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Assignment 4-RADIOSS Material Laws Challenge

RADIOSS Material Laws Aim - To run the simualtion for the plate and rigid ball by using Jhonson Cook Material and Elasto Plastic Material with Brittle Failure as per the cases given in the question by using Radioss solver. Objective - Run the simulation for all the 7 cases as given in the question.…

Yeshwanth N
updated on 21 Sep 2021

RADIOSS Material Laws

Aim -

To run the simualtion for the plate and rigid ball by using Jhonson Cook Material and Elasto Plastic Material with Brittle Failure as per the cases given in the question by using Radioss solver.

Objective -

Run the simulation for all the 7 cases as given in the question.
Run the simulation by changing the material,shell properties and failure parameters.
Run the simulation by converting Failure Jhonson Model to LAW 1.
Tabulate the total number of cycles, Energy Error,Mass Error and Simulation Time.
Plot the graphs for all the 7 cases.
Compare all the 7 cases results.

Theoretical Framework -

In FEA,the materials are specified to conduct simulations and analyze how a particular material behaves under certain stress and loading conditions.
Th attention should be provided to the material type chosen and the material properties provided. There could be different material properties needed as input to fully characterize a material for analysis purposes. Any unclear or illogical data provided during material characterization will lead to uncertain results.
Choosing the right material and providing the reliable material data in performing a simulation is very important.
RADIOSS provides one of the most comprehensive material and rupture libraries in the industry. The material laws and rupture criteria span across definitions for concrete, foam, rubber, steel, composites,biomaterials, and more.
In Radioss,We are specifying the materials and type,The materials are categorized in two forms called

1) In the form of Material Cards [Material Laws].

2) In the form of Material Properties.

In the form of Material Cards [Material Laws].

Law 1 – Elastic.
Law 2 – Johnson-Cook.
Law 27 – Elastic-Plastic Brittle.
Law 36 – Elastic-Plastic Tabulated.
Law 42 – Ogden (Visco Hyperelastic).
Law 70 – Foam.

In the form of Material Properties.

Isotropic Elasticity.
Isotropic Elasto-Plastic.
Composite and Anisotropic.
Viscous.
Hydrodynamic.
Explosives.

Law 1 [Isotropic Elasticity.] :

This Law /MAT/ELAST 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.
Useful for elements attached to rigid body.This material law is used to model purely elastic materials.
This law is only applicable for small deformations.
The material stiffness is determined by only two values: the Young’s modulus (E), and Poisson’s ratio ( $nu$ ). The shear modulus (G) can be computed using E and $nu$ .
$G=E/2(1+nu)$

*Description*	*Model Name*	*Keyword/MAT*	*Model Law*
Linear Elastic	Elastic [Hooke's].	/ELAST	1
Hyper Elastic	Tabulated Hyper Elastic.	n/a	69
Hyper Elastic	Ogden.	n/a	82

Table-1

Isotropic Elasto-Plastic :

This law represents an isotropic elasto-plastic material using the Johnson-Cook material model.
This model expresses materialstress as a function of strain, strain rate and temperature.
A built-in failure criterion based on the maximum plastic strain is available.

Isotropic Elastic Plastic Piecewise Linear Material [Law36] :

This is a Isotropic elasto-plastic material.
It's a user-defined function for the work-hardening portion of the stress-strain curve.
It's available for brick and shell elements.
Elastic portion of material stress-strain curve defined by Young modulus and Poisson’s ratio.
Material plasticity curves can be given for up an arbitrary number of strain rates.
Linear interpolation of strain-stress curve.
i) For a given strain rate.
ii) For a given plastic strain.
In order to avoid poor curve extrapolation during the strain calculation, a dummy curve defined for a high strain rate value can be added in the model—typically the highest strain rate curve is repeated.
The curves have to be defined such as they don’t intersect themselves in the strain range being used. Otherwise the calculationmay fail.

