The numerical simulation code of Qi ZHANG. This work was supported by the RGC Postdoctoral Fellowship Scheme (RGC Ref. No. PDFS2223-5S04) and the Start-up Fund for RAPs under the Strategic Hiring Scheme (Grant No. P0043879).
A benchmark example that concerns the bearing capacity of foundation soil was added on 02/08/2023 (mm/dd/yyyy). The NS-FEM result could match perfectly with the Prandtl solution. The surface of discontinuity was also qualitatively correct. Change the UMAT file (to D-P) in the assemble function.
Another example that tries to reproduce one case from the following paper was added on 06/03/2023 (mm/dd/yyyy). In order to match the reference result, the stabilization (tunning) parameter should be altered (a value of 1 would lead to inconsistent result). However, the effective stress distribution has some spurious oscillations, which is the weakness of SNS-FEM compared to standard FEM. By default, Mohr-Coulomb law should be used, despite that we use the Drucker-Prager model here.
Sloan, S.W. and Abbo, A.J. (1999), Biot consolidation analysis with automatic time stepping and error control Part 2: applications. Int. J. Numer. Anal. Meth. Geomech., 23: 493-529.
! A new "GasHM" folder has been created,
! which describes how to incorporate gas into hydro-mechanical coupling FEM.
+ The folder contains an assembly function, a constitutive model for transversely isotropic geomaterial,
+ one verification example, and one application example.
@@ To run the example, you need to move files to the main directory. @@In a nutshell, trade-off among computational efficiency (Highest: T6 FEM), spurious oscillations (numerical instability: NS-FEM based on T3 linear interpolation), and overly rigid solution (T3 FEM). SNS-FEM is in between.
The deformation equation is discretized by using the Smoothed Finite Element Method. The direct nodal integration on the smoothing domain is also modified to stabilized conforming nodal integration (SCNI). This is reflected in this file.
The code is designed for hydromechanical coupling analysis (poromechanics). Therefore, the pore pressure stabilization technique is included. In addition, for simplicity, the biot coefficient is set to be 1 and Biot modulus is set to be infinite. It should be not too difficult to modify our code for a more general case by using relevant pre-defined matrices such as the Mass matrix "integral(N^T*N)" from this file.
You can run this file directly. The (max) strip load is 0.05 MPa applied in 100 seconds. The top surface is fully drained. In the main file, the most time-consuming part is the assembly process, whose function is given in this file. The constitutive file is also called in the assembly process.
This file pre-aseembles a template for the 2 by 2 block stiffness matrix. It makes the actual assemble code more concise. However, it only works for constant biot coefficient/tensor and mobility, i.e., some material properties will not change with (x,y,z).
The assign_tractionBC2 is designed to calculate the equivalent nodal force vector "integral_line(N^T*traction)" in FEM. The user only need to define the traction_f as a vectorial function of (x,y,z,time) (P.S. the element-wise multiplication .* should be adopted).
PFEM (Particle-FEM) feature has not been incorporated yet since it will affect the code structure.
The calculations of the equivalent plastic strain is based on the deviatoric plastic strain tensor.
- The undeformed mesh
- The deformed mesh
- The contour of horizontal and vertical displacements
- The contour of (effective) stress field (4 components: xx, yy, zz, xy)
- The contour of equivalent deviatoric plastic strain