The Fractal Scale-Invariant Structure of a Temporal Hierarchy in the Relaxation Processes

Abstract

The phenomena of elastic aftereffects during loading/unloading of viscoelastic and capillary-porous bodies, relaxation of their stresses is accompanied by the energy accumulation and dissipation to be taken into account in the theory of oscillations which also considers the behavior of materials when the force is applied to them, the elastic aftereffect and stress relaxation forms ostensibly opposite energy processes that’s why the main problem to one is to understand and discovery laws for such aftereffects. The goal of the research to show that the distribution of relaxation time in viscoelastic and capillary-porous media may have a scale-invariant structure and that the indirect confirmation of the scale invariance of relaxation time hierarchy can be the principle of temperature-time superposition according to which the experimental relaxation functions obtained for different temperatures can be combined with each other using the appropriate coordinate axes stretching. We used methods of viscoelastic theory, fractal analysis and methods of mathematical physics. So, in this paper, an attempt has been made to harmonize both these theories and numerous experiments on the destruction of materials described in the academic literature. It is shown that the hierarchy of times determining shear and bulk relaxation in viscoelastic/capillary-porous medium has a fractal structure and it was observed that the presence of time fractality eases the modeling of viscoelastic/capillary-porous bodies resulting in the universal relaxation function of a rather simple kind.