Thermodynamic compatibility conditions of a new class of hysteretic materials

The thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

[1]  S. Sessa,et al.  An inverse identification strategy for the mechanical parameters of a phenomenological hysteretic constitutive model , 2020 .

[2]  L. Rosati,et al.  Formulation of a finite deformation model for the dynamic response of open cell biphasic media , 2011 .

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

[4]  Aguinaldo Fraddosio,et al.  Seismic Response of a Historic Masonry Construction Isolated by Stable Unbonded Fiber-Reinforced Elastomeric Isolators (SU-FREI) , 2014 .

[5]  D. C. Drucker,et al.  A DEFINITION OF STABLE INELASTIC MATERIAL , 1957 .

[6]  Daniele Losanno,et al.  A novel family of multiple springs models suitable for biaxial rate-independent hysteretic behavior , 2021 .

[7]  Giorgio Serino,et al.  Wire rope isolators for seismically base-isolated lightweight structures: Experimental characterization and mathematical modeling , 2017 .

[8]  Y. Wen.  Equivalent Linearization for Hysteretic Systems Under Random Excitation , 1980 .

[9]  C. Hsu,et al.  STRESS-STRAIN BEHAVIOR OF CONCRETE UNDER CYCLIC LOADING , 1998 .

[10]  G. Alotta,et al.  Cross-correlation and cross-power spectral density representation by complex spectral moments , 2017 .

[11]  Ian D. Aiken,et al.  AN ANALYTICAL HYSTERESIS MODEL FOR ELASTOMERIC SEISMIC ISOLATION BEARINGS , 1997 .

[12]  James M. Kelly,et al.  Pacific Earthquake Engineering Research Center Analytical and Experimental Study of Fiber-Reinforced Elastomeric Isolators , 2003 .

[13]  R. Hill.  A general theory of uniqueness and stability in elastic-plastic solids , 1958 .

[14]  N. Vaiana,et al.  Preliminary Investigation of Aging Effects on Recycled Rubber Fiber Reinforced Bearings (RR-FRBs) , 2021, Journal of Earthquake Engineering.

[15]  Nicola Caterino,et al.  Experimental and analytical characterization of steel shear links for seismic energy dissipation , 2018, Engineering Structures.

[16]  Ziqi Wang,et al.  The Tail Equivalent Linearization Method for Nonlinear Stochastic Processes, Genesis and Developments , 2017 .

[17]  Armen Der Kiureghian,et al.  TAIL EQUIVALENT LINEARIZATION METHOD FOR NONLINEAR RANDOM VIBRATION , 2007 .

[18]  Salvatore Sessa,et al.  A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials , 2018 .

[19]  Salvatore Sessa,et al.  An accurate and computationally efficient uniaxial phenomenological model for steel and fiber reinforced elastomeric bearings , 2019, Composite Structures.

[20]  Francesco Paolo Pinnola,et al.  Exact frequency response of bars with multiple dampers , 2017 .