There are 4 damage and rupture parameters :

$εp^max$ is the maximum plastic strain for element deletion for any loading (tensile , shear or compression).
εt is the beginning of tensile damage. From this point the stress value defined in the curve is reduced by the factor
Where ε1 is the largest principal strain $sigma=sigma(ε_m-ε_1 //ε_m-ε_t)$ .
εm is the end of the tensile damage. The stress value is null, but the element is not deleted.
εf is the tensile failure strain value for element deletion.

Elasto-Plastic Material with Brittle Failure [Law27] :

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.
Yield surface definition same as Johnson-Cook (Law2).
Useful for modeling brittle failure of glass.
Damage and rupture defined with 4 parameters for each principal direction:
$e_t$ = Strain at the beginning of tensile failure.
$e_m$ = Maximum tensile strain at which the stress in the element is set to a value dependent on dmax1.
$d_max$ = Maximum damage factor ef = Maximum tensile strain for element deletion.

Viscous Material :

The viscous materials are classified into two types called

1) Hyper Elastic [/MAT/OGDEN or /MAT/LAW42 : Ogden, Mooney-Rivlin].

2) Tabulated Foam [/MAT/FOAM_TAB or /MAT/LAW70: Tabulated Foam].

1) Hyper Elastic [/MAT/OGDEN or /MAT/LAW42 : Ogden, Mooney-Rivlin].

They are Visco Hyperelastic behavior (non-linear elastic).
This law is generally used to model incompressible rubbers, polymers, foams, and elastomers.
This material can be used with shell and solid elements.
Generally used to model polymers and elastomers.

2) Tabulated Foam [/MAT/FOAM_TAB or /MAT/LAW70: Tabulated Foam].

Visco-elastic behavior
Stress – strain relationship defined by functions according to strain rate
Unloading behavior defined by:
$***$ Curves.
$***$ Hysteresis Parameters.

Procedure -

Phase 1-Import the Starter File into the Solver Deck Radioss

While opening hypermesh software,A user profile window will pop up,Switch to the radioss user profile as shown in below figure 18 and start importing the model into the solver deck.

Figure 1-User Profile Window.

Now after switch the user profile to radioss,import the model (starter file) into the radioss solver deck.
To import the model,Go to Standard Panel >> Import >> Import Solver Deck.

Figure 2-Importing Model into Radioss Block.

Import Solver Deck option should be selected to import the radioss starter file.

Figure 3-Selecting the Starter File to Import.

Here the import browser will appear as shown in above figure 3,Select the appropriate starter file to import into GUI.
Switch the File Type to Radioss Block and import the model into GUI.

Figure 4-Model Imported into GUI.

Here the model is in wireframe mode,Switch to the shaded mode as shown in below figure 5.
To switch to shaded mode,Go to Visualization Tab >> Shaded Elements and Mesh Lines.

Figure 5-Visualization Tab to Switch to the Shaded Elements and Mesh Lines.

Figure 6-Shaded Elements and Mesh Lines Mode.

Case 1-Running the Simulation as it is default :

Now after importing the model into the GUI,Go to the solver browser and select the begin card to inorder to check the unit system,which is shown in below figure 7.

Figure 7-Unit System.

Now go and check the material card by selecting it in model browser inorder to check whether the appropriate properties have been assigned or not,The material property card is shown in below figure 8.

Figure 8-Material Properties.

Now go and check the property card.In the property the parameters have been assigned to the material given,Which is shown in below figure 9.

Figure 9-Property Card.

Now run the simulation,To run simulation,Go to Analysis Panel as shown in figure 28.
Go to Analysis Panel >> Radioss >> Select the Input File >> Save it in Different Folder and Rename it as Case-1 >> Run.
Check the Include Connectors,If there are any connectors in the model,The connectors will also be taken into account.
Type -NT 4 in options tab,This will make the simulation faster.
Where NT indicates No of threads,4 indicates assigning the task to 4 cores in the system.

Figure 10-Analysis Panel.

Figure 11-Radioss Sub-Panel.

