SDT-visc         Contents     Functions              PDF Index

1.1  Introduction

Linear viscoelasticity assumes [] that stress is a function of strain history. This translates into the existence of a relaxation function h(t) given by

(1.1)

Using Laplace transform, one sees that this hypothesis is equivalent to the existence of a complex modulus Λ(s) (transform of h(t)) such that

(1.2)

From a practical point of view, one can solve viscoelasticity problems as elasticity problems with a complex modulus that depends on frequency. This property is known as the elastic/viscoelastic equivalence principle [].

For a strain tensor, the number of independent coefficients in Λ is identical to that in Hooke's law for an elastic material (for the same reasons of material invariance). For homogeneous and isotropic materials, one thus considers a Young's modulus and a Poisson coefficient that are complex and frequency dependent.

The separate measurement of E(ω) et ν(ω) is however a significant experimental challenge [] that has no well established solution. Practice is thus to measure a compression E(ω) or a shear modulus G(ω) and to assume a constant Poisson's ratio, although this is known to be approximate.

Section ?? analyzes the main representations of complex moduli. Section ?? lists representations used to account for the effect of environmental factors (temperature, pre-stress, ...). Domains of applicability for different models are given at the end of the chapter.

For more details, Ref. [] a detailed account of viscoelasticity theory. Refs [, ] present most practical representations of viscoelastic behavior.