r7.02.18 Hydromechanical element coupled with XFEM

Summary:

In this document we present the formulation of a new type of finite element. It is a hydromechanical element crossed by a discontinuity (an interface or a crack) whose design is based on the use of the extended finite element method in the formulation of the discretized equations of the poromechanical model for a porous medium saturated with fluid.

• 1. Introduction
• 2. Problem overview
  • 2.1. Definition of the field of study
  • 2.2. Assumptions and notations
• 3. Constitutive equations of the HM- XFEM model
  • 3.1. Equations for mechanics
  • 3.2. Equations for hydrodynamics
  • 3.3. Equations of the poromechanical model
• 4. Variational formulation
  • 4.1. Weak formulation of the mechanical problem
  • 4.2. Weak formulations of the hydrodynamic problem
• 5. Discretization of the problem
  • 5.1. Temporal discretization
  • 5.2. Discretization with XFEM
  • 5.3. Extension to the multi-cracked case
  • 5.4. Imposition of a flow in a hydraulic interface
• 6. Solving the coupled problem
  • 6.1. Linearization of the coupled problem
  • 6.2. Writing basic terms with XFEM
• 7. Bibliography
• 8. Description of document versions