Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

Abstract

The paper presents a method to calculate the difference of principal stresses and strains in linear viscoelastic optically sensitive polymeric materials from a time-dependent fringe pattern. The governing equations are derived using the direct and inverse Laplace transforms Keywords: photoelasticity, linear viscoelastic optically sensitive polymeric material, direct and inverse Laplace transformsIntroduction. The current level of development of the photoelastic method allows solving engineering problems [3,5] in various fields. The dynamic photoelastic method has recently been developed to be used in the mechanics of anisotropic bodies [8].Optically sensitive polymeric materials used for photoelastic modeling are known [2, 4] to have viscoelastic properties; therefore, it is reasonable to ask the question whether viscoelastic materials can be used for modeling dynamic processes in elasticity [6]. To minimize the error of an experimental method, use is usually made of photoelastic materials with low viscoelastic characteristics, which is quite justified [3,4]. Photoelastic data on the dynamic stresses and fracture of orthotropic plates with cracks can be found in [1,9].The present paper proposes a method to calculate the difference of principal stresses and principal strains in compressible linear viscoelastic optically sensitive materials from a time-dependent fringe pattern. We will establish the relationship between the mechanical and optical characteristics of viscoelastic bodies under dynamic loading.1. Original Equations. The photoelastic modeling of the mechanical behavior of elastic bodies involves the selection of a modeling material with mechanical behavior similar to that of the modeled material, the determination of the stresses and strains in the model, and the transformation to the stresses and strains in the real material.In optical modeling, the stresses are determined from the linear dependence of the fringe order m on the stresses (s 1 , s 2 ) alone with stress optical coefficient Ñ s as a coefficient of proportionality or on the strains (e 1 , e 2 ) alone with strain optical coefficient Ñ e as a coefficient of proportionality:

Development and application of radiowave photoelasticity for the fracture analysis of dielectrics

“…The polarization plane makes an angle a x with the quasiprincipal axis of the dielectric tensor ¿ ij characterizing a medium with microcracks (18).…”

Theoretical and Experimental Study of the Distribution of Stress Waves in Linear Viscoelastic Media

“…The behaviour of many polymers can be described with sufficient accuracy using linear differential or integral operators. The definition of such operators in the general case is a rather complicated task [5]. The fractional models are a valuable tool for describing the dynamic properties of real materials, specifically, in polymers which usefor controlling the sounds and vibrations [6,7].…”