General solutions for uniform precritical states
In this section we construct general solutions of the linearised equations of motion for compressible and incompressible bodies under the uniform precritical state (2.69). As earlier, we shall use Lagrangian co-ordinates x j ≡ x j which in the natural (undeformed) state coincide with Cartesian ones. We extract the time mul- tiplier expiΩτ and investigate the TLTDBS problem, which was set up in Sect. 11, in the form, common for elastic, elastoplastic, viscoelastic and viscoelastoplastic bodies in the context of the finite initial (precritical) deformations theory and the first and the second variants of the small initial deformations theory. We construct general solutions for plane, anti-plane and three-dimensional problems separately for compressible and incompressible bodies, assuming in so doing that perturbations of volume and surface forces are equal to zero.
KeywordsGeneral Solution Lame Constant Isotropic Body Elastic Potential Strain Energy Density Function
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