Homogenization of a Cracked Poroelastic Medium - Numerical calculation of the coefficients and damage

This work is devoted to the use of double scale asymptotic expansions and the posterior use of numerical tools in order to get the coe cients for an homogeneous macroscopic model starting from heterogeneous microscopic description. The particular problem of this project is a cracked poroelastic medium, that is a Biot-type problem both in the grains and in the cracks. In order to solve the expanded problem resulting from the double scale asymptotic expansions a nite element code is used. Numerical simulations allow one to obtain the homogenized coe cients for a macroscale description. These results are not isotropic despite having isotropic microscale coe cients due to the crack geometry and orientation. In a second part of the project damage is introduced in the cracks. Damage depends on the crack's opening, this makes the problem nonlinear and makes necessary the use of appropriate numerical tools to nd the solution. The commercial nite element code used in the rst part can not reproduce the damage problem, therefore a Matlab code is developed. This code consists of a FEM implementation in the porous part, with the appropriate linking conditions for the cracks to create the macrograin in the REV. In order to nd the solution for the di erent nonlinearities of the problem iterative procedures such as the secant method are introduced. The resulting model is able to reproduce any time-history of strain, and an evolution of the homogenized coe cients can be obtained from this time-history, unlike in the linear case, bifurcation phenomena can be observed for the damage problem.

Grantor dc:publisher

Université Joseph Fourier – Grenoble INP

Year dc:date

2013

Author dc:creator

• Argilaga, Albert

Contributors dc:contributor

• Caillerie, Denis
• Dal Pont, Stefano
• Marinelli, Ferdinando

• Homogenization
• asimptotic
• cracked poroelastic medium
• damage
• numerical homogenization
• Engineering, computing & technology
• Materials science & engineering
• Ingénierie, informatique & technologie
• Science des matériaux & ingénierie

Statement dc:rights

• open access
• info:eu-repo/semantics/openAccess

Licence

• http://purl.org/coar/access_right/c_abf2

Language dc:language

en

Identifier

info:hdl:2268/218567

OAI identifier oai:identifier

oai:orbi.ulg.ac.be:2268/218567