Computer Modelling of Concrete using DEM

Analytical solution for elastic normal impacts

In order to understand the behaviour of particles and there interaction with each other as well as the relationship of applied forces on the particles. These are the numerical calculations for the elastic impact of two identical spheres with no spin along the line. Both spheres have the same material properties. This will help us to understand the behaviour of particles. [20]

Where V₁ and V₂ donates to the incoming velocities of sphere 1 and sphere 2 respectfully, and the duration t_duration of the collision of two identical spheres is given by the following equation:

Where:

• E = the Young's modulus of the spheres materials
• ν = the Poisson's ratio
• ρ = the density of the spheres materials
• r = the radius of each sphere

Thus, the maximum normal contact displacement α_max for the elastic impact of two identical spheres with no spin along the line will be:

And the contact force P_Max for the elastic impact of two identical spheres with no spin along the line.

Analysis solution for a sphere impacting
on a rigid plane surface

In this experiment we are trying to analysis and investigate the impact of a solid sphere failing under gravity, into a rigid plane surface using the theory behinds Newton's second law of motion. [20]

The sphere has the same material properties as the rigid surface. Also the sphere's incoming velocity will be donated as V₁. Also this experiment has been simulated using the EDEM software (see Simulation tape).

The contact duration t_duration for a sphere impacting on a rigid plane with incoming velocity V₁ can be determined from the following equation:

The maximum contact displacement α_Max for a sphere impacting on a rigid plane with incoming velocity V₁ can be determined using the following equation:

The maximum contact force P_Max for a sphere impacting on a rigid plane with incoming velocity V₁ can be determined from the following equation:

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