EXPLICIT FORMS OF THE MATERIAL FUNCTIONS FOR CERTAIN NON-LINEAR MATERIALS WITH MEMORY.
POLYTECHNIC INST OF BROOKLYN N Y
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The explicit restrictions on the forms of the kernels material functions in Green and Rivlins integral representation of the tensor-valued constitutive functionals are studied for certain classes of materials, namely, materials with no ageing effects, materials which exhibit no creep recoveries, and materials whose deformations are completely recoverable upon complete unloading. The results may be helpful in the experimental characterization of the non-linear viscoelastic materials. It is shown that for materials which do not exhibit ageing effects the variables in each of the kernels should appear as the difference between the present and the past time variables. For materials with no creep recoveries the present time variable in the kernels of the creep integral laws must vanish. Finally, it is shown that for completely recoverable materials, if the limit of each kernel in the creep integral laws exists as the present time variable tends to infinity, then the limit should vanish identically. Procedures for experimental determination of the kernels for each class of materials are also discussed. Author