Simulation of a Solid Sphere Impact onto A Sheet metal For Various Material Properties of Sheet using Radioss
OBJECTIVE :
To Perform a simulation of a Sphere pressing on a plate for different material laws (as shown below)
Case {i} : Law 2 with Eps_max_Failure
Case {ii} : Law 2 with Eps_max_Crack
Case {iii} : Law 2 with Eps_max_No-Fail
Case {iv} : Simple Law 2
Case {v} : Law 1
Case {vi} : Law 27
Case {vii} : Law 36
and compare them on the basis of :
- Total number of cycles, Energy error, mass error and simulation time.
- Difference in animation, especially the failure mode (Whether elements crack or get deleted during failure)
- Difference in Energy Graphs
A report is to be compiled from the data obtained and the most ideal case which represents the on-field scenario is to be Noted.
THEORY :
* Material Laws :
Law 1 : Isotropic Elasticity :
This Law defines an isotropic, linear elastic material using Hooke's law. This law represents a linear relationship between stress and strain. It is available for truss, beam (type 3 only), shell and solid elements.
This material law is used to model purely elastic materials. The material stiffness is determined by only two values: the Young's modulus (E), and Poisson's ratio ( υ">υ ). The shear modulus (G) can be computed using E and ν">ν , as:
`G = E/(2(1+nu)`
Law 2 : Isotropic Elasto-Plastic : Johnson-Cook Model :
This law represents an isotropic elasto-plastic material using the Johnson-Cook material model. This model expresses material stress as a function of strain, strain rate and temperature. A built-in failure criterion based on the maximum plastic strain is available.
- This law includes strain rate and temperature effects.
- In this model the material behaves as a linear-elastic material when the equivalent stress is lower than the plastic yield stress. For higher stress values, the material behavior is plastic and the stress is calculated as :
In general cases, Johnson-Cook model is defined using limits for Max. Stress or Max. Strain that an element can withstand, but that does not reflect reality.
- Hence the law has an optional failure mode can defined using additonal parameters D1,D2,D3. (Depends on Stress-Strain Relationship)
- Also, another parameter `I_(xfem)` can be defined which controls how an element fails.
- If `I_(xfem)` = 0 : The elements are subjected to deletion
- If `I_(xfem)` = 1 : The elements are subjected to Cracks
Law 27 : Elastic - Plastic Brittle :
- This law combines an isotropic elasto-plastic Johnson-Cook material model with an orthotropic brittle failure model. Material damage is accounted for prior to failure. Failure and damage occur only in tension. This law is applicable only for shells.
- It is commonly used for brittle materials like Aluminium, Glass etc.
- The damages and Ruptures are defined with 4 parameters for each principal direction :
`epsilon_t` - Strain at Tensile failure beginning
`epsilon_m` - Maximum Tensile strain : but element is not deleted.
`epsilon_f` - Maximum Tensile strain for element deletion
`d_max` - Maximum Damage Factor
- This law allows the modeling of material damage and brittle failure in two principal directions (1 and 2).
Law 36 : Isotropic Elasto-Plastic : Plastic Tabulated :
- This law models an isotropic elasto-plastic material using user-defined functions for the work-hardening portion of the stress-strain curve (for example, stress vs. plastic strain) for different strain rates.
- It is available for Brick and Shell elements.
- Elastic portion of the curve is defined by Young's modulus and Poisson's ratio.
- Material plasticity curves can be given for arbitrary number of strain rates.
- The Ruptures are defined with 4 parameters :
`epsilon_t` - Strain at Tensile failure beginning
`epsilon_m` - Maximum Tensile strain : but element is not deleted
`epsilon_f` - Maximum Tensile strain for element deletion
`epsilon_p` - Maximum Plastic strain for element deletion for all loading directions.
* Energy Error :
- The difference in Energy level in the system between the starting of simulation to the energy level in system at each or final time step is called energy error.
- The value is always computed in percentage and
- If the error is negative, it means that some energy has been dissipated.
- If the error is positive, there is an energy creation with the system.
- The formula for computing Energy error is shown below :
* Mass Error :
- The difference in Mass in the system between the starting of simulation to the energy level in system at each or final time step is called energy error.
* Rigid Wall Forces :
- The force experienced by the Rigid wall due to the effect of the simulation is called Rigid Wall Forces.
- In this case the force experienced as a consequence of the impact of the tube on the wall is computed.
