Computational micromechanics model for the convection of a cracks population in a brittle material

We stated in S anchez et al. (Proc. 15th IMACS World Congress, Vol. 5, 1997, p. 513), the objective rate law governing the general evolution, nucleation, growth and convection, of a diluted 3D population of arbitrarily oriented, penny-shaped, non-interacting stable microcracks that is dragged along the flow of a regular motion of a simple continuous body of brittle material. This requires the prior analysis of the convection process in the hypothesis of ignoring crack nucleation. It follows that the evolution of the microcrack population is here due only to the rotation of the crack planes as a consequence of the deformation processes of the microcracked brittle solid. The determinant role of this case in the general evolution problem, is also so in its numerical treatment. In this paper, use is made of the Bubnov–Galerkin spectral method with respect to the angular variable defining the orientation of a crack to numerically solve the mathematical model of the pure convection of microcracks in the nonucleation hypothesis. The paper is completed with three applications. The corresponding microcracks evolutions have been graphically displayed showing a behaviour that agrees with the expected. Indications about the computer codes implementing the numerical algorithm are included in an appendix