MICROMECHANICAL APPROACH TO VISCOELASTIC BEHAVIOR OF FRACTURED MEDIA
DOI:
https://doi.org/10.26512/ripe.v2i29.21790Keywords:
Fractures. Micromechanics. Viscoelasticity.Abstract
This paper presents a micromechanical approach to overall viscoelastic properties of randomly fractured media. 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, the first part of the analysis is dedicated to derive close-form expressions for the homogenized elastic stiffness tensor of the fractured medium. The effective viscoelastic behavior is then assessed from the elastic homogenization in Laplace framework and making use of the correspondence principle. In this context, a specific procedure for performing the inverse of Carson-Laplace transform is developed, allowing for the analytical derivation of homogenized relaxation and creep tensors. It is shown that the viscoelastic behavior can generally be described by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximation of the effective behavior by a Burger”“like model is formulated in the last part of the paper.
Downloads
References
Advani, S. G., Tucker III, C. L., 1987. The use of tensors to describe and predict fiber orientation in short fiber composites. Journal of rheology. vol. 31, pp. 751”“784.
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, v. 12, pp. 81”“97.
Dormieux, L., Kondo, D., Ulm, F. J.,2006. Microporomechanics. John Wiley & Sons.
Dutra, V. F. P., 2012, Um modelo constitutivo para o concreto reforçado com fibras de aço via teoria da homogeneização. PhD thesis, Federal Univesity of Rio Grande do Sul/Porto Alegre.
Le, Q. V., Meftah, F., He, Q. ”“C., Le Pape, Y., 2007. 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, vol. 45, n. 8, pp. 1273”“1286.
Maghous, S., Dormieux, L., Kondo, D., Shao, J. F., 2011. Micromechanics approach to poroelastic behavior of a jointed rock. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 37, pp. 111”“129.
Maghous, S., Lorenci, G., Bittencourt E., 2014. Effective poroelastic behavior of a jointed rock. Mechanics Research Communications, vol. 509, pp. 54”“69
Nemat-Nasser, Hori, M., 1993. Overall properties of heterogeneous materials. North Holland
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., 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., Jeannin, L., Dormieux, L L., Renard, F., 2013, Fracturing of viscoelastic geomaterials and application to sedimentary layered rocks. Mechanics Research Communications, vol. 49, pp. 50”“56
Mura, T., 1987. Micromechanics of defects in solids. Kluwer Academic Publishers.
Selençon, J., 2009. Viscoélasticité pour le calcul des structures. L’École Polytechnique.
Downloads
Published
How to Cite
Issue
Section
License
Given the public access policy of the journal, the use of the published texts is free, with the obligation of recognizing the original authorship and the first publication in this journal. The authors of the published contributions are entirely and exclusively responsible for their contents.
1. The authors authorize the publication of the article in this journal.
2. The authors guarantee that the contribution is original, and take full responsibility for its content in case of impugnation by third parties.
3. The authors guarantee that the contribution is not under evaluation in another journal.
4. The authors keep the copyright and convey to the journal the right of first publication, the work being licensed under a Creative Commons Attribution License-BY.
5. The authors are allowed and stimulated to publicize and distribute their work on-line after the publication in the journal.
6. The authors of the approved works authorize the journal to distribute their content, after publication, for reproduction in content indexes, virtual libraries and similars.
7. The editors reserve the right to make adjustments to the text and to adequate the article to the editorial rules of the journal.