Computational Mechanics

Intro block 计算固体力学(侧重接触、断裂等问题)以及颗粒材料

Introduction to the laboratory

Our group is interested in computational mechanics, with special emphases on geomechanical problems. We aim to build a bridge connecting individual grains with engineering applications, such as geologic hazards, by developing numerical algorithms based on solid formulations. We also explore the physical mechanisms of the mechanical behaviors of granular materials. Our current research lies in the following areas:

  • Numerical models with voxel-meshes for real bodies constructed from 3D scanning images, focusing on the contact algorithms and means to impose boundary conditions.

  • Assessment of fault reactivations triggered by the change of hydraulic pressure.

  • Multiscale and multiphysical models for granular materials

  • Structural and rheology analyses for granular materials.


Image-based simulations using voxel-based meshes

We capture the geometries of sand grains via Micro-CT scanning images. Instead of using conformal meshes, we discretize the grains using cubic elements that compose surrogate domains. We concern two main problems, i.e. imposing boundary conditions and frictional contacts. The shift domain method is implemented to apply Dirichlet boundary conditions under the framework of an updated Lagrangian algorithm to simulate the damage of the grain. We also develop an unbiased Nitsche’s algorithm for frictional contacts using an implicit material point method enhanced by level sets. With these techniques, we can:

1. generate databases (constitutive laws considering real shapes) for machine learning;

2. introduce realistic mechanical behaviors of assemblies of grains to the multi-scale modeling.

Some applications are as follows.

(1) Soil fabric (clay structures in microscopic scales) 

Clay behavior considering soil structures        

                   Flocculated structure                                                          Dispersed structure

(2)  Isotropic compression of an assembly of four grains reconstructed from scanning images


(3) Macroscopic behaviors of granular assemblies considering stress-fields of individual grains (please click the figure, it is an animation)


            The framework of force chains                                    Macroscopic constitutive laws

(4) Brazilian test for an elastic disc (also click the figure)

(5) Shift domain method to apply boundary conditions

   Scanning image          Level set                        Surrogate domain                    Damage field

Assessment of fault reactivation triggered by the change of fluid pressure

Faults are geological entities of rock where relative displacement can occur in the plane of the fault. During industrial activities such as disposal of waste water or CO2, fault slip may reactivate due to the changes in hydraulic pressures and deformations of the rock matrix. The motion of faults may threaten the stability of wells, even induce seismicity. Therefore, accurate and efficient simulation techniques are required to assess the potential for fault reactivation.

We employ the extended finite element method (X-FEM) to approximate different types of discontinuous physical fields, such as strong discontinuities for displacement and strong/weak discontinuities for pressure, and the interaction between fault surfaces is modeled using the

Mohr-Coulomb criterion. We assess the reactivation of various faults triggered by a change of pressure. We also implement a new integration scheme to eliminate the need for element partitioning to integrate discontinuous functions over elements.

Some results are as follows.

(1) Fluid flow within a domain containing jagged faults (integration without element-partitioning)

                      Numerical model                                    Pressure distributions for various cases

(2) Branched and intersecting faults

                        Comparison of meshes used in FEM and X-FEM

               Comparisons of distributions of pressures using different methods

(3) Assessment of the reactivation of a typical fault


                       Numerical model


Distribution of pressure after 8 hours of the injection                Displacement field


Material point method for granular materials

The material point method (MPM) is a meshfree method that can alleviate the issue of mesh-distortion confronted in the FEM for large deformation problems. We develop a serious of models based on the MPM to simulate granular flows.

(1) Coupling of the MPM and the DEM for granular flows impacting simulations

We adopt the MPM to model granular flows and the deformable DEM to model blocks. Each block is treated as comprising nine material points to couple the MPM and DEM, and the acceleration of grid nodes arising from the contacts between granular material and blocks is projected to the discrete element nodes working as body forces.  Some results are shown below (click the figure to see the animation).

(2) Two-phases MPM

We use two set material points representing solid and fluid, respectively to consider the hydro-mechanical coupling problems. An experiment is conducted as a reference for validation. The results are shown below. 


                 Sliding surface in the experiment    Plastic strain distributions in simulations

(3) Hierarchy multi-scale modelling framework for granular materials using the MPM and DEM

Under this multi-scale framework, each material point is connected with a representative volume element consisting of an assembly of spheres. We abandon the phenomenological constitutive laws of granular materials and directly extract the constitutive relationships for each RVE using the DEM. Thus, we can link the macroscopic behaviors (such as plastic strain) and the microscopic mechanisms (such as force chains). 


     Schematic of the modelling scheme                  Connections of the macroscopic plastic strain and local packings 


          Displacements of the collapse of the granular pile simulated using the multiscale modelling scheme.

(4) Simulations of debris flows

We incorporate the domain terrain to simulate the process of a debris flow. The process is shown as flows (click the figure to see the animation)


                        The process of debris flow (simulated by others using our code)