Challenge

Assignment 4-RADIOSS Material Laws Challenge

BB Pavan Kumar3 Apr 2021

1. Objective:

To apply the various cases as mentioned in the above question on the given failure johnson cook material.
To plot the graphs(Post-processing) with respect to the obatined values from those cases.
To compare the obtained results, from those cases.

2. Software used: Altair Hyperworks Desktop 2020.

3. User profile: Radioss

4. Pre-requisites:

In general, the purpose of a material is to indicate some parameters such as thickness, density, youngs modulus etc., of a component. When a material is known, So many aspects can have a solution. Like what type of analysis can be perfomed( Which includes the behavior of the material when any external forces applied on it). So, a material plays a prominent role.

In the same scenario, the materials should be specified in radioss also. Inorder to analyze it's behavior. In radioss, the materials are categorized in two ways. They are:

Based on the form of material cards.
Based on the material property categories.

Based on the form of material cards:-

In this method, there are so many material cards(represented in the form of laws). But Some of them are widely used in radioss, Because they were tested priorly. They are:

Law 1 (Used to represent the elastic materials)
Law 2 (Used to represent the Johnson-cook material).
Law 27(Used to represent the Elasic-plastic brittle materials).
Law 36(Used to represent the Elastic-plastic tabulated materials).
Law 42(Used to represent the ogden materials).
Law 70(Used to represent the foam materials).

Based on the material property categories:-

There are some majorly used materials, that are specified by the property of the materials. They are:

Isotropic elastic materials
Isotropic Elasto-plastic materials
Composite & Anisotropic materials
Viscous materials
Hydro-dynamic materials
Explosives

These are explained by combining them, below.

Isotropic elastic (Law 1):-

The meaning of isotropic is "A material which exhibits the same properties in all directions". And elastic means " A material which has an ability to regain its original shape, when the applied load is removed". So, this law suggests the material which possess both isotropic & elactic properties.
These materials are represented by Law 1.
This law is applicable for trusses, beams(Type 3only), shell & solid elements.
Applicable only for the elastic materials.
This law is applicable only for small deformations.

Description	Model name	Key word/MAT	Model Law
Linear elastic	Elastic( Obeys Hooke's law)	/ELAST	1
Hyper elastic	Tabulated hyper elastic	n/a	69
Hyper eleastic	ogden	n/a	82

Isotropic elasto-plasic(Law 2 & Law 36):-

This law represents the materials that possess both elastic & plastic properties along with isotropic properties.
This model expresses the material stress as a function of strain, strain rate & temperature.
In crash, temperature change is neglected. To simplify some of the calculation, for this material the graph is plotted from the yield point.

Where: `sigma`---> Stress

`varepsilon`p ---> Plastic strain

a ---> yield stress

b ---> Hardening modulus( Which depicts how well the curve bends).

n ---> Hardening exponent(Which depicts how quickly the curve bends from vertical to horizontal direction.

c ---> strain rate co-efficient(Says after changing the strain rate, what about factor of changes done to stress).

`varepsilon`. ---> represents the strain rate.

`varepsilon`o ---> represents the reference strain rate.

And majorly, We will go with only plastic strain(i.e., if there is no data regarding strain rate, it will be neglected). So, the a, b, n values should be calculated.

We can represent this model in two ways:-

By a,b,n values & eps_max(i.e., plastic strain).
By a,b,n values & D1, D2, D3, Ixfem.

In this second way, The Ixfem depicts that, how to fail the elements & material. It is explained in the below table:

Ixfem=0	Simply deleting the elements.
Ixfem=1	It will break the element, as per the given force& load conditions.

From the results the thing noticed is, the energy is dissipated better in a elasto-plastic material (i.e., with less stresses in generated). If we use failure value eps_max, we will get more accurate result.

Note: Ixfem is applicable only for shell elements.

