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PeriDEM folder contains examples for multi-particle simulation and Peridynamics provides examples for single particle deformation.

PeriDEM: Examples

We next highlight some key examples. For more details, look at the create_input_file() within problem_setup.py or input_0.yaml in example folders.

To create input files, the python script is included. Python script allows easy parameterization of various modeling and geometrical parameters and creating .geo files for gmsh and particle locations file. Typically, the input files consists of:

  • input.yaml - the main instruction file for PeriDEM with details about material models, particle geometries, time step, etc
  • particle_locations.csv - this file provides location and other details of the individual particles. Each row in the file consists of
    • i - zone id that particle belongs to
    • x - x-coordinate of the center of the particle. Next two columns are similarly for y and z coordinates
    • r - radius of the particle
    • o - orientation in radians. This is used to give particle (particle mesh) a rotation
  • mesh.msh - mesh file for the reference particle or wall. For example, in compressive test example, there are four mesh files: one each for the circular and hexagon-shaped particle and one each for the fixed and mobile wall.

Two-particle tests
Circular without damping Circular with damping
Different materials Different radius Different radius different material

Two-particle with wall test
Concave particles

Compressive tests

Setup for this test consists of 502 circular and hexagonal-shaped particles of varying radius and orientation inside a rectangle container. The container's top wall is moving downward at a prescribed speed, resulting in the compression of the particle system. The quantity of interest is the compressive strength of the media. The reaction force (downward) on the moving wall should increase with the increasing penetration of this wall; however, after a certain amount of compression of the media, the damage will initiate in individual particles, especially those connected by force chains, resulting in the yielding of the system. For more details, we refer to Jha et al. 2021
Compressive test setup
Top: Plot of reaction force per unit area on the top wall. Bottom: Particle state at four times. Color shows the damage at nodes. Damage 1 or above indicates the presence of broken bonds in the neighborhood of a node.
Compressive test simulation

Attrition tests - Particles in a rotating container

We consider mix of different particles in a rotating container. Particles considered include circular, triangular, hexagonal, and drum shaped. Particles come in large and small shapes (their sizes are purturbed randomly). In order to to introduce diversity of material properties, we considered large particles to be tougher compared to the smaller ones. Setup files are in PeriDEM/attrition_tests
Rotating cylinder (setup) Rotating cylinder with center of rotation offset (setup)

Complex container geometries can be considered as well. For example, the image below is from attrition_tests and includes rotating rectangle with opening and internal groves of different shapes. The rotating container with particles inside is contained within another rectangle which is fixed in its place.

Running simulations

Assuming that the input file is input.yaml and all other files such as .msh file for particle/wall and particle locations file are created and their filenames with paths are correctly provided in input.yaml, we will run the problem (using 4 threads)

<path of PeriDEM>/bin/PeriDEM -i input.yaml -nThreads 4

Some examples are listed below.

Two-particle with wall

Navigate to the example directory PeriDEM/two_particles_wall/concave_diff_material_diff_size/inp and run the example as follows

mkdir ../out # <-- make directory for simulation output. In .yaml, we specify output path as './out'
<peridem build path>bin/PeriDEM -i input_0.yaml -nThreads 2

You may also use the included problem_setup.py to modify simulation parameters and run the simulation using run.sh (in directoy PeriDEM/two_particles_wall/concave_diff_material_diff_size). run.sh shows how different input files are created for the simulation.

❗ You may need to modify the path of PeriDEM executable in run.sh file.

In all problem_setup.py files in the example and test directory, the main function is create_input_file(). Here we set all model parameters, create .yaml input file, and .geo files for meshing.

Important remark on modifying input.yaml file

To test the examples quickly, you can directly modify the input.yaml and re-run the simulation as shown above. For example, you can alter Final_Time, Time_Steps, Contact_Radius_Factor, Kn, and other fields in the yaml file.

However, some care is required when changing the geometrical details of particles and walls in the input.yaml file. If you change these details in the .yaml file, you will have to ensure that the .msh file correspond to the new geometry.

Except geometrical parameters of walls and particles, rest of the parameters in input.yaml can be modified.

In due time, we will provide more information on setting up input files and covering all aspects of the simulation.

Compressive test

Navigate to the example directory PeriDEM/compressive_test/n500_circ_hex/run1/inp and run the example as follows (note that this is a computationally expensive example)

mkdir ../out 
<peridem build path>bin/PeriDEM -i input_0.yaml -nThreads 12

As before:

Compute times for various examples (From old version of the code!)

For reference, we list the compute times for various examples.

  • T is the total compute time in units of second
  • T(n) means compute time when running the example with n threads.
Test T(1) T(2) T(4) T(8)
two_particles/circ_damp 143.7 95.1 76.4 78.6
two_particles/circ_damp_diff_radius 164 114.6 96.7 99.4
two_particles/circ_diff_material 287.7 190.1 152.7 160
two_particles/circ_diff_radius_diff_material 329.1 229.4 195.3 200
two_particles/circ_no_damp 143.8 94.5 76.7 78.5
two_particles_wall/concave_diff_material_diff_size 2749.9 1534.6 980.8 691.1

Visualizing results

Simulation files output_*.vtu can be loaded in either ParaView or VisIt.

By default, in all tests and examples, we only output the particle mesh, i.e., pair of nodal coordinate and nodal volume, and not the finite element mesh (it can be enabled by setting Perform_FE_Out: true within Output block in the input yaml file). After loading the file in ParaView, the first thing to do is to change the plot type from Surface to Point Gaussian. Next, a couple of things to do are:

  • Adjust the radius of circle/sphere at the nodes by going to the Properties tab on the left side and change the value of Gaussian Radius
  • You may also want to choose the field to display. For starter, you could select the Damage_Z variable, a ratio of maximum bond strain in the neighborhood of a node and critical bond strain. When the Damage_Z value is below one at a given node, the deformation in the vicinity of that node is elastic, whereas when the value is above 1, it indicates there is at least one node in the neighborhood which has bond strain above critical strain (meaning the bond between these two nodes is broken)
  • You may also need to rescale the plot by clicking on the Zoom to Data button in ParaView
  • Lastly, when the Damage_Z is very high at few nodes, you may want to rescale the data to the range, say [0,2] or [0,10], so that it is easier to identify regions with elastic deformation and region with fracture.

Single particle deformation

In Peridynamics/circle, circular-shaped particle is deformed by clamping one part of the circle and specifying displacement in the other part. To run the example, you can either run using PeriDEM executible or the Peridynamics app which only handle single particle deformation:

# assuming you are in Peridynamics/circle directory
mkdir -p out
# use PeriDEM
<path to PeriDEM>/PeriDEM -i input_0.yaml -nThreads 4
# or use Peridynamics in apps
<path to Peridynamics app>/Peridynamics -i input_0.yaml -nThreads 4

The example in Peridynamics/rectangle is similar to the above example. It uses the in-built mesh for rectangle.
Circle deformation Rectangle deformation