Abstract
A review of the basic definitions of stress and strain was given in Chap. 2. It was noted that a linear elastic solid in uniaxial tension or pure shear is governed by Hooke’s law given by,
where σ (or τ) is the applied stress, ε (or γ) is the resulting strain, and E (or G) is the elastic modulus and is applicable for many materials under certain circumstances of environment for small stresses and small strains.
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Notes
- 1.
The reader is cautioned that Eq. 5.29 must be used with care in order to include all initial conditions properly. Significant differences arise depending upon whether the time begins at 0+ or 0−. In most circumstances used herein, f(t) = 0 for t < 0 but in creep or relaxation the jump discontinuity at t = 0 must be included.
- 2.
What is now known as the correspondence principle for converting viscoelastic problems in the time domain into elastic problems in the transform domain was first discussed by Turner Alfrey in 1944. As a result, the principle is sometimes referred to as Alfrey’s correspondence principle. Later in 1950 and in 1955 the principle was generalized and discussed by W.T. Read and E. H. Lee respectively. (See bibliography for references.)
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Brinson, H.F., Brinson, L.C. (2015). Differential Constitutive Equations. In: Polymer Engineering Science and Viscoelasticity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7485-3_5
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