Development of three-dimensional enriched crack tip finite element for linear poroelastic materials.

摘要

The computation of stress intensity factors in poroelastic materials have long been an important concept in fracture mechanics. Poroelastic materials consist of a solid, linearly elastic skeleton (also called the matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). There are many industrial application involving poroelastic materials. For example, in the field of geomechanics, it is desirable to understand and model the rock fracture behavior in order to effectively construct tunnels and predict landslides. In the field of oil mechanics, modeling rock breakage and rock drilling is a very important factor in determining oil drilling. Poroelastic materials may also be applied to integrated circuits, because they have very low dielectric constants due to the presence of pores, which makes them excellent candidates for use as dielectric materials.;FRAC3D is a program developed by researchers at Lehigh University specifically to solve fracture mechanics problems with the benefits of enriched elements, which provide the user an advantage over standard commercial codes (ANSYS, ABAQUS, etc.) in terms of singularity and mesh refinement issues. This is achieved by utilizing the correct asymptotic crack tip stress field for direct computation of the stress intensity factors. The proposed poroelastic model presented in this study allows for solid-fluid interaction that couples pore pressure to solid skeleton displacements, and utilizes enriched finite element approach to model the fracture behavior of poroelastic materials. This study focuses on the development of the local stiffness matrix formulation for a poroelastic enriched crack tip element.;A 20-noded hexahedron enriched-poroelastic element has been added to the FRAC3D program. To verify the correct setup of the enriched-poroelastic stiffness matrix, two sample problems involving a 1-element and 8-element poroelastic model have been solved using the newly modified enriched-poroelastic FRAC3D program with the enriched-poroelastic element. Each model contains a set of various special boundary conditions such as constraining the pore pressures, constraining the stress intensity factors, and decoupling of the pore pressure-mechanical displacements. FRAC3D results using the newly defined enriched-poroelastic element are compared with the original FRAC3D program. All cases resulted in very good agreement, with an average percent error of less than 0.0002% in nodal displacements, and an average percent error of less than 0.00046% for the nodal pressure diffusion, indicating the correct formulation of the enriched-poroelastic stiffness matrix.