ESyS-Particle Overview

The Lattice Solid Model (LSM) [MoraPAGEOPH1994], [PlaceJCompPhys1999] is a particle-based model similar to the Distinct Element Model [CundallGeotech1979]. The model consists of particles which are characterized by their shape, mass, position, orientation and velocity. The particles interact with their nearest neighbours by imparting contact forces. Typically, Discrete Element Model (DEM) particles are spherical and the contact forces consist of a linear elastic normal component and linear elastic tangential component. ESyS-Particle is a parallel implementation of the LSM with a Python scripting interface.

Particle Types

Currently, there exist three types of ESyS-Particle spherical particles: non-rotational, rotational, thermal-rotational:

Non-rotational Spheres

Non-rotational spherical particles possess no rotational degrees of freedom. Objects of class esys.lsm.NRotSphere represent non-rotational spherical particles.

Rotational Spheres

Rotational spherical particles possess orientation information. Particles of this type change orientation according to the applied moments. Objects of class esys.lsm.RotSphere represent rotational spherical particles.

Thermal Rotational Spheres

Thermal rotational spherical particles are the same as "Rotational Spheres" with the addition of thermal properties (temperature and thermal expansion). Objects of class esys.lsm.RotThermalSphere represent thermal rotational spherical particles.

Inter-particle Interactions

Interactions between model particles are also classified as non-rotational and rotational. Two spherical particles involved in a non-rotational interaction have all forces applied at the centre of mass. Two spherical particles involved in a rotational interaction experience moments due to forces which are, typically, applied at a contact point. The inter-particle interactions include:

Non-rotational Elastic

Purely linear elastic repulsion of particles when in contact.

Non-rotational Bonded

Linear elastic attraction and repulsion while bond remains intact. Bond breaks when a threshold separation distance is reached.

Non-rotational Friction

Linear elastic repulsion, linear elastic shear rigidity and Coulomb dynamic friction law.

Rotational Elastic

Linear elastic repulsion as well as linear elastic shear rigidity.

Rotational Bonded

Linear elastic tension, compression, shear, torsion and bending forces while bond remains intact. Bond breaks if a threshold force limit is reached.

Rotational Friction

Linear elastic repulsion, linear elastic shear rigidity and Coulomb dynamic friction law.

Thermal Non-rotational Elastic

Linear elastic repulsion as well as heat transfer.

Thermal Rotational Bonded

Same as "Rotational Bonded" with addition of heat transfer.

Thermal Rotational Friction

Same as "Rotational Friction" with addition of heat transfer and heat generation during frictional slip.

Fixed objects

Particles not only interact with other particles, but also with fixed objects within the model. These fixed objects are not subject to the laws of motion and provide a means of imposing particular types of boundary conditions. Fixed objects include:

Walls

An infinite plane characterized by position and normal direction.

Linear Mesh

A piecewise linear mesh which can be used to represent a surface in 2D.

Triangular mesh

A triangular mesh which can be used to represent a surface in 3D.

References

[CundallGeotech1979]

P.A. Cundall and O.A.D Strack (1979) "A Discrete Numerical Model for Granular Assemblies", Ge'otechnique, vol. 29, pp. 47-65.

[MoraPAGEOPH1994]

P. Mora and D. Place (1994) "Simulation of the Stick-Slip Instability", Pure Appl. Geophys., vol. 143, pp. 61-87.

[PlaceJCompPhys1999]

D. Place and P. Mora (1999) "The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction", J. Comp. Physics, vol. 150, pp. 332-372.