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

Abstract | References | Similar Articles | Additional Information

Abstract: Certain thermodynamic properties of elastic-plastic materials with work-hardening are discussed and their corresponding free-energy functions are determined.

**[1]**M. Lucchesi, D. R. Owen, and P. Podio-Guidugli,*Materials with elastic range: A theory with a view toward applications. Part*III, Arch. Rational Mech. Anal.**117**, 53-96 (1992) MR**1134672****[2]**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) MR**938382****[3]**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) MR**1031084****[4]**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)**[5]**M. Šilhavý,*Foundations of continuum thermodynamics*, New Perspectives in Thermodynamics (J. Serrin, ed.), Springer, Berlin, 1986, pp. 33-48 MR**848767****[6]**D. Owen,*A first course in the mathematical foundations of thermodynamics*, Springer-Verlag, Berlin and New York, 1984 MR**725673****[7]**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) MR**0495795****[8]**M. Šilhavý,*Lectures on the theory of plasticity*, CNUCE, Mimeographed notes, Pisa, 1986**[9]**M. Šilhavý and J. Kratochvil,*A theory of inelastic behavior of materials, Part*I.*Ideal materials*, Arch. Rational Mech. Anal.**65**, 97-129 (1977) MR**0495385****[10]**J. Kratochvil and M. Šilhavý,*A theory of inelastic behavior of materials, Part*II.*Inelastic materials*, Arch. Rational Mech. Anal.**65**, 131-152 (1977) MR**0495386****[11]**M. Lucchesi and M. Šilhavý,*Il'yushin's conditions in non-isothermal plasticity*, Arch. Rational Mech. Anal.**113**, 121-163 (1991)**[12]**E. Melan,*Zur Plastizitat des raumlichen Kontinuums*, Ing. Arch.**9**, 116-126 (1938)**[13]**R. Hill,*The mathematical theory of plasticity*, Oxford Univ. Press, Oxford, 1950 MR**0037721****[14]**M. Lucchesi,*Esistenza e unicita' dello sforzo per materiali idealmente plastici soggetti a deformazioni finite*, Boll. Un. Mat. Ital.**4-B**, 1-16 (1990)**[15]**D. R. Owen,*Thermodynamics of materials with elastic range*, Arch. Rational Mech. Anal.**31**, 91-112 (1968) MR**1553520****[16]**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) MR**574161**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
73E05,
73B30

Retrieve articles in all journals with MSC: 73E05, 73B30

Additional Information

DOI:
https://doi.org/10.1090/qam/1218370

Article copyright:
© Copyright 1993
American Mathematical Society