Simulation of internal mechanics of materials of high restitution

• xortdsc
In summary, the conversation discusses a numerical simulation that investigates the internal mechanics of collision impact in different materials. The simulation uses a simple model with basic elements, links between elements, and dynamic links to simulate repulsive forces. The starting condition and outcomes of the simulation are described, with a focus on energy conservation and the emergence of macroscopic effects from microscopic ones. The conversation then moves on to discussing the concept of high restitution materials and how they reflect almost all energy without converting it into vibrational energy. It is concluded that high restitution occurs when the internal links are very stiff compared to the stiffness of the collision and that restitution depends on the ratio of internal to collision stiffness. The speaker asks if there is an equation to translate these quantities.
xortdsc
Hello,

just for some basic understanding I wrote a (1D) numerical simulation to investigate the internal mechanics of collision impact in different materials.
For a start I work with a really simple model which consists of:
- basic elements (circles of fixed radius and mass and their current position and velocity)
- links between elements (hookes springs with fixed k and desired distance)
- when 2 elements overlap a dynamic link is added between them for the current timestep to simulate repulsive forces on collision

All computations are to be performed on each element or link individually, so it is like simulating "huge simplified atoms". After all I want to see how macroscopic effects emerge from microscopic ones.

Now the scenario is simple. The starting condition is:
- An "object" on the left consisting of a single element moving with velocity 1 to the right
- An "object" on the right consisting of 2 linked elements (with initial separation of 1) which is stationary
- the masses of all elements are set to 1, so the left object has a total mass of 1 and the right object has a total mass of 2
Code:
Left Object
Element x=-0.1, v=1.0
Overall x=-0.1, v=1.0
Energy pot=0.0, kin=0.5, vib=0.0, tot=0.5
Right Object
Element x=1.0, v=0.0
Element x=2.0, v=0.0
Overall x=1.5, v=0.0
Energy pot=0.0, kin=0.0, vib=0.0, tot=0.0
Total energy=0.5, impulse=1.0
Since there is no internal friction of any sort, energy and impulse (in any case) should be conserved and it is. The simulation goes mostly as expected: the left body moves towards the right one, collides, bounces off and returns with some of its momentum transferred to the right body.
Looking at the numbers I get the following at the end of the simulation (post collision):
Code:
Left Object
Element x=0.01978705, v=-0.13026643
Overall x=0.01978705, v=-0.13026643
Energy pot=0.0, kin=0.008484671, vib=0.0, tot=0.008484671
Right Object
Element x=1.4102714, v=0.56778127
Element x=2.4689417, v=0.56248504
Overall x=1.9396065, v=0.56513315
Energy pot=0.0, kin=0.3193755, vib=0.1721171, tot=0.49149257
Total energy=0.49997723, impulse=0.9999999
(This is just a snapshot as the velocities and relative displacements of the elements of the right object would oscillate, while the overall velocity of both elements is constant)

Now as you can see energy as well as impulse is conserved (disregarding the tiny numerical error). Also some of the energy is transformed into vibrational energy inside the right object (its 2 elements are vibrating relative to each other). This is also the reason, why the final velocities are not the expected -1/3, +2/3 as an impulse-based collision response with CoR=1 would suggest as some kinetic energy is converted into vibrational energy of the right body.
Changing the stiffness of the springs will yield the same results, the only difference is the vibrational frequency, which seems okay.

Now the actual question would be: How do high restitution materials (e.g. a superball with CoR of about 0.95 or so) reflect almost all energy without converting it into vibrational energy ? What would be the property of such material in that simple model ? What would need to change in the simulation to get something close to a fully elastic collision ? Using internal friction does not solve the problem, because as it reduces the internal vibration that energy is lost.

Does anybody have some insight into this ?

Last edited:
I figured it out. So to answer my own question: High restitution happens if the internal links are very stiff compared to the stiffness of the collision.
Restitution appears to depend solely on the ratio k_internal/k_collision. The remainder of the energy, if restitution is less then one, goes into internal vibrational energy.

Is there an equation which translates these quantities ? So I could compute the ratio of internal to collision stiffness from restitution and vice versa ?

Last edited:

1. What is the purpose of simulating internal mechanics of materials of high restitution?

The purpose of simulating internal mechanics of materials of high restitution is to understand how these materials behave under different conditions and how they respond to external forces. This can help in designing and improving materials with high restitution, which are important in various industries such as sports, construction, and automotive.

2. What are some common methods used for simulating internal mechanics of materials of high restitution?

Some common methods used for simulating internal mechanics of materials of high restitution include finite element analysis, molecular dynamics simulations, and discrete element method. These methods use mathematical models and computer simulations to predict the behavior of materials under different loading and boundary conditions.

3. What factors affect the internal mechanics of materials of high restitution?

The internal mechanics of materials of high restitution can be affected by various factors such as material properties, microstructure, loading conditions, and temperature. For example, the restitution coefficient of a material may change with temperature, affecting its overall behavior and performance.

4. How accurate are the simulations of internal mechanics of materials of high restitution?

The accuracy of simulations of internal mechanics of materials of high restitution depends on various factors such as the complexity of the material, the accuracy of the mathematical models used, and the input parameters. Generally, these simulations are considered to be reliable and can provide valuable insights into the behavior of materials.

5. What are some potential applications of simulation of internal mechanics of materials of high restitution?

The simulation of internal mechanics of materials of high restitution has a wide range of applications, including designing and optimizing high-performance materials, understanding failure mechanisms, and predicting the behavior of materials under extreme conditions. It can also be used in product development, quality control, and research in various industries.

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