Using an internal-variable formalism as a starting point, we describe the viscoelastic complement of a previously-developed viscoplasticity formulation of the complete potential structure type. It is mainly motivated by experimental evidence for the presence of rate/time effects in the so-called quasilinear, reversible, material response range. Several possible generalizations are described, in the general format of hereditary-integral representations for nonequilibrium, stress-type, state variables, both for isotropic as well as anisotropic materials. In particular, thorough discussions are given on the important issues of thermodynamic admissibility requirements for such general descriptions, resulting in a set of explicit mathematical constraints on the associated kernel (relaxation and creep compliance) functions. In addition, a number of explicit, integrated forms are derived, under stress and strain control to facilitate the parametric and qualitative response characteristic studies reported here, as well as to help identify critical factors in the actual experimental characterizations from test data that will be reported in Part II.
A General Time Dependent Constitutive Model: Part I— Theoretical Developments1
Contributed by the Materials Division for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received by the Materials Division March 26, 1999; revised manuscript received April 28, 2000. Associate Technical Editor: S. Mall.
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Saleeb, A. F., and Arnold, S. M. (April 28, 2000). "A General Time Dependent Constitutive Model: Part I— Theoretical Developments." ASME. J. Eng. Mater. Technol. January 2001; 123(1): 51–64. https://doi.org/10.1115/1.1288595
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