Abstract
The formal structure of generalized continuum theories is recovered by means of the extension of canonical thermomechanics with dual weakly non-local internal variables. The canonical thermomechanics provides the best framework for such generalization. The Cosserat, micromorphic, and second gradient elasticity theory are considered as examples of the obtained formalization.
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Toupin R.A.: Elastic materials with couple stresses. Arch. Ration. Mech. Anal. 11, 385–414 (1962)
Eringen, A.C., Suhubi, E.S.: Nonlinear theory of simple microelastic solids I & II. Int. J. Eng. Sci. 2, 189–203, 389–404 (1964)
Mindlin R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)
Capriz G.: Continua with Microstructure. Springer, Heidelberg (1989)
Eringen A.C.: Microcontinuum Field Theories, vol. I. Springer, New York (1999)
Rice J.R.: Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455 (1971)
Mandel J.P.: Thermodynamics and plasticity. In: Domingos, J.J., Nina, M.N.R., Whitelaw, J.H. (eds) Foundations of Continuum Thermodynamics, pp. 283–304. MacMillan, London (1974)
Kestin J.: Internal variables in the local-equilibrium approximation. J. Non-Equilib. Thermodyn. 18, 360–379 (1993)
Maugin G.A., Muschik W.: Thermodynamics with internal variables. J. Non-Equilib. Thermodyn. 19, 217–249 (1994)
Maugin G.A.: The Thermomechanics of Nonlinear Irreversible Behaviors. World Scientific, Singapore (1999)
Houlsby G.T., Puzrin A.M.: A thermomechanical framework for constitutive models for rate-independent dissipative materials. Int. J. Plast. 16, 1017–1047 (2000)
Magnenet V., Rahouadj R., Ganghoffer J.-F., Cunat C.: Continuous symmetries and constitutive laws of dissipative materials within a thermodynamic framework of relaxation. Part I: formal aspects. Int. J. Plast. 23, 87–113 (2007)
Maugin G.A.: On the thermomechanics of continuous media with diffusion and/or weak nonlocality. Arch. Appl. Mech. 75, 723–738 (2006)
Maugin G.A.: On canonical equations of continuum thermomechanics. Mech. Res. Commun. 33, 705–710 (2006)
Forest S., Sievert R.: Nonlinear microstrain theories. Int. J. Solids Struct. 43, 7224–7245 (2006)
Ván P., Berezovski A., Engelbrecht J.: Internal variables and dynamic degrees of freedom. J. Non-Equilib. Thermodyn. 33, 235–254 (2008)
Maugin G.A.: Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993)
Kienzler R., Herrmann G.: Mechanics in Material Space. Springer, Berlin (2000)
Maugin G.A.: Internal variables and dissipative structures. J. Non-Equilib. Thermodyn. 15, 173–192 (1990)
Gurtin M.E.: Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92, 178–192 (1996)
Maugin G.A.: On the structure of the theory of polar elasticity. Phil. Trans. R. Soc. Lond. A 356, 1367–1395 (1998)
Forest, S.: Generalized continua. In: Buschow, K., Cahn, R., Flemings, M., Ilschner, B., Kramer, E., Mahajan, S. (eds.) Encyclopedia of Materials: Science and Technology. Updates, pp. 1–7. Elsevier, Oxford (2005)
Forest S., Sievert R.: Elastoviscoplastic constitutive frameworks for generalized continua. Acta Mech. 160, 71–111 (2003)
Aifantis E.C.: Update on a class of gradient theories. Mech. Mater. 35, 259–280 (2003)
Engelbrecht J., Berezovski A., Pastrone F., Braun M.: Waves in microstructured materials and dispersion. Philos. Mag. 85, 4127–4141 (2005)
Engelbrecht J., Cermelli P., Pastrone F.: Wave hierarchy in microstructured solids. In: Maugin, G. (eds) Geometry, Continua and Microstructure, pp. 99–111. Hermann Publ., Paris (1999)
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Berezovski, A., Engelbrecht, J. & Maugin, G.A. Generalized thermomechanics with dual internal variables. Arch Appl Mech 81, 229–240 (2011). https://doi.org/10.1007/s00419-010-0412-0
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DOI: https://doi.org/10.1007/s00419-010-0412-0