Micromechanics of three-dimensional fibrewebs: constitutive equations

This paper extends the fibre–network theory of Cox to three–dimensional anisotropic fibrewebs. It presents a micromechanical model employing fibre axial deformation as the elemental deformation mechanism giving rise to assembly stress as a result of applied normal and shearing strain field. This model predicts the elastic constants of an assembly in terms of fibre linear density, fibre elastic modulus, fabric bulk density and the first 15 spherical harmonic coefficients of direction distribution function. A computer simulation has been performed to study the effect of structure on the initial elastic moduli of fibrewebs. This simulation shows that: (a) Young's modulus evaluated for each fabric axis is directly dependent on the fibre orientation distribution density (FODD) along the same axis; (b) shear modulus in any reference plane is maximized when orientation distribution function is isotropic in that plane and it decreases with increasing FODD along the direction normal to that plane; and (c) Poisson's ratio, &ngr;ij, increases as the FODD along the i–axis decreases and the FODD along the j–axis increases, but the effect of FODD along the k–axis is minimal.

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