Elastic properties of an orthotropic binary fiber-reinforced composite with auxetic and conventional constituents

Closed-form expressions for the nine effective elastic constants of a binary fiber-reinforced composite with transversely isotropic constituents with positive (conventional) and negative (auxetic) Poisson’s ratio are considered. Such formulae were obtained by means of the asymptotic homogenization method and were verified numerically with an independent finite element model. The overall properties display explicit dependence on (i) the properties of the constituents, (ii) the volume fraction or radius of inclusion and (iii) the array periodicity. They are finally obtained by solving a normal infinite symmetric linear system of algebraic equations by truncation to a relatively small order term. This allows a fast solution and low computation cost. The overall orthotropy of the elastic properties is obtained by varying the distance between the fibers in two of the principal directions leading to different spacial aspect ratio for fiber distribution. In addition to this, an analytical relation between the effective properties based on the symmetry of the stiffness tensor is introduced. With the previous elements, we present reliable predictions for auxetic and conventional composites of this kind wherein a significant enhancement in Young’s modulus is found in a composite with an auxetic matrix reinforced by conventional fibres. Finally, we compute auxeticity windows (i.e., intervals of volume fraction where the composite is auxetic) when the fibres are auxetic. It is reported that spacial fiber aspect ratio plays a key role in the composite auxetic behavior.

► Closed-form expressions for the effective elastic properties are given. ► Fast numerical calculation involves solution of low order linear system. ► Spatial aspect ratio distribution plays a key role in composite’s auxeticity. ► Enhanced effective Young’s modulus is obtained if one phase is auxetic. ► Auxeticity windows are examined.