1.3 Further Reading
19
Miniaturisation requires continuum modelling to capture length-scale effects as
predicted by Generalised Continua. A small selection are the authoritative treatises
by Eringen [94–96] on micro-continuum and non-local field theories, the unifying
account by Iesan [97] on thermo-elasticity of generalised continua, the comprehensive overview by Madenci and Oterkus [98] on peridynamics modelling, and the
differential-geometry-driven treatise by Steinmann [99] on higher-order elasticity
and plasticity.
The above set of topics from the arena of continuum mechanics, material modelling and their periphery together with the corresponding references are by no means
exhaustive. However, these are representative and shall serve as a good starting point
if more detailed information is needed.
References
1. C. Truesdell, R. Toupin. The classical field theories, in Principles of classical Mechanics and
Field Theory (Springer, Berlin, 1960), pp. 226–858
2. C. Truesdell, W. Noll, The Non-linear Field Theories of Mechanics (Springer, Berlin, 2004)
3. C. Truesdell, A First Course in Rational Continuum Mechanics (Academic, Cambridge, 1992)
4. W. Flügge, Tensor Analysis and Continuum Mechanics (Springer, Berlin, 1972)
5. W. Prager, Introduction to Mechanics of Continua (Dover, Illinois, 2004)
6. P. Chadwick, Continuum Mechanics: Concise Theory and Problems (Dover, Illinois, 2012)
7. A.J.M. Spencer, Continuum Mechanics (Dover, Illinois, 2004)
8. K. Washizu, Variational Methods in Elasticity and Plasticity (Pergamon Press, Oxford, 1975)
9. L.E. Malvern, Introduction to the Mechanics of a Continuous Medium (Prentice Hall, Upper
Saddle River, 1969)
10. M.E. Gurtin, An Introduction to Continuum Mechanics (Academic, Cambridge, 1982)
11. A.C. Eringen, Mechanics of Continua (R.E. Krieger Publishing Co., 1980)
12. A.C. Eringen, Continuum Mechanics of Single-substance Bodies (Academic, Cambridge, 2016)
13. I-S. Liu, Continuum Mechanics (Springer, Berlin, 2013)
14. G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley,
Hoboken, 2000)
15. G.A. Maugin, The Thermomechanics of Nonlinear Irreversible Behaviors: An Introduction
(World Scientific, Singapore, 1999)
16. M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua (Cambridge
University Press, Cambridge, 2010)
17. M. Silhavy, The Mechanics and Thermodynamics of Continuous Media (Springer, Berlin, 2013)
18. E.B. Tadmor, R.E. Miller, R.S. Elliott, Continuum Mechanics and Thermodynamics: From
Fundamental Concepts to Governing Equations (Cambridge University Press, Cambridge,
2012)
19. A.I. Murdoch, Physical Foundations of Continuum Mechanics (Cambridge University Press,
Cambridge, 2012)
20. Y. Basar, D. Weichert, Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical
and Physical Concepts (Springer, Berlin, 2013)
21. W.M. Lai, D.H. Rubin, E. Krempl, D. Rubin, Introduction to Continuum Mechanics
(Butterworth-Heinemann, Oxford, 2009)
22. J.N. Reddy, An Introduction to Continuum Mechanics (Cambridge University Press, Cambridge, 2007)
23. J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials (Cambridge University Press, Cambridge, 1994)
19
Miniaturisation requires continuum modelling to capture length-scale effects as
predicted by Generalised Continua. A small selection are the authoritative treatises
by Eringen [94–96] on micro-continuum and non-local field theories, the unifying
account by Iesan [97] on thermo-elasticity of generalised continua, the comprehensive overview by Madenci and Oterkus [98] on peridynamics modelling, and the
differential-geometry-driven treatise by Steinmann [99] on higher-order elasticity
and plasticity.
The above set of topics from the arena of continuum mechanics, material modelling and their periphery together with the corresponding references are by no means
exhaustive. However, these are representative and shall serve as a good starting point
if more detailed information is needed.
References
1. C. Truesdell, R. Toupin. The classical field theories, in Principles of classical Mechanics and
Field Theory (Springer, Berlin, 1960), pp. 226–858
2. C. Truesdell, W. Noll, The Non-linear Field Theories of Mechanics (Springer, Berlin, 2004)
3. C. Truesdell, A First Course in Rational Continuum Mechanics (Academic, Cambridge, 1992)
4. W. Flügge, Tensor Analysis and Continuum Mechanics (Springer, Berlin, 1972)
5. W. Prager, Introduction to Mechanics of Continua (Dover, Illinois, 2004)
6. P. Chadwick, Continuum Mechanics: Concise Theory and Problems (Dover, Illinois, 2012)
7. A.J.M. Spencer, Continuum Mechanics (Dover, Illinois, 2004)
8. K. Washizu, Variational Methods in Elasticity and Plasticity (Pergamon Press, Oxford, 1975)
9. L.E. Malvern, Introduction to the Mechanics of a Continuous Medium (Prentice Hall, Upper
Saddle River, 1969)
10. M.E. Gurtin, An Introduction to Continuum Mechanics (Academic, Cambridge, 1982)
11. A.C. Eringen, Mechanics of Continua (R.E. Krieger Publishing Co., 1980)
12. A.C. Eringen, Continuum Mechanics of Single-substance Bodies (Academic, Cambridge, 2016)
13. I-S. Liu, Continuum Mechanics (Springer, Berlin, 2013)
14. G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley,
Hoboken, 2000)
15. G.A. Maugin, The Thermomechanics of Nonlinear Irreversible Behaviors: An Introduction
(World Scientific, Singapore, 1999)
16. M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua (Cambridge
University Press, Cambridge, 2010)
17. M. Silhavy, The Mechanics and Thermodynamics of Continuous Media (Springer, Berlin, 2013)
18. E.B. Tadmor, R.E. Miller, R.S. Elliott, Continuum Mechanics and Thermodynamics: From
Fundamental Concepts to Governing Equations (Cambridge University Press, Cambridge,
2012)
19. A.I. Murdoch, Physical Foundations of Continuum Mechanics (Cambridge University Press,
Cambridge, 2012)
20. Y. Basar, D. Weichert, Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical
and Physical Concepts (Springer, Berlin, 2013)
21. W.M. Lai, D.H. Rubin, E. Krempl, D. Rubin, Introduction to Continuum Mechanics
(Butterworth-Heinemann, Oxford, 2009)
22. J.N. Reddy, An Introduction to Continuum Mechanics (Cambridge University Press, Cambridge, 2007)
23. J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials (Cambridge University Press, Cambridge, 1994)