Materials with memory

In continuum physics, materials with memory, also referred as materials with hereditary effects are a class of materials whose constitutive equations contains a dependence upon the past history of thermodynamic, kinetic, electromagnetic or other kind of state variables.

See also

• Biomaterial
• Biomechanics
• Dielectric relaxation
• Hysteresis
• Rheology
• Viscosity
• Visocelasticity
• Viscoplasticity

References

• Alberty, Robert A.; Silbey, Robert J. (2001) [1948], Physical Chemistry, New York: John Wiley & Sons, p. 969, ISBN 0-471-38311-2, OCLC 959753597.
• Allen, Samuel M.; Thomas, Edwin L. (1999), The Structure of Materials, The MIT Series in Materials Science & Engineering, New York: John Wiley & Sons, pp. xvi+464, ISBN 0-471-00082-5.
• Amendola, Giovambattista; Fabrizio, Mauro; Golden, John Murrough (2012), Thermodynamics of Materials with memory. Theory and Applications, New York: Springer Verlag, pp. xv+574, doi:10.1007/978-1-4614-1692-0, ISBN 978-1-4614-1691-3, MR 2856615, Zbl 1237.80001 {{citation}}: Unknown parameter |subscription= ignored (|url-access= suggested) (help) (also available as e-book with ISBN 978-1-4614-1692-0).
• Bloom, Frederick (1981), Ill-posed problems for integrodifferential equations in mechanics and electromagnetic theory, SIAM Studies in Applied Mathematics, vol. 3, Philadelphia: SIAM, pp. IX+222, ISBN 0-89871-171-1, MR 0635277, Zbl 0465.45010.
• Crandall, Stephen H.; Dahl, Norman C. Dahl; Lardner, Thomas J., eds. (1972), An introduction to the mechanics of solids (2nd ed.), New York: McGraw-Hill Book Company, pp. XII+628, ISBN 0-07-013441-3, Zbl 0433.73001.
• Dimitrienko, Yuriy I. (2011), Nonlinear continuum mechanics and large inelastic deformations, Solid Mechanics and Its Applications, vol. 174, Dordrecht: Springer Verlag, pp. xxiv + 721, doi:10.1007/978-94-007-0034-5, ISBN 978-94-007-0033-8, MR 3025695, Zbl 1209.74002 {{citation}}: Unknown parameter |subscription= ignored (|url-access= suggested) (help) (available also as e-book with ISBN 978-94-007-0034-5).
• Fabrizio, Mauro; Morro, Angelo (1992), Mathematical Problems in Linear Viscoelasticity, SIAM Studies in Applied Mathematics, vol. 12, Philadelphia PA: SIAM, pp. ix+203, ISBN 0-89871-266-1, MR 0153021, Zbl 0753.73003.
• Fabrizio, Mauro; Morro, Angelo (1992), Electromagnetism of continuous media. Mathematical modelling and applications, Oxford Science Publications, Oxford: Oxford University Press, pp. xvii+668, doi:10.1093/acprof:oso/9780198527008.001.0001, ISBN 0-19-852700-4, MR 1996323, Zbl 1027.78001 {{citation}}: Unknown parameter |subscription= ignored (|url-access= suggested) (help).
• Lemaitre, Jean; Chaboche, Jean Louis, Mechanics of solid materials, translated by Shrivastava, B., with a foreword to the French edition by Paul Germain and a foreword to the English edition by Fred Leckie, Cambridge–New York–Melbourne–Madrid–Cape Town–Singapore–Sao Paulo–Delhi: Cambridge University Press, pp. xxv + 556, doi:10.1017/CBO9781139167970, ISBN 0-521-32853-5, Zbl 0743.73002
• Graffi, Dario (1992), "L'opera di Vito Volterra sui fenomeni ereditari e alcune sue conseguenze", in Amaldi, E.; Amerio, L.; Fichera, G.; Gregory, T.; Grioli, G.; Martinelli, E.; Montalenti, G.; Pignedoli, A.; Salvini, Giorgio; Scorza Dragoni, Giuseppe (eds.), Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990) [International congress in memory of Vito Volterra (8–11 October 1990)], Atti dei Convegni Lincei (in Italian), vol. 92, Roma: Accademia Nazionale dei Lincei, pp. 39–76, ISSN 0391-805X, MR 1783028, Zbl 0977.01022. "The work of Vito Volterra on hereditary phenomena and some of their consequences" is an ample technical survey paper on the research work of Vito Volterra on hereditary phenomena in mathematical physics.
• Truesdell, Clifford (1992), "Functionals in the modern mechanics of continua", in Amaldi, E.; Amerio, L.; Fichera, G.; Gregory, T.; Grioli, G.; Martinelli, E.; Montalenti, G.; Pignedoli, A.; Salvini, Giorgio; Scorza Dragoni, Giuseppe (eds.), Convegno internazionale in memoria di Vito Volterra (8–11 ottobre 1990) [International congress in memory of Vito Volterra (8–11 October 1990)], Atti dei Convegni Lincei, vol. 92, Roma: Accademia Nazionale dei Lincei, pp. 39–76, ISSN 0391-805X, MR 1783036, Zbl 1043.74501. An introduction to modern rational continuum mechanics by one of its leading contributors.
• Volterra, Vito (1913), Leçons sur les fonctions de lignes, Collection de Monographies sul la Théorie des Fonctions (in French), recueil et rèdigèes par Joseph Pérès, Paris: Gauthier-Villars, pp. vi+230, JFM 44.0458.01 (see also JFM 44.0410.01).
• Volterra, Vito (1959) [1930], Fantappiè, Luigi (ed.), Theory of functionals and of integral and integro-differential equations, with a Foreword of G. C. Evans, a biography of Vito Volterra and a bibliography of his published works by Sir Edmund Whittaker (2nd ed.), New York: Dover Publications, pp. [39]+XIV+226, JFM 56.1010.01, MR 0100765, Zbl 0086.10402 (see also JFM 55.0814.01: the JFM reviews refer to the original 1930 English edition).