Mechanical modelling of composites with reinforcements in finite deformation

Abstract

Although the mechanical behaviour of particle-reinforced and fibre-reinforced composites have been studied extensively in infinitesimal deformation regime, their properties under finite deformation are still not well understood due to the complex interaction mechanisms between matrix and reinforcement, the intrinsic material and geometry nonlinearities. In this work, theoretical analysis, numerical simulation, and experimental data in the literature are employed to investigate the mechanical properties of composites with reinforcement in finite deformation. First, a three-dimensional Representative Volume Element (RVE) is developed for neo-Hookean composite, in which the incompressible neo-Hookean matrix is reinforced with spherical neo-Hookean particles. Four types of finite deformation (i.e., uniaxial tension/compression, simple shear and general biaxial deformation) are simulated using the RVE models with periodic boundary conditions enforced. The simulation results show that the overall mechanical responses of the incompressible particle-reinforced neo-Hookean composite (IPRNC) can be well predicted by another simple incompressible neo-Hookean model. The results also indicate that the effective shear modulus of IPRNC with different particle volume fraction and different particle/matrix stiffness ratio can be well predicted by the classical linear elastic estimation. In the second half of the study, the significance of the fibre-matrix interaction in the Human Annulus Fibrosus (HAF) is identified and analysed in detail. Based on the experimental results in the literature it is shown that the mechanical behaviour of the matrix can be well simulated by the incompressible neo-Hookean type model, but the effective stiffness of the matrix depends on fibre stretch ratio, which can only be explained by fibre-matrix interaction. Furthermore, it is found that this interaction takes place anisotropically between the matrix and the fibres distributed in different proportions in different directions. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by this fibre orientation dispersion.