Method for constructing rheological models of incompressible media under finite deformations

TL;DR

This paper introduces a method to derive constitutive equations for incompressible rheological media undergoing finite deformations, utilizing symbolic diagrams and nonlinear theories to model elastic and viscous behaviors.

Contribution

The paper presents a novel approach combining symbolic diagrams with nonlinear elasticity and viscous fluid theories to construct rheological models for incompressible media under finite deformation.

Findings

Method effectively models elastic and viscous interactions

Applicable to incompressible materials under large deformations

Provides a systematic way to derive constitutive equations

Abstract

This paper offers a method of obtaining constitutive equations for rheological medium. The method has been developed using the symbolic diagram illustrating the behavior of incompressible material. The studied medium operates under finite deformations. Elastic and viscous interrelations between the diagram points are described by equations of the nonlinear elasticity theory and the nonlinear viscous fluid.