Keywords: finite element method, laminated composites, fiber reinforced polymer, anisotropic constitutive model, user defined material routine, numerical implementation.

In order to predict the response of laminated composites made of unidirectional fiber reinforced polymers, it is commonly accepted to combine a kinematic laminate model with a constitutive model for the homogenized ply material. In the formulation of such a constitutive model the nonlinear ply behavior should be accounted for in order to exploit the potential of modern material systems. This requirement is realized in the constitutive model developed by the authors, which is briefly reviewed in the present paper. The implementation of the constitutive model for the commercial finite element package Abaqus/Standard and its application in structural finite element analyses is discussed in more detail.

The constitutive model distinguishes 'stiffness degradation' and 'plastic strain accumulation', two types of phenomena which both lead to pronounced nonlinear ply behavior. Stiffness degradation is attributed to microscopic brittle matrix cracking, fiber/matrix debonding, as well as progressive fiber failure. Its anisotropic effect is modeled using a special approach ranked among continuum damage mechanics, whereby the ply material behavior is included using the behavior of a fictitious material. Plastic strain accumulation is associated with the formation of microscopic areas with inelastic deformed matrix material. Based on phenomenological assumptions, plastic strain accumulation is modeled using two plasticity mechanisms. These mechanisms treat the evolution of plastic in-plane shear strains and the evolution of plastic normal strains of the ply.

Since finite element methods are state-of-the-art tools for structural analyses, the proposed constitutive model is implemented as a user defined material routine for the commercial finite element package Abaqus/Standard 6.9. With this, the numerical procedure is presented which is utilized to compute the stress state induced by an prescribed strain increment and the preceding loading history. The numerical procedure is built up of several hierarchically arranged levels of operations including integration of the implicitly formulated constitutive equations. Furthermore, the computation of the material Jacobian matrix is addressed in the present work since its consistent computation is a prerequisite for the quadratic convergence of the global Newton-Raphson iteration of the finite element program.

In order to demonstrate the application of the implemented constitutive model, results from finite element simulations of open hole tension tests with different specimen layups are presented. Qualitative discussion of these results shows that crucial intra-ply mechanisms are captured well by the proposed constitutive model.

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