# MICROMECHANICS-BASED CRITERION FOR MICRO-FRACTURE PROPAGATION IN VISCOELASTIC MATERIALS

## Palavras-chave:

Propagation Criterion, Viscoelasticity, Micromechanics, Homogenization, Fractures## Resumo

Most of engineering materials exhibit natural or load-induced fractures, which strongly

affect both the instantaneous and delayed mechanical behaviors at macroscopic level. Unlike cracks,

fractures are mechanically regarded as interfaces able to transfer normal and tangential efforts. The

aim of this paper is to formulate the conditions for fracture propagation in randomly-micro-fractured

viscoelastic materials. The homogenized viscoelastic relaxation tensor was formulated by applying the

correspondence principle upon the already-known homogenized elastic stiffness tensor. Extending the

Griffith-like thermodynamic framework to the macroscopic viscoelastic context, the propagation

criterion is first formulated, once again comparing the energy release rate to the critical energy.

Mathematical evidences shows the energy release rate is written as the derivative of the macroscopic

elastic energy, written to the viscoelasticity, with respect to the parameter which represents the

damage in the macroscopic scale. Under certain conditions, the elastic energy derivative can be

simplified, being reduced only to an instantaneous term, leading to a simplified propagation criterion.

It was notably found that for constant strain loadings, the fracture propagation is exactly driven by

elastic components. Analyses performed for constant strain rates on specimen made of Burger solid

matrix show that the energy release rate increases from zero to a constant asymptotic value. This

asymptotic energy release rate is used in a time-independent propagation criterion, evidencing an

interval to initial damage parameter where the propagation is possible. The main contribution of

asymptotic energy release rate, however, refers to the estimative of final damage parameter after the

end of propagation.