On polymeric materials containing fibrils with a phase transition. II. The mechanical consequences of matrix shear

The mechanical behavior of a system of parallel fibrils, capable of a phase change and embedded in a matrix, is analyzed by considering a simplified model. The model consists of a single infinitely long isolated fibril together with its associated matrix. Furthermore, it is assumed that slippage cannot occur at the fibril-matrix interface but that the matrix deforms in both tension and in shear. The phase change occurring in the fibrils gives rise to large discontinuous local strains in the fibril and is characterized by a “critical stress” and an “equilibrium stress.” Analysis of the model shows that distinct zones of the secondary phase will form consecutively along the fibril length when the system is extended. These zones are mobile and the stress fields in the matrix associated with each zone result in the mutual repulsion of adjacent zones. Stress-strain curves for both extension and recovery are calculated using linear and nonlinear forms of the system parameters. It is suggested that the model studied is relevant to the mechanical behavior of keratin fibers.