Calculating the rigidity of a composite with allowance for flexural deformations of the filler

Models for describing the mechanical properties of inhomogeneous fine-structure polymer systems with marked asymmetry ( a large aspect ratio) of one of their components are proposed. Solution of this problem by traditional methods of composite mechanics is limited by two circumstances. The first consists in marked flexural deformations of the fine objects, which are not taken into account in the well-developed analytical techniques based on self-consistency approximations. The second is that the marked structural asymmetry causes significant difficulties in the use of numerical techniques for solving boundary-value problems of composite mechanics because the small thickness of the inclusions ( along with their great length) necessitates strong discretization of the continual equations. The backbone deformation model proposed in this study for a composite containing a fine-structure rigid cluster is based on the theory of bending of thin beams. A new numerical technique, which does not require an overly fine partition of the integration domain, is developed as well. An important role of flexural deformations is demonstrated; among other things, they lead to a significant decrease in the elastic moduli of the composites.