By Bengt Sundström (ed.)
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Extra resources for Handbook of Solid Mechanics
Sample text
Plastic deformation is thus assumed to occur instantaneously on a change in the state of stress and the size is assumed to be independent of the rate of stress. Many metallic materials are almost isotropic after initial manufacturing. On further processing the material becomes anisotropic which is difficult to determine and describe. A initially isotropic behaviour is usually considered appropriate. The plastic deformation gives increasing orientation effects but this can only be partly considered in the follow ing treatment.
Which for an arbitrary stress history gives the strain if d σ ( τ ) / d τ is interpreted in a generalized sense as above. Between E and J there is a unique relation The relaxation modulus can be written in the following general form where f ( τ ) is named the relaxation spectrum. It is usual, in order to describe real materials, to use an approximation with a number of discrete relaxation times by a Dirichlet series where E0 , Ei andti are constants. The material is assumed to be in a virgin state for t<0 .
2 Linear viscoelastic materials The description of viscoelastic materials may be done in several ways. The basic rela tions are presented first followed by descriptions by differential equations for the sim plest uniaxial model materials. A systematic presentation is then given for uniaxial and multiaxial cases and thermorheologically simple material. 1 DEFINITIONS AND BASIC RELATIONS The definition of a linear viscoelastic material is in uniaxial theory given as follows: For a material there exists a linear, time invariant and causal transformation L which to every strain history ε (t) (t is natural time) associates a stress history σ (t) such that where L has properties which are described in different ways below.
