Based on previous work by the authors, a model for anisotropic, kinematic hardening materials is constructed to describe constitutive equations and evolution laws in rate-independent, small deformation plasticity on the basis of thermodynamics. Unlike other theories developed earlier wherein only internal state variables are chosen to describe inelastic deformation, the present paper also considers inelastic strain as an independent variable. This can be shown to reduce to the well-known plastic strain in the case of rate-independent plasticity.
GermainP.NguyenQ. S.SuquetP.Continuum thermodynamics. J. Appl. Mech., 198350, 1010–1020.
2.
ColemanB. D.GurtinM. E.Thermodynamics with internal state variables. J. Chem. Phys., 196747, 597–613.
3.
RiceJ. R.Inelastic constitutive relations for solids: An internal variable theory and its application to metal plasticity. J. Mech. Phys. Solids, 197119, 433–455.
4.
HillR.RiceJ. R.Elastic potentials and the structure of inelastic constitutive laws. SIAM J. Appl. Math., 197325, 448–461.
5.
AsundiA.WooC. W.DengW.Advances in Engineering Plasticity and Its Applications (Ed. LeeW. B.), 1993 pp. 273–280 (Elsevier Science Publishers BV, Amsterdam).
6.
WooC. W.AsundiA.DengW.On rate-dependent plasticity—linear viscoelastic constitutive equations. Int. J. of Solids Struct., 199532, 1793–1803.
LemaitreJ.ChabocheJ.-L.Mechanics of Solid Materials, 1990 (New York).
9.
DruckerD. C.A more fundamental approach to plastic stress-strain relations. In First US Congress onApplied Mechanics, 1952 pp. 487–491 (American Society of Mechanical Engineers, New York).
10.
ChristensenR.M.Theory of Viscoelasticity, 1982 (Academic Press, New York).
11.
WardI. M.Mechanical Properties of Solid Polymers, 2nd edition, 1983 (John Wiley, New York).
12.
ShamesI. H.CozzarelliF. A.Elastic and Inelastic Stress Analysis, 1992 (Prentice-Hall, Englewood Cliffs, New Jersey).
13.
DruckerD.Conventional and unconventional plastic response and representation. Appl. Mech. Rev., 198841, 151–167.
14.
NaghdiP. M.Stress-strain relations in plasticity and thermo-plasticity. In Plasticity (Eds LeeE. H.SymondsP. S.), 1960 pp. 121–167 (Pergamon, New York).
15.
CaseyJ.SullivanT. D.Pressure dependency, strength differential effect, and plastic volume expansion in metals. Int. J. Plasticity, 19851, 39–61.
16.
PrigogineI.Introduction to Thermodynamics of Irreversible Problems, 1961 (John Wiley, New York).
