Frequently Encountered Assumptions in Viscoelastic Stress Analysis

4 Frequently Encountered Assumptions in Viscoelastic Stress Analysis 

In solving viscoelastic stress analysis problems, assumptions on the material properties are often essential as gathering accurate time dependent data for viscoelastic properties is difficult and time consuming. Thus, one often only has properties for shear modulus, G(t) or Young s modulus, E(t), but not both. Yet of course for even the simplest assumption of a homogeneous, isotropic viscoelastic material, two independent material properties are required for solution of two or three dimensional stress analysis problems. Consequently, three assumptions relative to material properties are frequently encountered in viscoelastic stress analysis. These are incompressibility, elastic behavior in dilatation and synchronous shear and bulk moduli. Each of the common assumptions defines a particular value for either the bulk modulus or Poisson s ratio as follows. 

Incompressibility For small deformation linear elastic problems incompressibility is assured if Poisson s ratio is equal to 0.5, which also means that the bulk modulus is infinite (see Eq. 9.6). Under this assumption then, V = 0.5 and Ko = Under the same conditions Poisson s ratio for an incompressible viscoelastic material is also a constant 0.5 and. 

Naturally, this assumption also implies that the dilatational strains are always zero. For computer simulations of viscoelastic problems, this assumption can sometimes cause numerical difficulties. Most standard finite 

Since the viscoelastic bulk modulus changes much less with time and temperature than the shear modulus, this assumption is often a good one in cases where one only has characterization data for one viscoelastic property. Note that with this assumption, the Poisson s ratio retains its time dependence. 

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