A General Time Dependent Constitutive Model: Part I— Theoretical Developments

[+] Author and Article Information
A. F. Saleeb

Department Civil Engineering, University of Akron, Akron, OH 44325

S. M. Arnold

National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135

J. Eng. Mater. Technol 123(1), 51-64 (Apr 28, 2000) (14 pages) doi:10.1115/1.1288595 History: Received March 26, 1999; Revised April 28, 2000
Copyright © 2001 by ASME
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Reversible and irreversible threshold surfaces
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Rate sensitivity of static stiffness, TIMETAL 21S
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Four element mechanical models depicting the deformation response of a material
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Three element mechanical model and corresponding creep and relaxation response history
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General hereditary behavior model indicated with appropriate partitioning of stress and strain
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Uniaxial depiction of reversible and irreversible domains
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Step-strain loading approximating functions γ(n)=(−1)n/hn ∑k=0n(−1)n−kn!/k!(n−k)!γ(kh) in the limit h→0. According to fading-memory assumption, stress relaxes to positive or negative values for even (case a, n=2) or odd (case b n=3) nth order derivatives.
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Total reversible strain in the 1 direction versus time given equal Poisson’s ratios, see cases 1–4 of Table 1
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Effective overall Poisson’s ratio versus time given equal Poisson’s ratios, see cases 1–4 of Table 1
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Total reversible strain in the 1 direction versus time given nonequal Poisson’s ratios, see cases 1, 5, 6, and 7 of Table 1. (a) 10γ. (b) 100γ.
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Effective overall Poisson’s ratio (V12) versus time given nonequal Poisson’s ratios, see cases 1, 5, 6 and 7 of Table 1. (a) 10 τ limit. (b) 100 τ limit.
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Influence of Es on normalized stress versus strain (Y) in the 1 direction, σo=6.895 MPa and E0=6.895 Gpa
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Influence of τ on total strain (Y1) in time response
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Influence of ρ on total strain (Y1) in time response



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