On constitutive modelling of fibre-reinforced composite materials

A relatively simple but comprehensive constitutive model is presented herein for predicting the nonlinear behaviour of laminated composite structures comprising layers of unidirectional and/or bidirectional (e.g. woven) fibre-reinforced materials (FRMs). The FRM layer is treated as an orthotropic but homogeneous continuum undergoing isothermal infinitesimal deformation. The proposed constitutive model for single layers of FRM is built within the framework of rate-independent theory of orthotropic elastoplasticity. The constitutive equations so developed, are then superimposed using the classical lamination theory, to arrive at the governing response relations for multilayer laminates. The model invokes a 3-parameter quadratic yield surface and the associated flow rule of plasticity. During plastic flow the evolution of the yield surface in the stress space is described by a non-proportional change in the parameters of the initial yield function. A 3-parameter quadratic failure surface similar in form to that of the initial yield surface is defined to mark the upper limit of plastic flow. Once failure is reached, it is identified as fibre or matrix mode of failure depending on the relative magnitude of various stress ratio terms appearing in the failure criterion. In the post-failure modelling, both brittle and ductile type of behaviour are considered in the direction of the offending stress. Unidirectional and bidirectional FRM layers are treated within the same general framework with the exception that yielding (and failure) in these layers are assumed to be governed by different criteria, namely, Hill's and Puppo-Evensen's yield (and failure) criteria, respectively. To completely quantify the proposed elastic-plastic-failure model three pieces of experimental stress-strain curves are required, namely, the uniaxial stress-strain curves along the two principal axes of orthotropy, and the in-plane shear stress-strain curve. Once established, these stress-strain curves are represented by bilinear approximations thus clearly defining the key parameters under the various loading programs. No provisions are made for the difference between tensile and compressive responses. Based on the proposed model, constitutive equations are properly formulated. A nonlinear finite element code is developed to incorporate the derived constitutive equations. The program is based on the conventional displacement method finite element procedure using two dimensional 8-node isoparametric elements. The nonlinearities in the equilibrium equations are handled by a mixed incremental and Newton-Raphson iterative procedure. Analysis restart and cyclic loading capabilities are also included to expand the program's usefulness. The performance of the program and the effectiveness of the model are verified for a number of in-plane loading paths applied to a wide variety of laminated FRMs with and without geometric discontinuities. The favourable comparisons of the model to experimental results available in the literature support the validity of the model.Applied Science, Faculty ofCivil Engineering, Department ofGraduat