Isotropic elastic plastic piecewise linear material(Law 36):-

It is represented in the form of PLAS_TAB.
The main advantage with this material card is, The lab data which is realistic can be given to the software in the form of stress-strain curve(i.e., We can create the new curves with respect to the values obtained from the lab & feed in to the software).
The limitation with this material card is, We can't predict the strain rates. But, this material card allows us to import the user-defined functions(Which are tested in the lab).
This is the most widely used material model in industriesat present.
It can be used for all types of elements(Shell & brick elements).
Higher the curve, Higher the strain rate, But earlier the failure takes place.
It had an advantage that, the johnson cook failure model can be added to it.

There are some parameters such as:

`varepsilon`t---> Tensile failue plastic strain(Once this point is reached, solver will reduce the stress to zero). It indicates the beginning of tensile damage.

`varepsilon`m---> It indicates, by the time(or) moment the stress becomes zero. From here, there is no more energy that can be absorbed by the element or material. If the strain is even increasing, it reaches till `varepsilon`f.

`varepsilon`f---> This is the point where element is deleted.

Idp---> This indicates the graph between yield stress & pressure. It is used to distinguish the behavior in tension & compression for certain materials.(i.e., pressure dependent yield).

Elasto-plastic isotropic material(/PLAS_BRIT/LAW 27):-

This is the special material card for brittle materials like aluminium & glass etc.
This law combines an isotropic elasto-plastic johnson-cook material with an orthographic brittle failure model.
Material damage is accounted even before failure.
Failure & damage occurs only in tension.
This material card is applicable only for shell elements.
Damage & rupture is defined with 4 parameters for each principal direction. They are: `varepsilon`t,`varepsilon`m,`varepsilon`f, Dmax. Where Dmax is the maximum damage factor(Which accelerates the falure of element).

Viscous materials:-

The viscous materials is classified in to two types. They are;

Model name: Hyper elastic

Keyword: /MAT/OGDEN

Law No: 42

Hyper elastic behavior means "Non-linear elastic". Generally, used to model polymers & elastomers.

2. Model name: Tabilated hyper visco-elastic

Keyword: /MAT/FOAM_TAB

Law No: 70

Law 70 material card is used for the applications with foam material. Foam material has an advantage, absorbs the energy with out developing the stress.

5. Procedure:

Case 1 (Running the simulation without any change):-

Initially, after opening the hyperworks software the user profile should be selected. For this challenge since analysis should be performed, Radioss is choosed as an user profile. After choosing the user profile, The solver deck should be imported. The file should be selected & cilck on import as shown in fig 5.1

fig 5.1

After importing the solver deck, the model appears in the graphical display as shown in fig 5.2.

fig 5.2

As it is seen in wireframe mode for better visualization, enable the option named "Shaded elements with mesh lines". After enabling it, the given model appears as shown in fig 5.3.

fig 5.3

Then in the solver browser some cards are verified, inorder to have clarity on some aspects. Among them, the first card to be checked is "Begin card". Inorder to check for the unit system. The unit system plays a prominent role for assigning all of the values. The unit system for this appears as shown in fig 5.4.

fig 5.4

The material card is the next card to be verified, inorder to see the properties assigned to the material. The material card appears as shown in fig 5.5.

fig 5.5

Next card to be verified is property card. In property card, the properties assigned to the given material is seen. The property card with the assigned parameters appears as shown in fig 5.6.

fig 5.6

As mentioned, this case is to be runned as usually with the base values. i.e., running the model without changing any value. The model can be runned with the help of command named "radioss" in the analysis panel. After opening the radioss panel, the file should be assigned with in some location. Then by clicking "save as", the files will be saved in that locations.

To increase the speed of the simulation, in the options bar which is highlighted in the fig 5.7, a value entered as "-nt 4", in which nt depicts the number of threads. And 4 depicts the number cores in the system takes the task simultaneously. Then click on "Radioss" to run the model.

fig 5.7

It takes few moments to run the simulation and generate the animation files, time history files. After completing the job of the radioss, a pop-up appears as shown in fig 5.8.

