdoch, A. I., & Kubik, J., 1995. On the continuum modelling of porous media containing fluid: a molecular viewpoint with particular attention to scale. Transport in Porous Media 19, 157–197.
[15] Murdoch, A. I., & Hassanizadeh, S. M., 2002. Macroscale balance relations for bulk, interfacial and common line systems in multiphase flows through porous media on the basis of molecular considerations. Int. J. Multiphase Flow 28, 1091–1123.
[16] Noll, W., 1955. Der Herleitung der Grundgleichen der Thermomechanik der Kontinua aus der statischen Mechanik. J. Rational Mech. Anal. 4. 627–646. (Translated as: Lehoucq, R., & von Lilienfeld, O. A., 2010. Derivation of the fundamental equations of continuum mechanics from statistical mechanics. J. Elasticity, 100, 5–24.)
[17] Atkins, P. W., 1996. The Elements of Physical Chemistry (2nd ed.). Oxford University Press, Oxford, UK.
[18] Murdoch, A. I., 2007. A critique of atomistic definitions of the stress tensor. J. Elasticity 88, 113–140.
[19] Carlsson, T., & Leslie, F. M., 1999. The development of theory for flow and dynamic effects for nematic liquid crystals. Liquid Crystals 26, 1267–1280.
[20] Murdoch, A. I., 2003. On the microscopic interpretation of stress and couple stress. J. Elasticity 71, 105–131.
[21] Kellogg, O. D., 1967. Foundations of Potential Theory (reprint of first edition of 1929). Springer-Verlag, Berlin.
[22] Israelachvili, J. N., 1974. The nature of van der Waals forces. Contemp. Phys. 15, 159–177.
[23] Gurtin, M. E., Fried, E., & Anand, L., 2010. The Mechanics and Thermodynamics of Continua. Cambridge University Press, New York.
[24] de Gennes, P. G., 1974. The Physics of Liquid Crystals. Oxford University Press, Oxford, UK.
[25] Toupin, R. A., 1962. Elastic materials with couple-stress. Arch. Rational Mech. Anal. 11, 385–414.
[26] Mindlin, M. D., & Tiersten, H. F., 1962. Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal. 11, 415–448.
[27] Murdoch, A. I., 1987. On the relationship between balance relations for generalised continua and molecular behaviour. Int. J. Eng. Sci. 25, 883–914.
[28] Sedov, L. I., 1965. Introduction to the Mechanics of a Continuous Medium. Addison-Wesley, Reading, MA.
[29] Reddy, J. N., 2006. An Introduction to Continuum Mechanics. Cambridge University Press, Cambridge, UK.
[30] Kröner, E. (ed.), 1968. Mechanics of Generalized Continua. Springer-Verlag, New York.
[31] Carlson, D. E., 1972. Linear thermoelasticity. In: Handbuch der Physik, VIa/2 (ed. C., Truesdell). Springer-Verlag, Berlin.
[32] Ohanian, H. C., 1985. Physics (Vol. 1). Norton, New York.
[33] Truesdell, C., & Toupin, R. A., 1960. The classical field theories. In: Handbuch der Physik III/1 (Ed. S. Flügge, ). Springer-Verlag, Berlin.
[34] Truesdell, C., 1969. Rational Thermodynamics. McGraw-Hill, New York.
[35] Atkin, R. J., & Craine, R. E., 1976. Continuum theories of mixtures: basic theory and historical development. Q. J., Mech. Appl. Math. XXIX, 211–244.
[36] Bowen, R. M., 1976. Theory of mixtures. In: Continuum Physics, III (Ed. A. C., Eringen). Academic Press, New York.
[37] Gurtin, M. E., Oliver, M. L., & Williams, W. O., 1973. On balance of forces for mixtures. Q. Appl. Math. 30, 527–530.
[38] Williams, W. O., 1973. On the theory of mixtures. Arch. Rational Mech. Anal. 51, 239–260.
[39] Oliver, M. L., & Williams, W. O., 1975. Formulation of balance of forces in mixture theories. Q. Appl. Math. 33, 81–86.
[40] Morro, A., & Murdoch, A. I., 1986. Stress, body force, and momentum balance in mixture theory. Meccanica 21, 184–190.
[41] Murdoch, A. I., & Morro, A., 1987. On the continuum theory of mixtures: motivation from discrete considerations. Int. J. Eng. Sci. 25, 9–25.
[42] Bedford, A., 1983. Theories of immiscible and structured mixtures. Int. J. Eng. Sci. 21, 863–890.
[43] Alblas, J. B., 1976. A note on the physical foundation of the theory of multipole stresses. Arch. Mech. Stos. 28, 279–298.
[44] Murdoch, A. I., 1985. A corpuscular approach to continuum mechanics. Arch. Rational Mech. Anal. 88, 291–321.