Here save the input file in a different folder, and rename it as case-1 which is shown in below figure 30.
Now run the solver by hitting on radioss.

Figure 12-Save the Input (Starter File) in a Separate Folder and Run the Simulation.

After completing the simulation,the radioss will pop up a solver window stating Radioss Job Completed which indicates the simulation has been completed,Which is shown in below figure 31.

Figure 13-End of Solver Output.

After running the simulation,The animation files will be generated where we specified a location to store the files which is shown in below figure 14.

Figure 14-Animation Files.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below figure 15.

Figure 15-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error-0.8%

$***$ Internal Energy-0.2730E+05

$***$ Kinetic Energy-67.81

$***$ External Work-0.2721E+05

$***$ Elapsed Time-95.36s

$***$ Mass Error-0

$***$ Total No of Cycles-49380

Next the 00001.rad file is opened to see the Tstop and Tfrequency value which is shown in below figure 16.

Figure 16-00001.rad File.

Phase 5 - Postprocessing

1) Review the Simulation using -HyperView.

2) Plot the graphs using -Hypergraph 2D.

1) Review the Simulation using HyperView :

Hyperview allows for loading and viewing result files obtained from several sources.
Based on the solver type of the files and the results you would like to visualize and analyze,there are differnt ways to load the input deck and their corresponding results into hyperview.
First to begin the postprocessing in the Hypermesh,Split the Screen as shown in below Figure 18.
Import the animation file .h3d into the hyperview.

Figure 17-Splitting the Screen.

Figure 18-Screen Splitted into Two.

And then activate the Client HyperView.

Figure 19-HyperView Panel.

To access the load model panel
Select Load Model Button from the HyperView Panel and open .h3d file as shown in below figure 19.

Figure 20-Opening .h3d File.

Figure 21-Model Loaded.

After loading the model into hyperview,It will be represented as shown in below Figure 21.

Figure 22-Model Imported into HyperView.

After importing the .h3d file into the GUI,Enable the contour.
The contour tool create contour plots of a model graphically visualize the analysis results.
To enable contour,Go to Results ToolBar >> Contour .

Figure 23-Contour Panel.

Now switch to the Von Misses Stress in result type and select the component,select the averaging method as simple and then click apply as shown in below figure 43.

Figure 23-Selecting the Paremeters in Contour Panel.

After applying ,Run the Simulation,The Simulation animation is shown in below Figure 24.

Figure 24-Case 1-HyperView Simulation Animation.

2) Plot the graphs using -Hypergraph 2D.

Now plot the graphs using Hypergraph 2D,We are plotting the graphs to see what is happening in the rail component.
Hypergraph 2D is a powerful data analysis and plotting tool with interfaces to many popular file formats.
It is sophisicated math engine capable of processing even the most complex mathematical expressions.
Hypergraph 2D combines these features with high quality presentation output and customization capabilities to create a complete data analysis system for any organization.

Figure 25-Switching to Hypergraph 2D.

Here switch to the Hypergraph 2D to plot the graphs.
To switch,Go to Client Selector >> Choose the Hypergraph 2D as shown in above Figure 25.

Figure 26-Screen Splitted into Three.

[Note : Before plotting the graphs,Make sure to split the screen into three or four as shown in above Figure 26 and then plot the graphs.]

The first graph is plotted for the Rigid Wall Forces.
To plot the graph,Go to Hypergraph 2D >> Data File >>Element_Formulation-Shell-3_assignmentT01 >> Apply.

Figure 27-Select the Appropriate T01 File.

Figure 28-Plotting Graph for Rigid Wall Forces.

Here the graph has been plotted for the Rigid Wall Forces as shown in below Figure 30.
There are various parameters in Rigid Wall like Normal Force,Tangent Force,FX-X Total Force,FY-Y Total Force,FZ-Z Total Force,Total Resultant Force.
We are selecting only Total Resultant Force,Because we don't know the exact axis of the component placed,So that's why we are selecting Total Resultant Force and then plotting the graph.

Figure 29-Units Profile.

