General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

Abstract

SUMMARY This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.

Time scales in the primary and secondary compression of soils

“…This theory as well as its variations has dominated the literature in the past several decades. In the context of one-dimensional deformation and flow processes, some major improvements on the theory have been made taking into consideration the effect of partial saturation, [1][2][3][4][5][6][7][8][9][10] time-dependent surface loading, [11][12][13][14][15][16][17] layered soil systems, [18][19][20][21][22][23][24] and simple nonlinearity including plasticity [25][26][27][28] and varying compressibility and permeabilitiy, 23,[29][30][31][32][33] among others. Even though the 1D kinematics have imposed limits on the applicability of these theories, they are still valuable contributions to the literature because they can be represented with closed-form analytical solutions.…”

A generalized phase field multiscale finite element method for brittle fracture

“…The procedure for evaluating the displacement field basis functions on a multinode coarse element on the basis of EMsFEM has been thoroughly described in the literature (see Reference ). In it, the prescribed boundary conditions required for the solution of Equation are considered to be piecewise linear (hat) functions defined over the boundary domain of the coarse element (see, e.g., Figure ).…”

“…In a nonlinear analysis procedure, the residual forces evaluated at the coarse nodes will inevitably result in a microresidual force vector at the microscale. To alleviate this, EMsFEM relies on a one‐step local correction of the microdisplacements by evaluating a set of perturbed displacements (see Reference ).…”

“…To alleviate this, generalized multiscale finite element methods (GMsFEM) were developed, which employ higher order coarse elements and enriched multiscale basis function spaces. A multinode coarse element strategy was also used in Reference to efficiently treat consolidation in highly heterogeneous soils.…”

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.…”