By R. M. Christensen
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Sample text
A Newtonian viscous fluid responds to a suddenly applied state of uniform shear stress by a steady flow process. There are, however, materials for which a suddenly applied and maintained state of uniform stress induces an instantaneous deformation followed by a flow process which may or may not be limited in magnitude as time grows. A material which responds in this manner is said to exhibit both an instantaneous elasticity effect and creep characteristics. This behavior is clearly not described by either an elasticity or a viscosity theory but combines features of each.
Viscoelastic Rayleigh Waves Problems References VII. 1. 2. 3. 4. 5. 6. Optimal Strain History Problems References VIII. 1. 2. 3. 4. 5. Simple Shear Flow Example Problems References IX. 1. 2. 3. 4. 5. 6. Nonlinear Theory Mechanical Properties Problems References Appendixes A. Step Functions and Delta Functions B. Laplace Transformation Properties References Index Preface to Second Edition Viscoelasticity theory has provided a rigorous and broadly based mathematical framework from which to predict material behavior.
It would, however, be convenient to have the means of treating discontinuous strain histories. This is accomplished in Ref. 5) as The derivation given in Ref. 5) through the integration of the resulting delta function. 5) will be allowed for use with discontinuous strain histories. 5) may be changed from 0 to —∞ through a shift of the time scale, as long as ij(t) → 0 as t → ∞. 5) is one form of the general viscoelastic constitutive relations. The integrating functions Gijkl(t) are mechanical properties of the material and are termed relaxation functions.