While plotting the graph,Units profile window will pop up,There select solver units and then plot the graph,Because the graphs will be plotted according to the solver units.
Now plot the graph for the rigid wall forces which is shown in below Figure 30.

Rigid Wall Forces :

Figure 30-Rigid Wall Forces Graph [Case-1].

Here,Intially there is no contact between the plate and rigid wall.So the curve is in origin.
When the rigid ball hits on the rupture plate,the curve starts increasing and suddenly the curve starts decreasing,
Cause after reaching the ultimate stress,the elements gets deleted and there will be no contact after the elements gets deleted which is shown in above Figure 24-Case 1:Simulation Animation,So the curve goes down and decreasing.
Now plot the graphs for all the energies,which is shown in below Figures 31 and 32.

All Energies Graph :

Figure 31-All Energies Graph Animation.

Figure 32-All Energies Graph Plotted.

Internal Energy :

Figure 33-Internal Energy Graph.

Here the internal starts from origin why because there is no contact between rigid ball and rupture plate.
Then the internal energy goes on increasing,why because the deformation or displacement is happening,when the displacement increases the internal energy increases.

Kinetic Energy :

Figure 34-Kinetic Energy Graph.

Here the kinetic energy is in origin,Why because there is no initial velocity,there is a imposed velocity.
The impose velocity is for rigid ball,Why because we are imposing the rigid ball to hit on the rupture plate,So that's the reason,why impose velocity is given.
The formula for Kinetic Energy= $1/2MV^2$ .
Here the initial velocity is zero,So the curve starts from origin.
After its increasing because,rigid ball is hitting rupture plate and again its slightly decreasing due to element breakage,After the elements deleted,there will be no contact,So its decreasing.

Why Kinetic Energy Curve is Zig-Zag ?🤔

Cause the Noise and Vibrations will be produced when the rigid ball hits the rupture plate,so the kinetic energy curve is in Zig-Zag form.

Total Energy :

Figure 35-Total Energy Graph.

Total Energy is sum of Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
Total Energy is the combination of all energies.
So its goes on increasing,Internal energy curve is similar to the total energy.

Contact Energy :

Figure 36-Contact Energy Graph.

Why contact energy is constant ?🤔

Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.

Hourglass Energy :

Figure 37-Hourglass Energy Graph.

Here the hourglass energy is constant,Because the recommended parameter Ishell=24 has been assigned to the property card,So the hourglass energy is constant.

Case 2-Change the Values in Jhonson Failure Card :

Here the Jhonsons Failure card is edited,and the values have been given in the failure card as per the values given the question.
But the law is same [LAW 2],Only the failure card is edited.
The values which are to be changed are Ifail_sh=1,Dadv=1,Ixfem=1.

[Note : $***$ D_{adv=1- Initiate the crack when it reaches ultimate stress.}

_$***$_{Ifail_sh=1-Shell is deleted or cracked, if there is one layer in the failure zone.}

_{$***$ Ixfem=1-Crack the elements and delete the elements. (Ixfem is only applicable for shell elements)].}

Figure 38-Jhonson Failure Card.

The values have been given in the failure card which is shown in below Figure 39.

Figure 39-Values Entered in Failure Card.

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 40.

Figure 40-Animation Files.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 41.

Figure 41-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error-4.1%

$***$ Internal Energy-0.3082E+05

$***$ Kinetic Energy-141.9

$***$ External Work-0.2980E+05

$***$ Elapsed Time-134.34s

$***$ Mass Error-0

$***$ Total No of Cycles-49217

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 42.

Figure 42-Case 2 Simulation Animation.

[Note : $***$ Here the maximum Eps_Max value =0.151,The elements should be deleted after reaching the Eps_Max=0.151.

$***$ But here the maximum strain shown here is 1.426E-01 which is 0.147,Why ?

$***$ Because the solver won't record when the elements get deleted,So this is the reason.

$***$ The elements will be failing and getting deleted,when the rigid ball goes on hitting the rupture plate.]

