4. Multidimensional Viscoelastic Relations

In this chapter we extend the viscoelastic constitutive relations to a three dimensional setting. An important subject is the determination of parameters to be used in the solution of real problems. Viscoelastic behavior is determined experimentally, mainly through uniaxial creep tests. To obtain 3D relations, some simplifying assumptions are made. In the case of concrete, it is assumed that the Poisson ratio does not change with time. In the case of polymers, as the creep in shear is more important than volumetric creep, this one is disregarded and the material is considered as elastic in bulk. The viscoelastic equations are here presented in a general form and then simplified for isotropic materials. Finally, a procedure based on the state variables approach is presented for a general anisotropic linear viscoelastic material.