Effective properties of a linear viscoelastic composite

Abstract

The relaxation moduli of a composite are determined. The relaxation of its components is described by various few-parameter kernels: Mittag-Leffler functions of different orders and Rzhanitsyn kernel. It is assumed that the composite components are made of model materials with volume relaxation. The Laplace transform and fractional rational approximation are used to develop an algorithm for reducing the relaxation functions of the composite to one class (series of decreasing exponents or exponents of fractional order). The relaxation moduli of a unidirectionally reinforced composite are determined as an example Keywords: viscoelastic composite, viscoelastic moduli, relaxation function Introduction. A composite combines several materials to optimize its mechanical properties. Many properties (viscous, thermal, electric, etc.) and characteristics (stiffness, strength, stability, etc.) can be corrected by properly choosing materials and volume fractions of composite components. The viscoelastic component of mechanical behavior is very important for many structural members, which necessitates accurate determination of the effective viscoelastic properties of composites.The hereditary mechanical behavior of composites can be described by methods of composite mechanics and viscoelasticity theory using experimental data on the deformation or relaxation of the composite components. Such an approach allows efficient modeling of the long-term properties of composites based on the properties and volume fraction of the components and the type of reinforcement. Micromechanical methods for predicting the effective elastic characteristics of composites based on the properties and volume fraction of the components are well-developed, whereas there are very few methods to determine the effective viscoelastic characteristics. The averaging method was used in [4] to solve quasistatic problems of linear viscoelasticity. The viscoelastic properties of a composite were described introducing a canonical viscoelastic operator. Bounds for the effective complex shear moduli of a bicomponent two-dimensional viscoelastic composite were studied in [16]. Bounds for the bulk and shear moduli were used to test the Mori-Tanaka [12] and finite-difference [21,22] schemes. The problem [12] was solved in the frequency domain, describing the relaxation bulk and shear moduli of the components within the framework of a standard mechanical model. The relaxation properties of bicomponent composites were determined in [20] using a linear combination of fractional exponential functions of the rheological characteristics of the component.We will assume that the relaxation properties of the component materials are described by one of the many rheological models that represent the constitutive equations in the form of Stieltjes convolution in the time domain:

Determination and analysis of the effective relaxation properties of a composite with viscoelastic components

“…The present paper determines the effective viscoelastic characteristics of a similar composite with viscoelastic components following an analogous approach and using methods developed in [4,5,23,25,28,29]. Omitting indices, we obtain…”

Influence of the viscoelastic properties of a composite on the stress distribution around an elliptic hole in a plate

“…And not only the limiting values, but also intermediate values of the moduli are significant. It is important to find intermediate values of the moduli with adequate accuracy in studying the mechanical properties of composites with viscoelastic components [2,16]. It may also be of necessity to analyze the stress state of bodies made of such composites [12].…”