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 43.

Figure 43-Rigid Wall Forces Graph.

Rigid Wall Forces :

Here the curve starts from origin,because there is no contact and it goes on increasing because the deformation happens (rigid ball comes into the contact with rupture plate).
Again its suddenly decreasing,Cause the elements are cracked and deleted,there will be no contact between rigid ball and rupture plate,So its slightly decreasing.
The graph is plotted for the internal energy which is shown in below Figure 44.

Figure 44-Internal Energy Graph.

Internal Energy :Here the curve is starting from origin because there is no contact and its goes on increasing due to the breakage of elements.

Figure 45-Kinetic Energy Graph.

Kinetic Energy : Here the kinetic energy starts from origin and goes on increasing due to deformation of elements,Its increasing after 4ms because the deformation of elements are controlled by jhonson cook material parametrs.And its suddenly decreasing because the elements getting deleted after crack and there will no contact,so its slightly decreasing.

Figure 46-Total Energy Graph.

Total Energy :

Total Energy is sum of Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
Total Energy is the combination of all energies.
So its goes on increasing,Internal energy curve is similar to the total energy.

Figure 47-Hourglass and Contact Energy Graph.

Hourglass Energy- Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.

Contact Energy- Simillarly as same as for case-1.

Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.

Case 3-Delete the Failure Jhonson Card :

Here the failure card is deleted to see any changes happening the result.

Figure 48-Delete Failure Card.

Figure 49-Failure Card Deleted.

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 50.

Figure 50-Animation Files.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 51.

Figure 51-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error-0.8%

$***$ Internal Energy-0.2744E+05

$***$ Kinetic Energy-87.08

$***$ External Work-0.2736E+05

$***$ Mass Error-0

$***$ Elapsed Time- 96.79 s

$***$ Total No of Cycles-49407

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 52.
Here the shell elements are getting deleted,when it reaches the maximum plastic strain epsmax value which is shown in below Figure 52.

Figure 52-Case 3 Simulation Animation.

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 53.

Rigid Wall Forces :

Figure 53-Rigid Wall Forces Graph.

Here the graph plotted for the case 3 rigid wall forces is very similar to case 1 rigid wall forces.

Internal Energy :

Figure 54-Internal Energy Graph.

The internal energy graph is plotted which is shown in above Figure 54.
Here the internal energy is also somewhat similar to the previous cases 1 and 2.

Kinetic Energy :

Figure 55-Kinetic Energy Graph.

The kinetic energy obtained here is somewhat less when compared to the previous case,The obtained kinetic energy graph is shown in above Figure 55.

Total Energy :

Figure 56-Total Energy Graph.

The total energy increases with increase in internal energy and kinetic energy,Cause the total energy is combination of all energies.
The obtained total energy graph is shown in above Figure 56.

Hourglass and Contact Energy :

Figure 57-Hourglass and Contact Energy Graph.

Hourglass and Contact Energy -

Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.
Simillarly as same as for case-3.
Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.
The obtained hourglass and contact energy graph is shown in above Figure 57.

Case 4 - Delete the EPS_P_Max Value from the Material Card :

Here delete the value of EPS_P_Max value and run the model with the name LAW2 but the same material card.
The value of plastic strain is removed which is shown in below Figure 59.

Figure 58- Material Card.

Figure 59-EPS_P_Max Value Removed.

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 60.

Figure 60-Animation Files Obtained.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 61.

Figure 61-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error-1.1%

$***$ Internal Energy-0.3879E+05

$***$ Kinetic Energy-3.931

$***$ External Work-0.3838E+05

$***$ Mass Error-0

$***$ Elapsed Time- 131.47s

$***$ Total No of Cycles-49303

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 62.
Here EPS_P_Max=0,So the shell elements will not be deleted which is shown in below Figure 62.

Figure 62-Case 4 Simulation Animation.

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 63.

Rigid Wall Forces :

Here the rigid wall forces starts from origin cause there will be no contact in the beginning and it goes on increasing cause deformation is happening to the plate.
And the curve slightly decreases because of the elements breakage.