Note: Those animation files, time history files & all essential files are stored in the location that has been choosed as a path which was choosed before running.

fig 5.8

As the running is completed, the location which is assigned before running. In that location, the files are stored. These files in that specified location appears as shown in fig 5.9

fig 5.9

Among those files, the 0001.out file is opened in the notepad++, which indicates the results in the form of numerical values(such as energy error, mass error, kinetic energy, internal energy, etc) as shown in fig 5.10.

fig 5.10

The obtained last cycle values are:

energy error = 0.8%

Internal energy = 0.2730E+05 KJ

Kinetic energy = 67.81 KJ

External work = 0.2721E+05 KJ

Mass error = 0

elapsed time = 112.27 s

Total number of cycles = 49380

Then the 0001.rad file is opened in the note pad, which shows the Tfrequency, run time(Tstop) values as shown in fig 5.11.

fig 5.11

The next step is to view the simulation. This is done by switching on to other window. In this window, the h3d file is imported and applied in the hyperview. The hyperview panel appears as shown in fig 5.12.

Note:

Always when we switched on to new window, the hyperview panel is enabled by default. To plot the graphs(i.e., post processing), the hypergraph 2D panel should be enabled by the user.
The h3d file is a combination of all animation files.

fig 5.12

After importing the h3d file in the hyperview panel, the model in the graphical display appears as shown in fig 5.13.

fig 5.13

To run the simulation, the contour panel should be enabled. Which appears as shown in fig 5.14. In this panel, the parameters such as result type as von misses, selection of components, selection of averaging method, and clicking on apply.

fig 5.14

After applying, the model is ready for simulation. The obtained simulation appears as shown in the below animation. Which results in deleting the elements, because the circular plate is assigned with the law 2. As it is assigned with material law 2, the plate possess both elastic & plastic behavior. The maximum von-mises stress is seen in the below animation.

Post-processing:

The next step is to do the post-processing, by plotting the obtained results in the form of various graphs. The first graph to be plotted is rigid wall forces. This is done by switcing in to the new window & enabling the Hypergraph 2D panel. In this panel, T01(Time history) file is impoted. And the parameters required for obtaining the result with respect to the rigid wall are selected as shown in fig 5.15.

fig 5.15

After selecting to apply, a pop-up appears as shown in fig 5.16. Which depicts to mention the unit system. As per the unit system seen in begin card from solver browser, the units selected are length(milli meter), Time(milli seconds), Mass(grams).

fig 5.16

Soon after applying the unit system, the graph is plotted which indicates the rigid wall total resultant force as shown in fig 5.17. Initially, the elemnts start observing the energy, when the spherical shaped rigid sphere hits the given component(Plate shaped). And due to this energy absobtion, the forces will reach till a peak value as shown in fig 5.17. And after reaching the peak value, the elements will start deleting, Which is shown in the fall of the rigid wall forces.

fig 5.17

The next step is to plot the graph for the energies such internal energy, kinetic energy, Total energy, hourglass energy. So for that, the parameters are selected in the hypergraph 2D panel as shown in fig 5.18. This should be done in the new window.

fig 5.18

The obtained graph with respect to the requested energies appears as shown in fig 5.19. As in this case the johson cook material with the law 2 is applied and represented by a,b,n, eps_max(plastic strain), the elements get deleted. The reasons for the obtaining the below graph are explained bekow:

Usually the internal energy energy starts from the origin, And it increases because of the increase in displacement.
The kinetic energy will slightly vary at the time of element breakage.
The total energy is the combination of all energies. So, it will increase as shown in fig 5.19.
The hourglass energy is constant through out the process. Because, the property card is assigned with the recommended values such as Ishell:24, Ismstr:2, Ish3n:2, Iplas:1, Ithick:1, N=5.