[45] Noll, W., 1973. Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal. 52, 62–92.
[46] MacLane, S., & Birkhoff, G., 1967. Algebra. Macmillan, London.
[47] Roberts, P. H., & Donnelly, R. J., 1974. Superfluid mechanics. In: Annual Review of Fluid Mechanics 6 (ed. van Dyke, M., Vincentini, W. G., & Wehausen, J. V.). Annual Reviews, Palo Alto, CA.
[48] Hills, R. N., & Roberts, P. H., 1977. Superfluid mechanics for a high density of vortex lines. Arch. Rational Mech. Anal. 66, 43–71.
[49] Piquet, J., 2001. Turbulent Flows (revised 2nd printing). Springer-Verlag, Berlin.
[50] Murdoch, A. I., 2003. Objectivity in classical continuum mechanics: a rationale for discarding the ‘principle of invariance under superposed rigid body motions’ in favour of purely objective considerations. Continuum Mech. Thermodyn. 15, 309–320.
[51] Murdoch, A. I., 2006. Some primitive concepts in continuum mechanics regarded in terms of objective space-time molecular averaging: the key rôle played by inertial observers. J. Elasticity 84, 69–97.
[52] Rivlin, R. S., 1970. Red herrings and sundry unidentified fish in nonlinear continuum mechanics. In: Inelastic Behavior of Solids (ed. Kanninen, M. G., Adler, D., Rosenfield, A. R., Jaffee, R. I.), McGraw-Hill, New York.
[53] Müller, I., 1972. On the frame dependence of stress and heat flux. Arch. Rational Mech. Anal. 45, 241–250.
[54] Murdoch, A. I., 1983. On material frame-indifference, intrinsic spin, and certain constitutive relations motivated by the kinetic theory of gases. Arch. Rational Mech. Anal. 83, 185–194.
[55] Wang, C. C., 1975. On the concept of frame-indifference in continuum mechanics and in the kinetic theory of gases. Arch. Rational Mech. Anal. 58, 381–393.
[56] Truesdell, C., 1976. Correction of two errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of material frame-indifference. Meccanica 11, 196–199.
[57] Speziale, G., 1981. On frame-indifference and iterative procedures in the kinetic theory of gases. Int. J. Eng. Sci. 19, 63–73.
[58] Svendsen, B., & Bertram, A., 1999. On frame-indifference and form invariance in constitutive theory. Acta Mechanica 132, 195–207.
[59] Edelen, G. B., & McLennan, J. A., 1973. Material indifference: a principle or a convenience. Int. J. Eng. Sci. 11, 813–817.
[60] Söderholm, L. H., 1976. The principle of material frame-indifference and material equations of gases. Int. J. Eng. Sci. 14, 523–528.
[61] Woods, L. C., 1981. The bogus axioms of continuum mechanics. Bull. Inst. Math. Applications 17, 98–102.
[62] Burnett, D., 1935. The distribution of molecular velocities and the mean motion in a non-uniform gas. Proc. Lond. Math. Soc. 40, 382–435.
[63] Murdoch, A. I., 1982. On material frame-indifference. Proc. R. Soc. Lond. A 380, 417–426.
[64] Liu, I.-S., 2003. On Euclidean objectivity and the principle of material frame-indifference. Continuum Mech. Thermodyn. 16, 309–320.
[65] Liu, I.-S., 2005. Further remarks on Euclidean objectivity and the principle of material frame-indifference. Continuum Mech. Thermodyn. 17, 125–133.
[66] Murdoch, A. I., 2005. On criticism of the nature of objectivity in classical continuum physics. Continuum Mech. Thermodyn. 17, 135–148.
[67] Edelen, D. G. B., 1976. Nonlocal field theories. In: Continuum Physics, IV (ed. A. C., Eringen). Academic Press, New York.
[68] Silling, S., 2000. Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48, 175–209.
[69] Lehoucq, R. B., & Sears, M. P., 2011. Statistical mechanical foundation of the peri-dynamic nonlocal continuum theory: Energy and momentum laws. Physical ReviewE 84(031112), 1–7.
[70] Silling, S. A., Epton, M., Weckner, O., & Askari, E., 2007. Peridynamic states and constitutive modelling. J. Elasticity 88, 151–184.
[71] Stone, A. J., 1984. Intermolecular forces. In: Molecular Liquids – Dynamics and Interactions (ed. A. J., , Barnes, ). Reidel, Dordrecht, The Netherlands.
[72] Landau, L. D., & Lifschitz, E. M., 1980. Statistical Physics (3rd ed. part 1). Pergamon Press, Oxford, UK.
[73] Irving, J. H., & Kirkwood, J. G., 1950. The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18, 817–829.
[74] Pitteri, M., 1986. Continuum equations of balance in classical statistical mechanics. Arch. Rational Mech. Anal. 94, 291–305.
