Keywords: viscoelasticity, fracture, damage, finite element method, rheological models, crack growth process.

The durability of civil engineering structures requires taking into account the time dependent behaviour coupled with damage or fracture analysis. Reinforced concrete, wood or concrete bituminous exhibit a viscoelastic behaviour. In pavement structures, the problem of the crack growth process limits the period to repair. This paper deals with a numerical model based on an incremental formulation for viscoelastic resolution implemented in the finite element method. According to isotropic and axisymmetry symmetries, a complex algorithm allows operation, in the time domain, the crack growth process coupled with an incremental viscoelastic subroutine implemented in a finite element software. The model can be employed assuming an homogeneous bituminous concrete or heterogeneous media by dissociating bitumen and aggregates.

The formulation is based on a spectrum decomposition of creep functions in the time domain or complex modulus in the frequency domain. According to a generalized Kelvin-Voigt model, this method allows the computation of the mechanical response step by step by integrating the complete past history mechanical fields. The rheological model is well adapted in the energy balance required by the fracture mechanic concepts [1].

Fracture parameters are evaluated in terms of the energy release rate performing the path-independent integral G theta_v generalized for the viscoelastic case which is characterized by a perfect separation between release and dissipated energy.

An application is proposed on the theme of the crack growth initiation and propagation in bitumen around granulates. The specimen is composed by a thin film fixed between two steel convex protuberances in which a testing machine imposes a displacement with different speeds [2].

Finally, this numerical tool can be coupled with a comprehensive approach for the pavement durability. Actually, the damage state and fracture presence can be evaluated using dynamic loading. Using our finite element approach, we propose to couple our model with a dynamic model.

1

F. Dubois, C. Petit, "Modelling of the crack growth initiation in viscoelastic media by the G theta-integral", Engineering Fracture Mechanics, 72, 2821-2836, 2005. doi:10.1016/j.engfracmech.2005.04.003

2

S. Maillard, C. de La Roche, F. Hammoum, L. Gaillet, C. Such, "Experimental investigation of fracture and healing of bitumen at pseudo-contact of two aggregates", Eurobitume, 1291-1304, 2004.

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