Stabilized generalized interpolation material point method for coupled hydro-mechanical problems
- PDF / 3,936,785 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 35 Downloads / 146 Views
Stabilized generalized interpolation material point method for coupled hydro-mechanical problems Xiaoqin Lei1,2,3
· Siming He1,2 · Lizhou Wu3
Received: 12 November 2019 / Revised: 20 July 2020 / Accepted: 8 September 2020 © OWZ 2020
Abstract The material point method (MPM) has been increasingly used to simulate coupled hydro-mechanical problems involving large deformations. However, when addressing saturated porous media with an almost incompressible liquid phase, the classic explicit MPM with low-order interpolation functions is not stable if no further stabilization approach is used. In this study, a solid-velocity–liquid-velocity-based hydro-mechanical governing formulation is adopted to construct a two-phase single-point explicit generalized interpolation material point (GIMP) method. To stabilize this set of formulation, the XPIC(m) (extended PIC of order m) method is extended to erase null space noise and damp high-frequency waves in both solid and liquid phases; additionally, a cell-based averaging approach is adopted to solve locking issues and smooth stress field variables. Several numerical examples have been presented to demonstrate the capabilities of the stabilized coupled GIMP method in simulating coupled hydro-mechanical problems involving dynamic effects and large deformations. Keywords Material point method · Hydro-mechanical · Large deformations · Numerical noise · Saturated soils
1 Introduction Large deformation problems involving hydro-mechanical couplings are of great interest in many geoscience fields, such as geotechnical engineering, earthquake engineering, and hydraulic engineering. These problems, which are difficult to be simulated with traditional mesh-based numerical methods owing to mesh distortion issues, can be solved successfully using mesh-free methods, such as the material point method (MPM), smoothed particle hydrodynamics (SPH), and particle finite element method (PFEM), in recent years [1–3]. Among them, the MPM originally proposed by Xiaoqin Lei was formerly worked at the Department of Civil Engineering, Aalto University, Finland.
B
Xiaoqin Lei [email protected]
1
Key Laboratory of Mountain Hazards and Surface Process, Institute of Mountain Hazards and Environment, CAS, Chengdu 610041, China
2
Centre for Excellence in Tibetan Plateau Earth Sciences, CAS, Beijing 100101, China
3
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China
Sulsky et al. [4] aims to retain the best features of both mesh-based and mesh-free methods. In the classic MPM, material continuum is represented by a set of Lagrangian material points possessing both material properties and history variables, which allows history-dependent constitutive models to be used. Additionally, an Eulerian background mesh is used to solve the momentum balance equation at each time step, which facilitates the computation of gradients and application of boundary conditions. Therefore, the MPM avoids mesh distortion issues related to
Data Loading...
