Incremental Equations for Soft Fibrous Materials

Abstract

The general theory of nonlinear anisotropic elasticity is extended to describe small-amplitude motions and static deformations that can be superimposed on large pre-strains of fibre-reinforced solids. The linearised governing equations of incremental motion are derived. Then they are solved for some illustrative situations which reveal a wide spectrum of possible behaviours compared to the case of initially isotropic materials. Particular attention is paid to the propagation of homogeneous waves and to the formation of static wrinkles. These objects prove useful in the investigation of the issues of material (in the bulk) and geometrical (at boundaries) stability. Attempts are also made at modelling some experimental observations made on (isotropic) silicone and (anisotropic) biological soft tissues.