Nonmonotonic Relaxation as a Result of Spatial Heterogeneity in the Model of In-series Blocks Chain

TL;DR

This paper investigates nonmonotonic relaxation phenomena in heterogeneous media, revealing new effects of viscous friction influenced by spatial heterogeneity through computer simulations, with implications for materials science and biological tissue modeling.

Contribution

It introduces a novel computer experiment demonstrating nonmonotonic relaxation caused by spatial heterogeneity in in-series block models, expanding understanding of nonlinear viscoelastic behavior.

Findings

Discovered nonmonotonic relaxation effects in heterogeneous media.

Showed rheological properties governed by first-order differential equations.

Highlighted relevance to biological tissues and new material design.

Abstract

Recently the materials possessing structure of molecular and supramolecular matrix are more and more actively studied. They are relative to many polymeric materials of a technological origin, such as rubber, and living biological tissues. Processes of mechanical deformation of these continuous media have peculiarities connected, first, with accounting for internal friction and dissipation of energy, and secondly, with nonlinearity of their elastic and viscous properties, that is with violation of Hook and Newtons laws. Traditional approaches to mechanics of viscoelastic bodies sometimes are excessively difficult, and more evident and available representations are necessary. The invaluable role in studying of the operating processes mechanisms of elastic deformation and motility of biological materials is played by the mathematical modeling. New effect obtained by means of computer experiment of nonmonotonic relaxation of deformation in heterogeneous media is considered in the present work. Rheological properties of described media are governed by the differential equations of the first order on time (the evolution equations), as well as a huge variety of other physical processes. The physical phenomena in nonlinear systems with dissipation have a big community, including such it would seem far areas, as dynamics of magnetization in ferrite. Therefore the problem of studying new effects of viscous friction in the conditions of nonlinearity and heterogeneity, is very actual as in respect of fundamental research nonlinear and non-uniform environments, and in many areas of materials science, design of new materials, engineering of biological substitutes of living tissues and development of the micromagnetic devices using essentially new opportunities.