Shear-lag model for failure simulations of unidirectional ®ber composites including matrix stiness

In this paper, we develop a shear-lag model and an in ̄uence superposition technique to quickly compute the stresses and displacements in 2D unidirectional ®ber composites in response to multiple ®ber and matrix breaks. Unlike previous techniques, both the ®ber and matrix are able to sustain axial load, and the governing shear-lag equations are derived based on the principle of virtual work and the ®nite element method. The main advantages of in ̄uence superposition techniques are that computation is tied to the amount of damage, rather than the entire volume considered and discretization is not needed, removing any uncertainties associated with meshing. For illustration, we consider a row of N (up to 301) contiguous ®ber breaks and highlight important in ̄uences that N and the matrix-to-®ber sti€ness ratio, qˆEmAm/Ef Af , have on stress redistribution. Comparisons with the Mode I plane orthotropic linear elasticity solution are favorable for both shear and axial tensile stresses. The best applications for such techniques are as numerical micromechanics tools in large-scale simulation codes of failure in ®brous composites. The present study is an important prerequisite for simulations and modeling of random fracture patterns, as would naturally develop in a real composite. Arbitrarily misaligned breaks are no more complicated to compute, and we reserve analyses of such cases to future simulation work involving random ®ber strengths. Ó 1999 Elsevier Science Ltd. All rights reserved.