Topological derivative-based a new hydraulic fracturing model in brittle material
M. Xavier1; A. A. Novotny1; N. Van Goethem2
1 Laboratório Nacional de Computação Científica (LNCC); 2 Universidade de Lisboa
doi:10.20906/CPS/CILAMCE2017-0147
Resumo
In this work, a novel hydraulic fracturing mechanical model based on the topological derivative concept is proposed. The basic idea consists in adapt the Francfort-Marigo damage model to the context of hydraulic fracturing phenomenon. The Francfort-Marigo damage model describes the behavior of brittle materials under the quasi-static loading assumption, focusing on the evolution of damage regions under an irreversibility constraint. In the context of hydraulic fracture, the loading comes out from a hydrostatic pressure acting within the damaged region used to mimic the hydraulic fracturing process. A shape functional given by the sum of the total potential energy of the system with the Griffith-type dissipated energy term is minimized with respect to a set of ball-shaped pressurized inclusions by using the topological derivative concept. In particular, the topological derivative of the proposed shape functional, with respect to the nucleation of a circular inclusion endowed with non-homogeneous transmission condition on its boundary, is presented. Then, the obtained result is used to devise a simple and efficient topology optimization algorithm specifically designed to simulate the whole nucleation and propagation hydraulic fracturing phenomenon. Finally, a numerical example is presented showing important features associated with hydraulic fracturing process.
Palavras-chave: Topological Derivative; Hydraulic Fracture Model; Topology Optimization Algorithm