Figure 63-Rigid Wall Forces Graph.

Internal Energy :

The internal energy graph is plotted which is shown below in Figure 64,her internal energy is somewhat similar to the previous case.

Figure 64-Internal Energy Graph.

Kinetic Energy :

The kinetic energy is plotted, which is shown in below Figure 65.The kinetic energy is also somewhat similar to the previous case.
Kinetic Energy produced here is little bit less cause deformation of elements is happening slowly.

Figure 65-Kinetic Energy Graph.

Total Energy :

The total energy is almost similar to the internal energy.
The total energy graph is plotted which is shown in below Figure 66.

Figure 66-Total Energy Graph.

Hourglass and Contact Energy :

Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.
Simillarly as same as for case-4.
Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.
The obtained hourglass and contact energy graph is shown in above Figure 67.

Figure 67-Hourglass and Contact Energy Graph.

Case 5 - Change the Material Card to LAW1 :

Here change the material card to LAW1,Here it will be elastic behaviour.
Don't change any material properties,Use default material properties like $rho$ density, $E$ youngs modulus and $nu$ poissons ratio.

Figure 68-Material Card LAW2.

Figure 69-Changed to Material Card LAW1.

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 70.

Figure 70-Animation Files Obtained.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 71.

Figure 71-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error- -7.4%

$***$ Internal Energy-0.7195E+06

$***$ Kinetic Energy-425.7

$***$ External Work-0.7780E+06

$***$ Mass Error-0

$***$ Elapsed Time- 117.85s

$***$ Total No of Cycles-47900

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 72.
Here EPS_P_Max=0,So the shell elements will not be deleted which is shown in below Figure 72.
The elements will not even split during the collison,Cause the LAW1 material card is assigned to the rupture plate.
So there will be an elastic behaviour[Ability to regain its original size and shape].

Figure 72-Case 5 Simulation Animaton.

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 73.

Rigid Wall Forces :

Here the rigid wall forces starts from origin cause there will be no contact in the beginning and it goes on increasing cause deformation is happening to the plate.
And the elements not getting deleted here,So its goes on increasing till to end.

Figure 73-Rigid Wall Forces Graph.

Internal Eenergy :

Here the internal energy starts from origin because in the beginning ,the rigid ball is not in contact to the plate.
Its increasing when the rigid ball hits the rupture plate,its goes on increasing.
The graph obtained for internal energy is shown in below Figure 74.

Figure 74-Internal Energy Graph.

Kinetic Energy :

Here kinetic energy is in initial condition,so its starts from origin.
It increases when the rigid ball hits the rupture plate.
And its slighlty decreasing,because after hitting the rupture plate,the rigid ball goes back to its position and there will be no contact.

Figure 75-Kinetic Energy Graph.

Total Energy:

The total energy increases with the increase in kinetic energy and internal energy,The graph obtained for total energy is shown in below Figure 76.

Figure 76-Total Energy Graph.

Hourglass and Contact Energy :

Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.
Simillarly as same as for case-5.
Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.
The obtained hourglass and contact energy graph is shown in below Figure 77.

Figure 77-Hourglass and Contact Energy Graph.

Case 6-Change the Material Card to LAW27 :

Here change the material card to LAW27 and change the shell properties to the recommended shell peroperties.
It is an isotropic elastoplastic jhonson cook material model with an orthographic brittle failure model.

Figure 78- Material Card Properties.

Now change the parameters which is shown in below Figure 79.

Figure 79-Changed to Recommended Parameters.

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 80.

Figure 80-Animation Files Obtained.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 81.

Figure 81-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error- 0.8%

$***$ Internal Energy-0.2954E+05

$***$ Kinetic Energy-65

$***$ External Work-0.2940E+05

$***$ Mass Error-0

$***$ Elapsed Time- 155.47s

$***$ Total No of Cycles-49506

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 82.
Here the shell elements will be deleted due to brittleness which is shown in below Figure 82.

