Incremental variational approach to the coupling between gradient damage and poroelasticity of saturated media

Abstract:

We aim at investigating the full coupling between gradient damage, poroelasticity and fluid flow phenomena in saturated porous media. To this end, we first extend the thermodynamics-based Biot-Coussy theory of poroelasticity to incorporate gradient damage processes. By introducing the concept of kinetic porosity to describe the interaction between skeleton deformation and fluid filtration in the connected pore space, we establish a four-field based incremental total energy functional. This functional accounts for poroelastic energy, as well as dissipation energy related to damage evolution together with Darcy-like fluid flow over time increments. The minimization of this functional is demonstrated as being able to describe this fully coupled problem. Moreover, with a suitable kinetic porosity approximation, this minimization procedure is reduced to a three-fields dependent one, which involves the displacement and damage fields of the skeleton phase as well as the fluid pore pressure field. The above formulation leads to an incremental variational principle, which governs the equilibrium state of the concerned saturated porous medium. We also propose a variational model for this fully coupled problem and implement it in the open-source platform FEniCS with a semi-staggered optimization algorithm. The proposed model is then applied to some engineering problems such as hydraulic fracturing and the evaluation of Excavation Damage Zones (EDZ) around underground waste storage galleries, etc. The approach demonstrates reliable predictive capabilities.

Short bio:

Long Cheng earned his B.S. in Physical Oceanography from Ocean University of China in 2009, and his M.S. and Ph.D. in Civil Engineering and Mechanics from Lille University in 2010 and 2013, respectively. Long was a postdoctoral researcher and Temporary Teaching and Research Assistant (ATER) at the Institut Jean Le Rond d’Alembert, Sorbonne University, from 2014 to 2015. He continued for two additional postdoctoral periods at the Laboratoire de Mécanique des Solides, École Polytechnique, until the end of 2016, and at the Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, Arts et Métiers ParisTech (Campus Metz) until July 2017. He has been serving as a Maitre de Conférences at the University of Lorraine since September 2017. His main research interests are in the field of mechanics of materials, particularly in multiphysical and multiscale modeling. He is currently working on the theoretical and numerical analysis of thermo-poro-mechanics coupled with gradient damage processes.