Abstract
An innovative method of effective composite mechanical properties estimation is applied to optimize the distribution of reinforcement in a functionally graded structural element. The concept is based on the assumption of the mechanical equivalence between two configurations: The real heterogeneous composite configuration and the fictitious quasi-homogeneous one. It allows to obtain the analytical formulae describing the dependence of the effective elastic composite properties on the volume fraction of reinforcing inclusions. As an example of application, a circular bar subjected to torsion is considered.
Highlights
The establishing of the macroscopic properties of a composite material from the properties of its constituents is of pivotal importance for the design process of composite structures
The need for homogenization is due to the fact that the components of the composite are most often homogenous, the final composite material is heterogeneous
The approach of mechanical equivalence between the real and fictitious material configurations, typically applied in continuum damage mechanics issues [1] was lately broaden to a general multi-dissipative material modelling by Egner and Ryś [2,3,4]
Summary
The establishing of the macroscopic properties of a composite material from the properties of its constituents is of pivotal importance for the design process of composite structures. The approach of mechanical equivalence between the real and fictitious material configurations, typically applied in continuum damage mechanics issues [1] was lately broaden to a general multi-dissipative material modelling by Egner and Ryś [2,3,4] This method allows us to describe both the elastic and plastic behaviour of the material, thanks to the use of the framework of thermodynamics of irreversible processes with internal state variables. It was described in detail in Reference [5] and compared with classical estimations like Voigt-Reuss [6,7], Hashin-Shtrikman [8], Mori-Tanaka [9], the self-consistent method and so forth. This results in a wide range of estimated values for the effective elastic properties of composites
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