Figure 82-Case 6 LAW27 Simulation Animation.

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 83.

Rigid Wall Forces :

The rigid wall forces starts increasing due to impact and decreases gradually,Because the elements are getting deleted and there will be no contact.
The rigid wall forces graph obtained is shown in below Figure 83.

Figure 83-Rigid Wall Forces Graph.

Internal Energy :

Figure 84-Internal Energy Graph.

Here the internal energy is similar to the previous case-3,The obtained internal energy graph is shown in above Figure 84.

Kinetic Energy :

Figure 85-Kinetic Energy Graph.

Here the kinetic energy obtained is somewhat similar to the case-3 kinetic energy,The kinetic energy obtained is shown in above Figure 85.

Total Energy :

Figure 86-Total Energy Error.

The total energy increase with increase in internal energy and kinetic energy,The obtained total energy graph is shown in below Figure 86.

Hourglass and Contact Energy :

Figure 87-Hourglass and Contact Energy Graph.

Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.
Simillarly as same as for case-6.
Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.
The obtained hourglass and contact energy graph is shown in above Figure 87.

Case 7- Change the Material Card to LAW36 :

Here change the material card to LAW36.
A shell paremeters are changed to the recommended parameters.
It's a elasto plastic piecewise linear material.

Figure 88-Material Card Properties.

Figure 89-Changed Material Card and Shell Element Parametrs.

After Defining the material card,We have to define a stress strain curve for this material.
We only want plastic region out of it,So we have to define a curve using given plastic strain and post-yield stress value manually.
The curve will be defined based on the values given which is shown in below Figure 90.

Figure 90-Plastic Strains and Post Yield Stress Values.

To create a Curve,Right Click on the Model Browser >> Create >> Curve >> Window Will Pop Up >> Define a Curve using Platic Strains and Post-Yield Stress Values.

Figure 91-Steps to Create a Curve.

Figure 92-Curve Defined with Plastic Strains and Post-Yield Stress Values.

[Note:For this material,we need only plastic region,So thats the reason we are defining only plasticity with the Plastic Strains and Post-Yield Stress Values.]

Now run the simulation using radioss,After running the simulation,The animation and TH files will be obtained in a required location,which is shown in below Figure 93.

Figure 93-Obtained Animation Files.

Now go and open the 00001.out file with notepad.
The obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error has been shown in below Figure 94.

Figure 94-Obtained values for Energy Error,Mass Error,Internal Energy Error,Kinetic Energy Error and Contact Energy Error.

The values obtained for this cycle are

$***$ Energy Error- 0.7%

$***$ Internal Energy-0.7078E+05

$***$ Kinetic Energy-21.31

$***$ External Work-0.7046E+05

$***$ Mass Error-0

$***$ Elapsed Time-143.60s

$***$ Total No of Cycles-49053

1) Review the Simulation using -HyperView.

After completion of running the simulation,Switch to the hyperview.
Open the appropriate .h3d file to review the simulation.
The .h3d file is loaded and it is shown in below Figure 95.
Here the shell elements will be deleted once it reaches maximum plastic strain which is shown in below Figure 95.
Cause the material is assigned with both elastic and plastic.

Figure 95-Case 7 Simulation Animation.

2) Plot the graphs using-Hypergraph 2D.

Now switch to the Hypergraph 2D and plot the graphs.
The rigid wall forces graph is plotted which is shown in below Figure 83.

Rigid Wall Forces :

Similarly as explained for the above case-1.The graph obtained for the rigid wall forces is shown in below Figure 96.
Here the elements are getting when it reaches maximum plastic strain.

Figure 96-Rigid Wall Forces Graph.

Internal Energy :

The internal increases as same as in previous case.
The obtained graph for internal energy is shown in below Figure 97.

Figure 97-Internal Energy Graph.

Kinetic Energy :

The kinetic energy is somewhat similar to the case-5.
The obtained kinetic energy graph is shown in below Figure 98.