[75] Admal, N. C., & Tadmor, E. B., 2010. A unified interpretation of stress in molecular systems. J. Elasticity 100, 63–143.
[76] Murdoch, A. I., & Bedeaux, D., 1993. On the physical interpretation of fields in continuum mechanics. Int. J. Eng. Sci. 31, 1345–1373.
[77] Murdoch, A. I., & Bedeaux, D., 1994. Continuum equations of balance via weighted averages of microscopic quantities. Proc. R. Soc. London A 445, 157–179.
[78] Murdoch, A. I., & Bedeaux, D., 1996. A microscopic perspective on the physical foundations of continuum mechanics: 1. Macroscopic states, reproducibility, and macroscopic statistics, at prescribed scales of length and time. Int. J. Eng. Sci. 34, 1111–1129.
[79] Murdoch, A. I., & Bedeaux, D., 1997. A microscopic perspective on the physical foundations of continuum mechanics – II. A projection operator approach to the separation of reversible and irreversible contributions to macroscopic behaviour. Int. J. Eng. Sci. 35, 921–949.
[80] Zwanzig, R., 1960. Ensemble method in the theory of irreversibility. J. Chem. Phys. 33, 1338–1341.
[81] Zwanzig, R., 2004. Nonequilibrium Statistical Mechanics. Oxford University Press, Oxford, UK.
[82] Kröner, E., 1971. Statistical Continuum Mechanics. C. I. S. M. E., Courses and Lectures No. 92. Springer-Verlag, Vienna.
[83] Belleni-Morante, A., 1994. A Concise Guide to Semigroups and Evolution Equations. World Scientific, Singapore.
[84] Jacobson, N., 1951. Lectures in Abstract Algebra, Vol. 1 – Basic Concepts. van Nostrand, Princeton, NJ.
[85] Lamb, W., Murdoch, A. I., & Stewart, J., 2001. On an operator identity central to projection operator methodology. Physica A 298, 121–139.
[86] Grabert, H., 1982. Projection Operator Techniques in Nonequilibrium Statistical Mechanics. Springer-Verlag, Berlin.
[87] Murdoch, A. I., & Bedeaux, D., 2001. Characterisation of microstates for confined systems and associated scale-dependent continuum fields via Fourier coefficients. J. Phys. A: Math. Gen. 34, 6495–6508.
[88] Halmos, P. R., 1958. Finite-Dimensional Vector Spaces. van Nostrand, Princeton.
[89] Goertzel, G., & Tralli, N., 1960. Some Mathematical Methods of Physics. McGraw-Hill, New York.
[90] Greub, W., 1978. Multilinear Algebra, 2nd edn. Springer-Verlag, New York.
[91] Apostol, T. M., 1957. Mathematical Analysis. Addison-Wesley, Reading, MA.
[92] Moeckel, G. P., 1975. Thermodynamics of an interface. Arch. Rational Mech. Anal. 57, 255–280.
[93] Gurtin, M. E., & Murdoch, A. I., 1975. A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal. 57, 291–323.
[94] Rusanov, A. I., 1971. Recent investigations on the thickness of surface layers. In: Progress in Surface and Membrane Science, Vol. 4. (ed. Danielli, J. F., Rosenberg, M. D., & Codenhead, D. A.) Academic Press, New York.
[95] Rowlinson, J. S., & Widom, B., 1982. Molecular Theory of Capillarity. Oxford University Press, London.
[96] Murdoch, A. I., 2005. Some fundamental aspects of surface modelling. J. Elasticity 80, 33–52.
[97] Ericksen, J. E., 1976. Equilibrium theory of liquid crystals. In: Advances in Liquid Crystals, Vol. 2. (ed. G. H., Brown). Academic Press, New York.
[98] Leslie, F. M., 1979. Theory of flow phenomena in liquid crystals. In: Advances in Liquid Crystals, Vol. 4. (ed. G. H., Brown). Academic Press, New York.
[99] Maugin, G. A., 1993. Material Inhomogeneities in Elasticity. Chapman & Hall, London.
[100] Gurtin, M. E., 2000. Configurational Forces as a Basic Concept of Continuum Physics. Springer-Verlag, Berlin.
[101] Coulson, C. A., 1961. Electricity. Oliver & Boyd, London.
[102] Rutherford, D. E., 1957. Vector Methods (9th ed.). Oliver & Boyd, London.
[103] Murdoch, A. I., 2003. Foundations of Continuum Modelling: a Microscopic Perspective with Applications. Center of Excellence for Advanced Materials and Structures. IPPT, Polish Academy of Sciences, Warsaw.
[104] Day, W. A., 1972. The Thermodynamics of Simple Materials with Fading Memory. Springer-Verlag, Berlin.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.