Abstract
We consider the effective modules of Voigt, Reiss for isotropic elastic composites. We have reformed the method for constructing iterative transformation of the upper and lower estimates of fork (Voigt-Reuss) towards two-component composite in case of an arbitrary number of components. The method is based on the fact that effective modules of Voigt and Reuss can be regarded as elementary symmetric functions introduced by Gauss. The conditions, which the iteratively – transformed efficient modules must fulfill at every iteration, are shown.
Highlights
One of the basic problems in the mechanics of composite materials is the determination of effective properties for non-homogeneous elastic bodies
We apply the theory of the effective module that represents the method of calculation of the elastic characteristics for a homogeneous comparison environment, in which the potential energy is as close as possible to the energy of the elastic composite
As for the theory of effective modules, the models of Voigt and Reuss (VR) [7], Hashin and Shtrikman (HS) [8, 9], as well as model Krishera [10], developed in relation to the problems of thermal conductivity, are the basic mathematical models for definition effective elastic modules of the composite which does not take into account the geometry of the inclusions
Summary
One of the basic problems in the mechanics of composite materials is the determination of effective properties for non-homogeneous elastic bodies. The elastic modules of the basic material and the inclusions are taken as inputs to solve the problem The solution of this problem allows obtaining estimates of the stress state of structures, without the need for studies related to consideration of the structure of composites. As for the theory of effective modules, the models of Voigt and Reuss (VR) [7], Hashin and Shtrikman (HS) [8, 9], as well as model Krishera [10], developed in relation to the problems of thermal conductivity, are the basic mathematical models for definition effective elastic modules of the composite which does not take into account the geometry of the inclusions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IOP Conference Series: Materials Science and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
