Emergence of fibrous fan morphologies in deformation directed reformation of hyperelastic filamentary networks

Abstract

Recently, the authors generalized a theory for modelling the scission and reforming of crosslinks in isotropic polymeric materials to include materials in which elastic fibers are embedded in an elastic matrix. The fibers were assumed to dissolve with increasing deformation and then to immediately reassemble in a direction defined as part of the model. The model was illustrated in detail for uniaxial stretching along the direction of the fibers. Fiber reassembly was along the original fiber direction and did not result in a change in fiber alignment. The present work examines the implications of this model when the direction of reassembly is uncorrelated with the original fiber direction. In particular, the fibers are assumed to reassemble in the direction of maximum principal stretch of the matrix. The specific case is treated when the deformation is simple shear and the initial fiber direction is perpendicular to the direction of shear. The resulting fiber elongation with increasing shear results in fiber dissolution over a constitutively determined interval of the amount of simple shear. Newly formed fibers align in the current principal direction of maximum stretch, which is a direction that changes with the amount of simple shear. The resulting interval of alignment angles generates a fan-like fiber morphology at each material point. The formation and structure of the fan is described. In addition, the relation between the shear and normal stresses and the amount of shear is discussed, both during loading and unloading. It is shown that there can be a state of permanent set that is related to the original shape by triaxial extension and shear.