Figure 98-Kinetic Energy Graph.

Total Energy :

The total energy increases with increase in internal energy and kinetic energy.
The obtained graoh for total energy is shown in below Figure 99.

Figure 99-Total Energy Graph.

Hourglass and Contact Energy :

Here hourglass energy is constant due to recommended parameters have been assigned.Here Ishell=24 QEPH is used,Due to this there is no houglass effect.
Simillarly as same as for case-7.
Because the rigid ball is rigid body and the rupture plate is deformable body,So the contact energy is constant.
If deformable bodies get in contact,then only the contact energy increases.
The obtained hourglass and contact energy graph is shown in below Figure 100.

Figure 100-Hourglass and Contact Energy Graph.

Comparison of all the 7 Cases :

Cases	Energy Error	Internal Energy	Kinetic Energy	External Work	Mass Error	Elapsed Time	Total Number of Cycles	Material Used	Changes in Material Parameters	Element Failure Behaviour
Case-1	0.8%	0.2730E+05	67.81	0.2721E+05	0	95.36s	49380	Jhoonson-Cook [LAW2]	Used Default Shell Parameters and Runned the Simulation.	Elements Deleted.
Case-2	4.1%	0.3082E+05	141.9	0.2980E+05	0	134.34s	49217	Jhoonson-Cook [LAW2]	Changed the Values for Ifail_sh,Dadv,Ixfem in the Failure Card.	Elements will be Cracked and Deleted.
Case-3	0.8%	0.2744E+05	87.08	0.2736E+05	0	96.79 s	49407	Jhoonson-Cook [LAW2]	Deleted the Failure Card from the Model Browser.	Elements Deleted.
Case-4	1.1%	0.3879E+05	3.931	0.3838E+05	0	131.47s	49303	Jhoonson-Cook [LAW2]	Changed the Value for Maximum Plastic Strain [Eps_Max=0].	Elements Deformed,Cracked but not Deleted.
Case-5	7.4%	0.7195E+06	425.7	0.7780E+06	0	117.85s	47900	Elastic [LAW1]	Changed the Material Card to LAW1 and Kept the Same Material Properties.	Elements Deformed,Cracked but not Deleted.
Case-6	0.8%	0.2954E+05	65	0.2940E+05	0	155.47s	49506	Elasto-Plastic-Brittle [LAW27]	Assigned the Rupture Parameters for the Plate and Used Recommended Element Parameters.	Elements Deleted.
Case-7	0.7%	0.7078E+05	21.31	0.7046E+05	0	143.60s	49053	Elasto-Plastic-Tabulated [LAW36].	Created a Plastic Stress Strain Curve by Using Plastic Strains and Yield Stress Values.	Elements Deleted.

Table-1

Damage and Rupture Parameters :

Figure 101-Stress Strain Curve.

εpmax is the maximum plastic strain for element deletion for any loading (tensile , shear or compression).
εt is the beginning of tensile damage. From this point the stress value defined in the curve is reduced by the factor.
Where ε1 is the largest principal strain $sigma=sigma( frac{varepsilon_m-varepsilon_1}{varepsilon_m-varepsilon_t})$ .
εm is the end of the tensile damage. The stress value is null, but the element is not deleted.
εf is the tensile failure strain value for element deletion.

Final Images :

Figure 101-Final Images.

Result :

Hence the simulation for all the cases were carried out with different materials laws.
Hence the simulation for all the cases were runned successfully.
Hence the simulation for all the cases were reviewed by hyperview.
Hence the graphs were plotted for all the cases successfully.
Atlast,Compared all the results for those cases.

Conclusion and Learning Outcome :

I conclude that LAW 36 is more suitable in real world testings,Cause it shows the behaviour of Elasticity and Plasticity in real world.
In this challenge,I came to know bout
The different materials cards and their behaviour.
The failure criteria for the material cards.
How the deformation is happening for the elements from material cards.
Damage and rupture parameters.
How to define a plastic region curve with plastic starin and post-yield stress values.