Accurate simulation of laboratory undrained and cyclic triaxial tests on granular materials using the Discrete Element Method (DEM) is a crucial concern. The evolution of shear bands and non-uniform stress distribution, affected by the membrane boundary condition, can significantly impact the mechanical behavior of samples. In this work, the flexible membrane is simulated by using the Finite Element Method coupled with DEM. In addition, we introduce a hydro-mechanical coupling scheme with a compressible fluid to reproduce the different undrained laboratory tests by using the membrane boundary. The evolution of pore pressure is computed incrementally based on the variation of volumetric strain inside the sample. The results of the membrane boundary condition are compared with more classical DEM simulations such as rigid wall and periodic boundaries. The comparison at different scales reveals many differences, such as the initial anisotropic value for a given preparation procedure, fabric evolution, volumetric strain and the formation of shear bands. Notably, the flexible boundary exhibits more benefits and better aligns with experimental data. As for the undrained condition, the results of the membrane condition are compared with experimental data of Toyoura sand and rigid wall boundary with constant volume. Finally, stress heterogeneity during undrained monotonic and cyclic conditions using the membrane boundary is highlighted.