* Internal Energy :
- The energy in a system arising from the relative positions and interactions of its parts.
- To run a defined simulation, Go to Radioss under Analysis Radio Button and set the values as shown below before clicking on Radioss button again.
- The value "-nt 4" is used to limit the number of cores of the computer processor to be used by the solver and can be varied as per requirement
- The input file can also be changed which will make the solver create a duplicate of the file and save the results at the new location.
* Post - processing :
Analysing the files through Explorer :
* Once the simulation is finished, it can be noted from explorer that, at the location of input file, lots of new files are created
.out Files
- The File_Name_0000.out and File_Name_0001.out files are the output files from the solver after processing the respective Input files of the same names.
- The .out files can be opened through notepad or any similar softwares.
- The _0000.out file contains inputs to the _0001 file and does not contain any results from the simulation. However the _0001.out file contains the energy datas and solver step datas as shown below :
The acceptable value for energy error is below -15% and the ideal value is -5%.
The first column of the output file shows the number of cycles the solver has iterated and at the end of the simulation, the time taken to finish the analysis is printed.
.h3d and Axxx Files
- The Axxx files (where xxx represent number of the animation steps from 001) and .H3D files contain information from all the Axxx files in one single files.
- Both these file types contain the animation of the simulation and can be opened through HyperView.
- The only difference between them is that each file in Axxx contains only 1 time step. To view the entire animation, all Axxx files must be kept in the same location and the first file should be opened through Hyperview, but in the case of an .h3d file, it is a standalone file which can be opened without any other files.
.T01 Files
- These files contain all numerical datas which are required for plotting purposes.
- They can be opened through Hypergraph 2D
Animating in Hyperview :
- As mentioned above, open the .h3d file or .A001 file in Hyperview
- With the Hyperview UI, the animation can be played, paused, the playback speed can be controlled.
- The Hyperview UI enables us to plot the values of stress, displacement etc while also enabling us to activate dynamic max-min which shows the node locaiton where the maximum and minimum of applied contour is.
The plotting can be done using the "Contour" option and enabling and disabling the Dynamic max-min comes under "Measures" Option as shown below :
Plotting in Hypergraph :
- Similarly, as mentioned above, open the .T01 file in Hypergraph 2D
- Select the parameters along x and y axis respectively and click on apply to generate the graph, the UI is shown below
STUDY OF PROVIDED FILE :
The Provided file contains a circular surface component meshed and a spherical rigid Body.
* By reading the cards defined :
- The units are noted
- The total time span of simulation and print interval for animation :
`T_(st op)` = 5.01 ms
`T_(f req)` = 0.5 ms
- The circular plate is defined to move towards the rigid sphere.
* The plate is currently defined using a Johnson-Cook model with an Eps_p_max value and an additional Failure mode has also been invoked.
Also A second file is provided with all the same components and cards except for The material card. The second file is defined using Law_27 as shown below :
Compared to the Johnson Cook models, this law is defined with values similar to the former but with more parameters of EPS to define it.
SIMULATION :
Case {i} : Law 2 with Eps_max_Failure
File name : Law2_epsmax_Failure
Changes made to Provided File : There is no need for any change to be done on the Provided file as it satisfies the requirement for the current case.
The simulation is run as shown above.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 49,479
Energy Error : 0.2%
Mass Error : 0.0
Simulation Time : 66.88s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it is clear that the elements get Deleted when failure is observed.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {ii} : Law 2 with Eps_max_Crack
File name : Law2_epsmax_Crack
Changes made to Provided File : The following changes are made to the Failure Johnson Card in provided file :
- Ifail_sh = 1
- Dadv = 1
- Ixfem = 1
The simulation is run once the above changes are made.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 49,396
Energy Error : 4.0%
Mass Error : 0.0
Simulation Time : 70.84s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it is clear that the elements follow Cracking when failure is observed.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {iii} : Law 2 with Eps_max_No-Fail
File name : Law2_epsmax_nofail
Changes made to Provided File : The following changes are made to the provided file :
- The Failure Johnson Card is Deleted
The simulation is run once the above changes are made.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 49,404
Energy Error : 0.8%
Mass Error : 0.0
Simulation Time : 65.96s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it is clear that the elements get Deleted when failure is observed.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {iv} : Simple Law 2
File name : Law2
Changes made to Provided File : The following changes are made to the provided file :
- The Failure Johnson Card is Deleted
- The value provided in Eps_p_max is Deleted
The simulation is run once the above changes are made.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 48,736
Energy Error : 3.0%
Mass Error : 0.0
Simulation Time : 64.75s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it can be seen that no failure of elements occur. Hence it is not possible to comment whether the elements will crack or get Deleted.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {v} : Law 1
File name : Law1
Changes made to Provided File : The following changes are made to the provided file :
- The Failure Johnson Card is Deleted
- The Material card is changed to M1_ELAST and the same values are provided for Rho_initial, Young's modulus 'E' and Nu.
