This article aims at the determination of the effective behavior of a microcracked linear viscoelastic solid. Due to the nonlinearity of the strain concentration in the cracks, the latter cannot be derived directly from a combination of the correspondence theorem with the Eshelby-based homogenization schemes. The proposed alternative approach is based on the linear relationship between the macroscopic strain and the local displacement discontinuity across the crack. An approximation of the effective behavior in the framework of a Burger model is derived analytically.
In the case of micro-cracked viscoelastic materials, the numerical approach is required to solve the problem of crack propagation. The step-by-step method is used to model, using the finite element method, a morphologically representative pattern of the media. The computation of the effective behaviour of the material in the case without crack propagation shows a very good validation with respect to the Burger effective model obtained by the analytical method. The case of crack propagation is solved numerically considering a morphologically representative pattern containing a single crack. We also develop the concept of critical rate of kinematic loading and of asymptotic damage.
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