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# Particle Mechanics Examples
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# Material Point Method (MPM) Examples
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This folder contains examples related to the [Particle Mechanics Application](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/ParticleMechanicsApplication) implemented in Kratos-Multiphysics.
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This folder contains examples related to the [MPM Application](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/MPMApplication) implemented in Kratos-Multiphysics.
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## Instruction
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- Please follow the instruction to download and install the latest version of the application and the GiD interface, [here](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/ParticleMechanicsApplication).
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- Please follow the instruction to download and install the latest version of the application and the GiD interface, [here](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/MPMApplication).
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- At the moment, we only support [GiD](https://www.gidhome.com/) for pre- and post-processing.
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- For unit testings of the currently available feature, please visit the [tests](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/ParticleMechanicsApplication/tests) folder in Particle Mechanics Application.
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- For unit testings of the currently available feature, please visit the [tests](https://github.com/KratosMultiphysics/Kratos/tree/master/applications/MPMApplication/tests) folder in MPM Application.
This is a 2D simulation of a cylinder on an inclined plane. A rotating as well as a frictionless sliding behaviour of the cylinder are regarded subsequently. The simulation is set up according to section 4.5.2 of (Iaconeta, 2019).
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This is a 2D simulation of a cylinder on an inclined plane. A rotating as well as a frictionless sliding behaviour of the cylinder are regarded subsequently. The simulation is set up according to section 4.5.2 of (Iaconeta, 2019).
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Linear, unstructured, triangular elements with a size of 0.01m are used to initialize the MPs. Three MPs per cell are considered. For the backgroundmesh linear, unstructured, triangular elements with a size of 0.02m are used.
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However, in contrast to section 4.5.2 of (Iaconeta, 2019), the inclined plane is modelled by a line with unstructured elements with size 0.01m. On that line a non conforming Dirichlet boundary condition is imposed by using the penalty method based on (Chandra et al., 2021).
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However, in contrast to section 4.5.2 of (Iaconeta, 2019), the inclined plane is modelled by a line with unstructured elements with size 0.01m. On that line a non conforming Dirichlet boundary condition is imposed by using the penalty method based on (Chandra et al., 2021).
The problem geometry as well as the boundary conditions are sketched below. The non conforming boundary condition is respresented by the copper coloured line.
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* Young's modulus (_E_): 200 MPa
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* Poisson ratio (_ν_): 0.3
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The time step is 0.001 seconds; the total simulation time is 1.0 seconds. The angle (_α_) of the inclined plane is 60°. The penalty-factor is 1e13.
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The time step is 0.001 seconds; the total simulation time is 1.0 seconds. The angle (_α_) of the inclined plane is 60°. The penalty-factor is 1e13.
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The contact between cylinder and inclined plane is modelled with the option "contact" (see line 53, file *ProjectParameters_contact.json*) in the first and with "slip" in the second case, based on (Chandra et al., 2021). Choosing "contact" leads to a rolling behaviour of the cylinder; "slip" to frictionless sliding.
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## References
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- Iaconeta, I. (2019). *Discrete-continuum hybrid modelling of flowing and static regimes.* (Ph.D. thesis). Universitat politècnica de Catalunya - Barcelona tech
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- Chandra, B., Singer, V., Teschemacher, T., Wüchner, R., Larese, A. (2021) *Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation*. Acta Geotech. 16, 2315–2335. https://doi.org/10.1007/s11440-020-01123-3
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- Iaconeta, I. (2019). *Discrete-continuum hybrid modelling of flowing and static regimes.* (Ph.D. thesis). Universitat politècnica de Catalunya - Barcelona tech
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- Chandra, B., Singer, V., Teschemacher, T., Wüchner, R., Larese, A. (2021) *Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation*. Acta Geotech. 16, 2315–2335. https://doi.org/10.1007/s11440-020-01123-3
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