Bouc–Wen-Type Models with Stiffness Degradation: Thermodynamic Analysis and Applications

In this paper, a thermodynamic analysis of Bouc–Wen models endowed with both strength and stiffness degradation is provided. This analysis is based on the relationship between the flow rules of these models and those of the endochronic plasticity theory with damage, discussed in a companion paper. Using the theoretical framework of that extended endochronic theory, it is shown that an elastic Bouc–Wen model with damage, i.e., without plastic strains, can be formulated. Moreover, a proper definition of the dissipated energy of these Bouc–Wen models with degradation is given and some thermodynamic constraints on the parameters defining the models behavior are emphasized and discussed. In particular, some properties of the energetic linear stiffness degradation rule as well as the so-called pivot rule, well known in the seismic engineering field, are illustrated and commented upon. An improved energetic stiffness degradation rule and a new stiffness degradation rule are proposed.

[1]  S. Erlicher,et al.  Application of the orthogonality principle to the endochronic and Mroz models of plasticity , 2008, 0812.1885.

[2]  S. Erlicher,et al.  Instantaneous Identification of Bouc-Wen-Type Hysteretic Systems from Seismic Response Data , 2007, 0812.1688.

[3]  Silvano Erlicher,et al.  Endochronic theory, non-linear kinematic hardening rule and generalized plasticity : a new interpretation based on generalized normality assumption , 2006, 0812.1884.

[4]  Luis Ibarra,et al.  Hysteretic models that incorporate strength and stiffness deterioration , 2005 .

[5]  José Rodellar,et al.  Adaptive control of a hysteretic structural system , 2005, Autom..

[6]  S. Masri,et al.  Identification of the state equation in complex non-linear systems , 2004 .

[7]  Y. Fujino,et al.  Multiaxial Behaviors of Laminated Rubber Bearings and Their Modeling. II: Modeling , 2004 .

[8]  Y. Fujino,et al.  Multiaxial Behaviors of Laminated Rubber Bearings and Their Modeling. I: Experimental Study , 2004 .

[9]  Kaspar Willam,et al.  A coupled elastoplastic damage model for geomaterials , 2004 .

[10]  Fabio Ferrario,et al.  Non-linear analysis of the low-cycle fracture behaviour of isolated Tee stub connections , 2002 .

[11]  Greg C. Foliente,et al.  Discussion of "Hysteretic Models for Deteriorating Inelastic Structures" , 2001 .

[12]  M. Frémond,et al.  Non-Smooth Thermomechanics , 2001 .

[13]  Gianmarco De Felice,et al.  Hysteretic Systems with Internal Variables , 2001 .

[14]  B. Nedjar,et al.  Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects , 2001 .

[15]  Alexander M. Puzrin,et al.  A thermomechanical framework for constitutive models for rate-independent dissipative materials , 2000 .

[16]  Shirley J. Dyke,et al.  Semiactive Control Strategies for MR Dampers: Comparative Study , 2000 .

[17]  M. V. Sivaselvan,et al.  Hysteretic models for deteriorating inelastic structures , 2000 .

[18]  Han-Chin Wu,et al.  A constitutive framework of plastically deformed damaged continuum and a formulation using theendochronic concept , 1999 .

[19]  Matti Ristinmaa,et al.  Thermodynamic formulation of plastic work hardening materials , 1999 .

[20]  Han-chin Wu,et al.  ENDOCHRONIC THEORY OF CONTINUUM DAMAGE MECHANICS , 1998 .

[21]  Guy T. Houlsby,et al.  Application of thermomechanical principles to the modelling of geotechnical materials , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  Billie F. Spencer,et al.  Models for hysteresis and application to structural control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[23]  Andrei M. Reinhorn,et al.  Modeling of Masonry Infill Panels for Structural Analysis , 1995 .

[24]  Greg Foliente,et al.  Hysteresis Modeling of Wood Joints and Structural Systems , 1995 .

[25]  C. L. Chow,et al.  An anisotropic model of damage mechanics based on endochronic theory of plasticity , 1992 .

[26]  Jean-Louis Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[27]  Fabio Casciati,et al.  Stochastic dynamics of hysteretic media , 1989 .

[28]  Y. K. Wen,et al.  Random vibration of hysteretic systems under bi‐directional ground motions , 1986 .

[29]  Ivan S. Sandler,et al.  On the Uniqueness and Stability of Endochronic Theories of Material Behavior , 1978 .

[30]  Martin A. Eisenberg,et al.  A theory of plasticity with non-coincident yield and loading surfaces , 1971 .

[31]  K. C. Valanis,et al.  A theory of viscoplasticity without a yield surface , 1970 .

[32]  A. Phillips,et al.  On the concept of the yield surface , 1965 .

[33]  Silvano Erlicher,et al.  Thermodynamic admissibility of Bouc-Wen type hysteresis models , 2004 .

[34]  Zdenk P. Baant.  ENDOCHRONIC INELASTICITY AND INCREMENTAL PLASTICITY , 2002 .

[35]  Robert L. Taylor,et al.  Two material models for cyclic plasticity: nonlinear kinematic hardening and generalized plasticity , 1995 .

[36]  Robert L. Taylor,et al.  A new model of generalized plasticity and its numerical implementation , 1993 .

[37]  K. Valanis.  A theory of damage in brittle materials , 1990 .

[38]  N. Xiaode.  Endochronic plastic constitutive equations coupled with isotropic damage and damage evolution models , 1989 .

[39]  Christoph Wehrli,et al.  The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function , 1987 .

[40]  K. Valanis,et al.  FUNDAMENTAL CONSEQUENCES OF A NEW INTRINSIC TIME MEASURE-PLASTICITY AS A LIMIT OF THE ENDOCHRONIC THEORY , 1980 .

[41]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[42]  Zdenek P. Bazant,et al.  ENDOCHRONIC THEORY OF INELASTICITY AND FAILURE OF CONCRETE , 1976 .

[43]  Richard Schapery,et al.  On a Thermodynamic Constitutive Theory and Its Application to Various Nonlinear Materials , 1970 .

[44]  J. Moreau,et al.  Sur les lois de frottement, de plasticité et de viscosité , 1970 .