A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media

Abstract

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi-node coarse element is adopted to describe the complex high-order deformation on the boundary of the coarse element for the two-dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one-dimensional and two-dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method.

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

“…The PFM for brittle fracture has been implemented in the commercial software Abaqus [237] via a User Element subroutine by Msekh et al [64], which was later extended by Liu et al [227]. Li et al [238], see also [239], combined the variational phase field model of brittle fracture with an extended Cahn-Hilliard model [240,241], and formulated a fourth-order phase field model suitable resolving crack propagation in anisotropic materials. Rate-dependent PFM models for modelling fracture in visco-elastic solids [242] have also been established.…”

A multiscale finite element method for the localization analysis of homogeneous and heterogeneous saturated porous media with embedded strong discontinuity model

“…This method was designed to bridge the coarse‐scale and fine‐scale with the numerical base functions constructed based on the fine‐scale features of the unit cell. For its convenience and efficiency of the upscale and downscale computations, this method has been widely adopted in the numerical analyses of various problems, such as the fluid flow problems , the consolidation and dynamic problems in heterogeneous porous media , two‐phase flow in the fractured undeformed porous media , and so on. Although the MsFEM has shown great advantages in effectively solving many large‐scale engineering problems with high heterogeneities, it has rarely been extended to the modeling of localization of the deformable porous media.…”