Abstract
Clay, rocks, concrete and other composite solids show evidence of a hierarchical structure. A fractal tree of nested viscoelastic boxes is proposed to describe the elastic after-effects in these composite solids. A generalized fractal transmission line approach is developed to relate the strain and stress responses. Power law for strain, under an applied stress step, is derived. The exponent in the power law is obtained as a well-defined function of the branching numbers and scaling parameters of the viscoelastic hierarchy. Then, a composite solid with both instantaneous (linear) elastic strain response and power law type (linear) elastic after-effect for an applied stress step, is considered. The stretched exponential stress relaxation to an applied strain step is derived as an approximation. For the same composite solid, the stretch parameter of the stretched exponential and the exponent of the power law result to be equal to each other.
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