Pseudopotentials and Loading Surfaces for an Endochronic Plasticity Theory with Isotropic Damage
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Volume 134, Issue 10
Abstract
The endochronic theory, developed in the early 70s, allows the plastic behavior of materials to be represented by introducing the notion of intrinsic time. With different viewpoints, several authors discussed the relationship between this theory and the classical theory of plasticity. Two major differences are the presence of plastic strains during unloading phases and the absence of an elastic domain. Later, the endochronic plasticity theory was modified in order to introduce the effect of damage. In the present paper, a basic endochronic model with isotropic damage is formulated starting from the postulate of strain equivalence. Unlike the previous similar analyses, in this presentation the formal tools chosen to formulate the model are those of convex analysis, often used in classical plasticity: namely pseudopotentials, indicator functions, subdifferentials, etc. As a result, the notion of loading surface for an endochronic model of plasticity with damage is investigated and an insightful comparison with classical models is made possible. A damage pseudopotential definition allowing a very general damage evolution is given.
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References
Auricchio, F., and Taylor, R. L. (1995). “Two material models for cyclic plasticity: Nonlinear kinematic hardening and generalized plasticity.” Int. J. Plast., 11(1), 65–98.
Baber, T. T., and Wen, Y.-K. (1981). “Random vibrations of hysteretic, degrading systems.” J. Engrg. Mech. Div., 107(6), 1069–1087.
Bažant, Z. P. (1978). “Endochronic inelasticity and incremental plasticity.” Int. J. Solids Struct., 14(9), 691–714.
Bažant, Z. P., and Bath, P. D. (1976). “Endochronic theory of inelasticity and failure of concrete.” J. Engrg. Mech. Div., 102(4), 701–722.
Bouc, R. (1971). “Modèle mathématique d’hystérésis.” Acustica, 24, 16–25 (in French).
Casciati, F. (1989). “Stochastic dynamics of hysteretic media.” Struct. Safety, 6(2–4), 259–269.
Chow, C. L., and Chen, X. F. (1992). “An anisotropic model of damage mechanics based on endochronic theory of plasticity.” Int. J. Fract., 55(2), 115–130.
Collins, I. F., and Houlsby, G. T. (1997). “Application of thermomechanical principles to the modelling of geotechnical materials.” Proc. R. Soc. London, Ser. A, 453, 1975–2001.
Eisenberg, M. A., and Phillips, A. (1971). “A theory of Plasticity with non-coincident yield and loading surfaces.” Acta Mech., 11, 247–260.
Erlicher, S., and Bursi, O. S. (2008). “Bouc–Wen type models with stiffness degradation: Thermodynamic analysis and applications.” J. Eng. Mech., 134(10), 843–855.
Erlicher, S., and Point, N. (2005). “On the associativity of the Drucker-Prager model.” Proc., VIII Int. Conf. on Computation Plasticity COMPLAS VIII, E. Oñate and D. R. J. Owen, eds., ECCOMAS-IACM, Barcelona, Spain.
Erlicher, S., and Point, N. (2006). “Endochronic theory, non-linear kinematic hardening rule and generalized plasticity: A new interpretation based on generalized normality assumption.” Int. J. Solids Struct., 43(14–15), 4175–4200.
Frémond, M. (2002). Non-smooth thermomechanics, Springer, Berlin.
Houlsby, G. T., and Puzrin, A. M. (2000). “A thermomechanical framework for constitutive models for rate-independent dissipative materials.” Int. J. Plast., 16(9), 1017–1047.
Jirásek, M., and Bažant, Z. P. (2002). Inelastic analysis of structures, Wiley, Chichester U.K.
Karray, M. A., and Bouc, R. (1989) “Étude dynamique d’un système d’isolation antisismique.” Les Annales de l'ENIT, 3(1), 43–60 (in French).
Lemaitre, J., and Chaboche, J.-L. (1990). Mechanics of solid materials, Cambridge University Press, Cambridge, Mass.
Lubliner, J., Taylor, R. L., and Auricchio, F. (1993). “A new model of generalized plasticity.” Int. J. Solids Struct., 30(22), 3171–3184.
Moreau, J. J. (1970). “Sur les lois de frottement, de plasticité et de viscosité.” C. R. Acad. Sci., Sèrie A, 271, 608–611 (in French).
Nedjar, B. (2001). “Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects.” Int. J. Solids Struct., 38(30–31), 5421–5451.
Phillips, A., and Sierakowski, R. L. (1965). “On the concept of yield surface.” Acta Mech., 1(1), 29–35.
Point, N., and Erlicher, S. (2008). “Application of the orthogonality principle to the endochronic and Mróz models of plasticity.” Mater. Sci. Eng., A, 483–484, 47–50.
Ristinmaa, M. (1999). “Thermodynamic formulation of plastic work hardening materials.” J. Eng. Mech., 125(2), 152–155.
Rockafellar, R. T. (1969). Convex analysis, Princeton University Press, Princeton, N.J.
Salari, M. R., Saeb, S., Willam, K. J., Patchet, S. J., and Carrasco, R. C. (2004). “A coupled elastoplastic damage model for geomaterials.” Comput. Methods Appl. Mech. Eng., 193(27–29), 2625–2643.
Sandler, I. S. (1978). “On the uniqueness and stability of endochronic theories of material behavior.” J. Appl. Mech., 45(2), 263–266.
Schapery, R. A. (1968). “On a thermodynamic constitutive theory and its applications to various nonlinear materials.” Proc., IUTAM Symp. East Kilbride, B. A. Boley, ed., Springer, New York.
Valanis, K. C. (1971). “A theory of viscoplasticity without a yield surface.” Arch. Mech. Stosow., 23(4), 517–551.
Valanis, K. C. (1980). “Fundamental consequences of a new intrinsic time measure. Plasticity as a limit of the endochronic theory.” Arch. Mech. Stosow., 32(2), 171–191.
Valanis, K. C. (1990). “A theory of damage in brittle materials.” Eng. Fract. Mech., 36(3), 403–416.
Wen, Y.-K. (1976). “Method for random vibration of hysteretic systems.” J. Engrg. Mech. Div., 102(2), 249–263.
Wu, H. C., and Nanakorn, C. K. (1998). “Endochronic theory of continuum damage mechanics.” J. Eng. Mech., 124(2), 200–208.
Wu, H. C., and Nanakorn, C. K. (1999). “A constitutive framework of plastically deformed damaged continuum and a formulation using the endochronic concept.” Int. J. Solids Struct., 36(33), 5057–5087.
Xiaode, N. (1989). “Endochronic plastic constitutive equations coupled with isotropic damage and damage evolution models.” Eur. J. Mech. A/Solids, 8(4), 293–308.
Ziegler, H., and Wehrli, C. (1987). “The derivation of constitutive relations from the free energy and the dissipation function.” Adv. Appl. Mech., 25, 183–238.
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© 2008 ASCE.
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Received: Oct 6, 2006
Accepted: Feb 14, 2008
Published online: Oct 1, 2008
Published in print: Oct 2008
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Note. Associate Editor: George Z. Voyiadjis
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