• Cássio Aguiar Universidade Federal do Rio Grande do Sul
  • Samir Maghous Universidade Federal do Rio Grande do Sul



Fracture. Viscoelasticity. Micromechanics. Damage propagation.


This paper presents a theoretical approach to fracture propagation in viscoelastic media, which combines a micromechanical reasoning and macroscopic thermodynamics arguments. Unlike cracks, fractures can be viewed as interfaces that are able to transfer efforts. Their specific behavior under shear and normal stresses is a fundamental component of the deformation and fracture in brittle materials such as geomaterials. Based on the implementation of the Mori-Tanaka linear homogenization scheme and correspondence principle, the first part of the paper is dedicated to assess the exact homogenized behavior of fractured viscoelastic materials. An approximate model for effective viscoelastic properties is also formulated in the framework of Burger model. Based on macroscopic thermodynamics principles, the free energy at macroscopic scale is then formulated, allowing for the analysis of damage propagation. It is shown that the thermodynamic force associated with damage propagation can be computed from the derivative of macroscopic free energy density with respect to fracture density parameter. Expression for the propagation criterion is therefore formulated based on the closed form expression previously obtained for the homogenized viscoleastic relaxation tensor.


Não há dados estatísticos.


Aguiar, C. B., 2016. Abordagem micromecânica da propagação de fraturas em meios elásticos e viscoelásticos. Master’s thesis, Federal University of Rio Grande do Sul/Porto Alegre.

Barton, N., Bandis, S., Bakhtar, K., 1985. Strength, deformation and conductivity coupling of rock joints. International Journal of Rock Mechanics and Mining Sciences, vol. 22, pp. 121”“140.

Bland, D. R., 1960. The theory of linear viscoelasticity. Pergamon Press.

Budiansky, B., O’Connell, R. J., 1976. Elastic moduli of a cracked solid. International Jounal of Solids Structures, Pergamon Press, vol. 12, pp. 81”“97.

Le, Q. V., Meftah, F., He, Q. ”“C., Le Pape, Y., 2008. Creep and relaxation functions of a heterogeneous viscoelastic porous medium using the Mori-Tanaka homogenization scheme and a discrete microscopic retardation spectrum. Mechanics of Time-Dependent Materials, vol. 11, n. 3, pp. 309”“331.

Maghous, S., Bernaud, D., Fréarad, J., Garnier D., 2008. Elastoplastic behavior of jointed rock masses as homogenized media and finite element analysis. International Journal of Rock Mechanics and Mining Sciences, v. 45, n. 8, pp. 1273”“1286.

Maghous, S., Lorenci, G., Bittencourt E., 2014. Effective poroelastic behavior of a jointed rock. Mechanics Research Communications, vol. 509, pp. 54”“69

Nguyen, S. T., 2010, Propagation de fissures et endommagement par microfissures dans un milieu viscoélastique linéaire non vieellissant. PhD thesis, University of Paris-Est/ Champs-sur-Marne.

Nguyen, S. T., Dormieux, L., Le Pape, Y., Sanhuja, J., 2010, Crack propagation in viscoelastic structures: Theoretical and numerical analyses. Computational Materials Sciences, vol. 50, pp. 83”“91.

Nguyen, S. T., Dormieux, L., Le Pape, Y., Sanhuja, J., 2011, A burger model for the effective behavior of a microcracked viscoelastic solid. International Journal of Damage Mechanics, vol. 20, n. 8, pp. 1116”“1129

Nguyen, S. T., Dormieux, L., 2014, Propagation of micro-cracks in viscoelastic materials: Analytical and numerical methods. International Journal of Damage Mechanics, vol. 24, n. 4, pp. 562”“581

Nguyen, S. T., Jeannin, L., Dormieux, L., Renard, F., 2013, Fracturing of viscoelastic geomaterials and application to sedimentary layered rocks. Mechanics Research Communications, vol. 49, pp. 50”“56

Salençon, J., 2009. Viscoélasticité pour le calcul des structures. Les Éditions de l’École Polytechnique ”“ Les Presses des Ponts et Chaussées, Paris.




Como Citar

Aguiar, C., & Maghous, S. (2017). FRACTURE PROPAGATION IN VISCOELASTIC MATERIALS: A MIXED MICRO-MACROSCOPIC APPROACH. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(29), 74–93.