Random fiber networks with inclusions: the effect of the inclusion stiffness

Abstract

The mechanical behavior of random fiber networks containing inclusions is studied in this work. Inclusions are considered spherical and of radius comparable to the network mean segment length. Their stiffness is varied in a broad range, from very soft to rigid. It is observed that the presence of inclusions modifies the small strain stiffness of the network but does not change the functional form of the non-linear part of the stress-strain curve which, therefore, remains independent of the inclusion stiffness. Soft, bending-dominated networks can be reinforced more efficiently than the stiffer and more affinely deforming axially dominated networks. The variation of the composite modulus with the stiffness of inclusions does not follow the prediction of continuum homogenization theory. Numerical data that allow predicting the homogenized stiffness are presented.