Our paper on stabilized mixed CG/EG formulation for poromechanics has been accepted for publication in Computer Methods in Applied Mechanics and Engineering.
Read the paper: Choo, CMAME 2019.
Abstract: Local (element-wise) mass conservation is often highly desired for numerical solution of coupled poromechanical problems. As an efficient numerical method featuring this property, mixed continuous Galerkin (CG)/enriched Galerkin (EG) finite elements have recently been proposed whereby piecewise constant functions are enriched to the pore pressure interpolation functions of the conventional mixed CG/CG elements. While this enrichment of the pressure space provides local mass conservation, it unavoidably alters the stability condition for mixed finite elements. Because no stabilization method has been available for the new stability condition, high-order displacement interpolation has been required for mixed CG/EG elements if undrained condition is expected. To circumvent this requirement, here we develop stabilized formulations for the mixed CG/EG elements that permit equal-order interpolation functions even in the undrained limit. We begin by identifying the inf–sup condition for mixed CG/EG elements by phrasing an enriched poromechanical problem as a twofold saddle point problem. We then derive two types of stabilized formulations, one based on the polynomial pressure projection (PPP) method and the other based on the fluid pressure Laplacian (FPL) method. A key finding of this work is that both methods lead to stabilization terms that should be augmented only to the CG part of the pore pressure field, not to the enrichment part. The two stabilized formulations are verified and investigated through numerical examples involving various conditions ranging from 1D to 3D, isotropy to anisotropy, and homogeneous to heterogeneous domains. The methodology presented in this work may also help stabilize other types of mixed finite elements in which the constraint field is enriched by additional functions.
Our research project entitled "3D cracking behavior of rocks under true triaxial stress conditions: Mechanistic modeling and investigations" has been approved for a General Research Fund of the Research Grants Council of Hong Kong. In this project, we team up with two renowned scholars in experimental rock mechanics – Dr. Louis N.Y. Wong of the HKU Earth Sciences Department, and Prof. Teng-fong Wong of the CUHK Earth System Science Programme.
Students interested in working on this project are advised to contact us at firstname.lastname@example.org.
We are extremely pleased to announce that Yidong Zhao has been selected to be a recipient of the prestigious Hong Kong PhD Fellowship this year and will join our group in September 2019. Currently he is pursuing his M.S. degree in Architectural Civil Engineering at Tongji University, where he also earned his B.S. degree as a Shanghai Outstanding Graduate in 2016. He has been the winner of China National Scholarships (two times), a National Second Prize in the 10th Zhou Pei-Yuan Mechanics National College Competition, and a First Prize in the 1st Mechanics Competition of Shanghai, among many others.
Yidong’s PhD research will focus on computational methods for large deformation problems in geomechanics. His official co-supervisor will be Prof. Kenichi Soga of the University of California, Berkeley.
Jinhyun Choo co-organizes a mini-symposium entitled "Computational Geomechanics, Poromechanics, and Granular Mechanics" at APCOM 2019, which will be held in Taipei, Taiwan, on December 18–21, 2019. Abstract submission is now open until May 15, 2019. The mini-symposium description is given below. We hope to have you there!
MS 1701: Computational Geomechanics, Poromechanics, and Granular Mechanics
Jinhyun Choo, The University of Hong Kong
Jidong Zhao, The Hong Kong University of Science and Technology
Geomaterials such as soils and rocks are porous granular materials that behave very differently from other materials in science and engineering. Computational modeling of these geomaterials plays vital roles in many problems related to civil infrastructure, energy, and the environment. This mini-symposium is intended to provide a forum for presentation and discussion of recent advances in the fundamentals and applications of geomechanics, poromechanics, and granular mechanics. Contributions are solicited in, but not restricted to, the following topic areas: (1) development, implementation, and validation of constitutive models for geomaterials, (2) computational methods and algorithms for coupled poromechanics and other multi-physics problems, (3) granular mechanics and other micromechanics approaches to geomaterials, (4) multiscale modeling techniques, (5) meshfree methods for large deformation problems, (6) numerical modeling of fracture and damage processes, and (7) uncertainty quantification and probabilistic methods.