Micromechanical approach to damage propagation criterion in fractured viscoelastic materials
Cássio Barros de Aguiar1; Felipe Schaedler de Almeida1; Samir Maghous1
1 UFRGS
doi:10.20906/CPS/CILAMCE2017-0081
Resumo
The paper presents a theoretical formulation for the condition of continuous damage propagation in fractured viscoelastic media. The approach is based upon a micromechanical reasoning together with macroscopic thermodynamic arguments. It is well-known that the specific behavior of discontinuities is a fundamental component of the deformation and strength in geomaterials. From a mechanical view point, two classes of discontinuities may be distinguished: cracks and fractures. Unlike cracks, fractures are interfaces that are able to transfer normal as well as tangential efforts. Making use of the Mori-Tanaka homogenization scheme as well as of the elastic-viscoelastic correspondence principle, the overall viscoelastic behavior of the fractured medium are first assessed from the properties of its constituents (matrix and fractures). It is shown that the macroscopic behavior of the fractured viscoelastic material can be represented by a generalized Maxwell rheological model. The crack density coefficient stands for the damage parameter at macroscopic scale, whose rate reflects the evolution of material damage. It is established from macroscopic thermodynamics principles extended to viscoelastic materials, and taking advantage of the micromechanics-based behavior previously formulated, that the condition for damage propagation can be formulated by comparing the energy release rate and a critical energy. The expression of the energy release rate is determined as the derivative of the homogenized material's free energy with respect to the damage parameter. Unlike linear elasticity, the viscoelastic expression of the free energy is the sum of an instantaneous contribution and a residual dissipation (time-dependent energy) terms that account for the delayed behavior. Relying upon the close-form expression of free energy associated with the homogenized behavior, the criterion for damage propagation is analytically formulated either in stress or strain spaces as a function of the constituent's properties and damage parameter
Palavras-chave: Fracture; Viscoelasticity; Micromechanics; Damage Propagation