Three-Dimensional Constitutive Equations

  • Danton Gutierrez-LeminiEmail author


This chapter generalizes to three dimensions the one-dimensional viscoelastic constitutive equations derived in earlier chapters. The concepts of homogeneity, isotropy, and anisotropy are introduced and the principle of superposition is used to construct three-dimensional constitutive equations for general anisotropic, orthotropic, and isotropic viscoelastic materials. So-called Poisson’s ratios are introduced, and it is shown that uniaxial tensile and shear relaxation and creep tests suffice to characterize orthotropic viscoelastic solids. A rigorous treatment extends applicability of the Laplace and Fourier transforms to three-dimensional conditions, and constitutive equations in both hereditary integral form and differential form for compressible and incompressible isotropic solids are developed and discussed in detailed.


Anisotropic Orthotropic Isotropic Symmetry Tensor Matrix Summation Indicial Transform Spherical Deviatoric Incompressible 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Special Products DivisionOil States Industries, Inc.ArlingtonUSA

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