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The Minimizing Strain‐Rate History and the Resulting Greatest Lower Bound on Work in Linear Viscoelasticity
Author(s) -
Breuer S.
Publication year - 1969
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19690490404
Subject(s) - viscoelasticity , work (physics) , upper and lower bounds , strain rate , relaxation (psychology) , isothermal process , compression (physics) , monotonic function , anisotropy , strain (injury) , modulus , tension (geology) , materials science , constant (computer programming) , exponential function , mathematics , function (biology) , mathematical analysis , dynamic modulus , stress relaxation , thermodynamics , composite material , physics , dynamic mechanical analysis , computer science , creep , optics , psychology , social psychology , biology , polymer , evolutionary biology , medicine , programming language
The paper considers isothermal deformations of a linear viscoelastic material in simple tension or compression. The relaxation modulus defining the material is assumed to be a sum of exponential functions, but need not necessarily be a monotonic function. The greatest lower bound on the work required to deform the material from its virgin state in a given time interval (0, T) is determined – independently of the strain‐rate history – in terms of T, the strain at the time T, and the constants entering the definition of the relaxation modulus. The optimum strain‐rate history, which actually produces the greatest lower bound on the work, is also determined. The results may be extended to the general deformations of a linear anisotropic viscoelastic solid.