Free-energy functions for elastic-plastic material elements
Author:
Massimiliano Lucchesi
Journal:
Quart. Appl. Math. 51 (1993), 299-318
MSC:
Primary 73E05; Secondary 73B30
DOI:
https://doi.org/10.1090/qam/1218370
MathSciNet review:
MR1218370
Full-text PDF Free Access
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Abstract: Certain thermodynamic properties of elastic-plastic materials with work-hardening are discussed and their corresponding free-energy functions are determined.
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M. Lucchesi and P. Podio-Guidugli, Materials with elastic range: A theory with a view toward applications. Part I, Arch. Rational Mech. Anal. 102, 23–43 (1988)
M. Lucchesi and P. Podio-Guidugli, Materials with elastic range: A theory with a view toward applications. Part II, Arch. Rational Mech. Anal. 110, 9–42 (1990)
M. Šilhavý, On measures, convex cones, and foundations of thermodynamics. I. Systems with vector-valued actions. II. Thermodynamic systems, Czechoslovak J. Phys. B30, 841–961 (1980)
M. Šilhavý, Foundations of continuum thermodynamics, New Perspectives in Thermodynamics (J. Serrin, ed.), Springer, Berlin, 1986, pp. 33–48
D. Owen, A first course in the mathematical foundations of thermodynamics, Springer-Verlag, Berlin and New York, 1984
B. Coleman and D. R. Owen, On the thermodynamics of semi-systems with restrictions on the accessibility of states, Arch. Rational Mech. Anal. 66, 173–181 (1977)
M. Šilhavý, Lectures on the theory of plasticity, CNUCE, Mimeographed notes, Pisa, 1986
M. Šilhavý and J. Kratochvil, A theory of inelastic behavior of materials, Part I. Ideal materials, Arch. Rational Mech. Anal. 65, 97–129 (1977)
J. Kratochvil and M. Šilhavý, A theory of inelastic behavior of materials, Part II. Inelastic materials, Arch. Rational Mech. Anal. 65, 131–152 (1977)
M. Lucchesi and M. Šilhavý, Il’yushin’s conditions in non-isothermal plasticity, Arch. Rational Mech. Anal. 113, 121–163 (1991)
E. Melan, Zur Plastizitat des raumlichen Kontinuums, Ing. Arch. 9, 116–126 (1938)
R. Hill, The mathematical theory of plasticity, Oxford Univ. Press, Oxford, 1950
M. Lucchesi, Esistenza e unicita’ dello sforzo per materiali idealmente plastici soggetti a deformazioni finite, Boll. Un. Mat. Ital. 4-B, 1–16 (1990)
D. R. Owen, Thermodynamics of materials with elastic range, Arch. Rational Mech. Anal. 31, 91–112 (1968)
B. Coleman and D. R. Owen, On the thermodynamics of elastic-plastic materials with temperature dependent moduli and yield stresses, Arch. Rational Mech. Anal. 70, 339–354 (1979)
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Article copyright:
© Copyright 1993
American Mathematical Society