The simulation is run once the above changes are made.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 47,968
Energy Error : 0.3%
Mass Error : 0.0
Simulation Time : 64.46s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it can be seen that no failure of elements occur. Hence it is not possible to comment whether the elements will crack or get Deleted.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {vi} : Law 27
File name : Law27
Changes made to Provided File : As discussed above, Since a secondary file is provided for Law 27, that file is opened and since it meets the requirements for this case, no changes are made.
The simulation is run as shown above.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 41,854
Energy Error : 4.4%
Mass Error : 0.0
Simulation Time : 58.1s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it is clear that the elements get Deleted when failure is observed.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
Case {vii} : Law 36
File name : Law36
Changes made to Provided File : The following changes are made to the provided file :
- Material Card Image is changed to M36_PLAS_TAB
- Provided values are assigned to the material parameters.
- A curve is defined using the provided co-ordinates of x and y.
- This curve defines a stress strain graph at a specific strain rate and is fed as an input to the material card.
The simulation is run after making the above changes.
Output file : Once the simulation has been completed, the output File_Name_0001.out file is opened from explorer using notepad where the necessary values can be noted. (As discussed above). The entire output file can be found in the file attached at the end. The ending of the output file alone which has the parameters to be noted is shown below.
From the above output file, the following Datas are noted down :
Number of Cycles : 53,179
Energy Error : -1.2%
Mass Error : 0.0
Simulation Time : 73.73s
Animation :
The animation obtained through Hyperview is shown below :
From the animation, it is clear that the elements get Deleted when failure is observed.
Graphs :
The following Graphs are plotted:
1. Time vs Rigid-Wall Forces :
2. Time vs Internal/Kinetic/Total Energy :
All datas obtained from graph and Animations have been noted down in a report and will be discussed in detial after running the simulation for all cases.
COMPARISON REPORT :
- Comparison of Output Files :
| Case | No.of Cycles | Energy Error | Mass Error | Simulation Time | Observation |
| Case 1 | 49,479 | 0.2 % | 0.0 | 66.88 s |
- Across all the cases, there is no variation in the mass error. - The number of cycles is found directly proportional to the complexity of the input and the duration the material takes to fracture. - Energy error varies a lot between the cases with the most error in case of Case 6 : Law 27. - Simulation time is directly propotional to the number of cycles |
| Case 2 | 49,396 | 4.0 % | 0.0 | 70.84 s | |
| Case 3 | 49,404 | 0.8 % | 0.0 | 65.96 s | |
| Case 4 | 48,736 | 3.0 % | 0.0 | 64.75 s | |
| Case 5 | 47,968 | 0.3 % | 0.0 | 64.46 s | |
| Case 6 | 41,854 | 4.4 % | 0.0 | 58.1 s | |
| Case 7 | 53,179 | -1.2% | 0.0 | 73.73 s |
- Comparison of Graphs :
The graphs were compiled onto a presentation and is attached at the end. The comparison slides are shown below :
Inference from the Simulation :
Coming to the question of which case would represent the actual failure in real life, it cannot be answered without knowing the nature of the plate being used. However certain comments can be made on each case.
- If the material in actual simulation is a Brittle aluminium, then Case 6 is the most realsitic simulation.
- The simulations in Case 2 and Case 7 can also be considered ideal as the elements crack before failing in case 2 as they do in real life and Case 7 is based on Data obtained from actual test results being provided as input by the user
- In nature, Aluminium is not known to be a perfect elastic material hence Cases 4 and 5 would be the most unnatural simulation.
- Case 1 and Case 3 will not be the most accurate representation of the actual scenario simply because of the element deletion and that better simulations are available.
CONCLUSION :
Thus the simulation of a Sphere pressing on a plate for different material laws was conducted and a detailed report created.
All relevant datas are attached in the link shared below :
https://drive.google.com/file/d/1C2PPESyneMxWJHbrjG3X481eqodGE7Yq/view?usp=sharing