Introduction

The MPM-Geomechanics is a implementation of the Material Point Method (MPM) to simulate large strain geomechanical problems in 3D. The main objective of this program is to provide an open source platform suitable for the study and application of the MPM in various geomechanical problems were materials are subjected to extreme deformation conditions. MPM-Geomechanics is a program that allows us to model the behavior of geo-materials, like soil and rock, when these materials are subjected to different initial and boundary conditions. Currently, the geo-materials are present in several areas of the society, like for example, in the slopes and excavation process in mining industry activities, or in the study of risk associated to naturals disasters. This program uses the Material Point Method (MPM) to integrate the motion equation of continuum mechanics:

\( \frac{\partial \sigma_{i j}}{\partial x_j}+\rho b_i=\rho \ddot{u}_i \) that can be expressed discretely, using the nodes of an Eulerian mesh:

\( \dot{p}_{i I}=f_{i I}^{i n t}+f_{i I}^{e x t} \)

where \( p_{i I}=\sum_p S_{I p} p_{i p}\) is the momentum, \( f_{i I}^{int}=-\sum_p \sigma_{i j p} S_{I p, j} V_p\) is the internal force, and \( f_{i I}^{e x t}=\sum_p m_p S_{I p} b_{i p}+\int_{\Gamma} \mathrm{t}_i N_I\left(x_i\right) d A\) is the external force at node \( I \). The function \( S_{I p} \) and its gradient \( S_{I p, j} \) are the weighting functions of node \( I \) evaluated at the position of particle \( p \), defined by \( S_{I p}=\frac{1}{V_p} \int_{\Omega_p \cap \Omega} \chi_p\left(x_{ip}\right) N_I\left(x_{ip}\right) dV \) and \( S_{I p, j}=\frac{1}{V_p} \int_{\Omega_p \cap \Omega} \chi_p\left(x_{ip}\right) N_{I, j}\left(x_{ip}\right) dV \).

The integration of the weight functions is performed analytically over the particle domain using linear functions for \( N_I\left(x_{ip}\right) \) and unit step functions for \( \chi_p\left(x_{ip}\right) \).

For more details on the formulation and integration process, refer to: Theory and Numerical Formulation

Program features

The main features of the program are:

Three-dimensional 3D formulation
Dynamic formulation
Shared memory parallelization using OpenMP
Many ways to crate bodies (polygons, particle list, pre-defined bodies)
Several constitutive models for soil and rock materials
Softening/hardening models to represent weakness during large deformations
Coupled fluid-mechanical formulation (under development)

Compiled binaries

For downloading the compiled binaries

Go to the Actions page.
Select the latest run of the MSBuild workflow for Window, or CI for Linux.
At the bottom, you will find the available artifacts under the Artifacts section.
Download the compiled-binaries artifact to get the compiled code.

Compilation in windows

For compiling the code in windows you can use the Visual Studio solution file /build/MPM-Geomechanics.sln, and build it by pressing Ctr+B. Alternatively you can compile it by using command in a Developer Command Prompt:

msbuild MPM-Geomechanics.sln -p:Configuration=Release

Compilation in Linux

For compile the code in a linux environment, execute the make command into the make folder, in with is located de makefile MPM-Geomechanics\build\make\makefile:

Documentation

The program documentation is generated using Doxygen:

doxygen Doxyfile

The HTML generated documentation is located in /docs/index.html.

Execution

In order to run simulations in several terminal, you can add the compiled code in the system PATH. After that, the common use is to call the program with the input file as argument: