EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS |
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Authors: | Guo Shaohua |
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Institution: | (1) College of Resources, Environment and Civil Engineering, Central South University, 410083 Changsha, China |
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Abstract: | Anisotropic viscoelastic mechanics is studied under anisotropic subspace. It is proved that there also exist the eigen properties
for viscoelastic medium. The modal Maxwell's equation, modal dynamical equation (or modal equilibrium equation) and modal
compatibility equation are obtained. Based on them, a new theory of anisotropic viscoelastic mechanics is presented. The advantages
of the theory are as follows: 1) the equations are all scalar, and independent of each other. The number of equations is equal
to that of anisotropic subspaces, 2) no matter how complicated the anisotropy of solids may be, the form of the definite equation
and the boundary condition are in common and explicit, 3) there is no distinction between the force method and the displacement
method for statics, that is, the equilibrium equation and the compatibility equation are indistinguishable under the mechanical
space, 4) each model equation has a definite physical meaning, for example, the modal equations of order one and order two
express the volume change and shear deformation respectively for isotropic solids, 5) there also exist the potential functions
which are similar to the stress functions of elastic mechanics for viscoelastic mechanics, but they are not man-made, 6) the
final solution of stress or strain is given in the form of modal superimposition, which is suitable to the proximate calculation
in engineering. |
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Keywords: | anisotropy viscoelasticity eigen theory modal equation |
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