fig 5.19

Case 2(Changing the values in failure card):-

In this case, the failure card is edited with respect to the given values. But the material law is same(i.e., law 2). Before changing the values in the failure card, it appears as shown in fig 5.20. The values to be changed are Ifail_sh = 1, Dadv = 1, Ixfem = 1.

fig 5.20

After changing the values in the failure card, it appears as shown in fig 5.21.

fig 5.21

The next step is to run the simulation by using the radioss. After running the simulation, the obtained files(Animation files, time history files) in the specified location appears as shown in fig 5.22.

fig 5.22

The next step is to view the 0001.out file. Inorder to check for the energy errors, mass errors, etc. The 0001.out file with the maximum values are shown in fig 5.23.

fig 5.23

The obtained last cycle values are:

energy error = 0.2%

Internal energy = 0.2708E+05 KJ

Kinetic energy = 113 .6 KJ

External work = 0.2721E+05 KJ

Mass error = 0

elapsed time = 114.38 s

Total number of cycles = 49217

The obtained h3d file is imported in the hyperview, inorder to simulate. The obtained simulation appears as shown in the below animation.

Post-processing:

The obtained rigid wall foce is represented in the form of a graph as shown in fig 5.24. The total resultant force reches to a peak value due to the impact of the rigid sphere towards the circular plate.

fig 5.24

The obtained graph for internal energy appears as shown in fig 5.25. As usually, the internal energy starts from the origin & the reaches to the peak value & after the breakage of elements, it reduces by a bit as shown in fig 5.25.

fig 5.25

The obtained kinetic energy graph appears as shown in fig 5.26. Here the kinetic energy starts varying right from the beginning.

fig 5.26

As the property assigned is with the recommended parameters such as the QEPH element with Ishell:24 is used, there will be no hourglass energy(Because, it will have integrated hourglass enenrgy). So, the hourglass energy is constant as shown in fig 5.27.

fig 5.27

Total energy increases with the increase in internal energy & kinetic energy. The obtained total energy appears as shown in fig 5.28.

fig 5.28

The contact energy also remains constant in all of the cases. Because the contacts are not specified.

Case 3(Deleting the failure johnson card):-

In this case, the failure card as shown in fig 5.29 is deleted to see any changes in the result.

fig 5.29

After deleting that card, the remaining cards appears as shown in fig 5.30

fig 5.30

Now, the simulation is runned without changing any further parameters. After running it, the files obtained in the saved location are shownin fig 5.31.

fig 5.31

Then by opening the 0001.out file energy errors, mass errors, etc. The 0001.out file with the maximum values are shown in fig 5.32.

fig 5.32

The obtained maximum values are:

energy error = 0.8%

Internal energy = 0.2744E+05 KJ

Kinetic energy = 87.08 KJ

External work = 0.2736E+05 KJ

Mass error = 0

elapsed time = 112.73 s

Total number of cycles = 49408

Then the obtained h3d file is imported in the another window, In order to view the simulation. The obtained simulation in terms of von-mises is shown in below animation.

From the above animation, noticed thing is that, the elements break because, the circular plate is assigned with elasto-plastic material.

Post-processing:

The next step is to view the results, by the obtained graphs. These graphs are obtained by importing the obtained T01 file in the next window. Initially, the rigid wall forces are obtained. The obtained graph is shown in fig 5.33.

fig 5.33

Then the internal energy is plotted, it appears as shown in fig 5.34. This will be some what similar to the previous cases.

fig 5.34

Then the kinetic energy graph is obtained, which appears as shown in fig 5.35. In this case the obtained kinetic energy will be some what less when compared to the case 2.

fig 5.35

fig 5.36

Total energy increases with the increase in internal energy & kinetic energy. The obtained total energy appears as shown in fig 5.37.

fig 5.37

Case 4(Deleting the eps_max value from the material card):-

In this case for the same material card, the plastic strain(eps_max) value which is 0.151 as shown in fig 5.38, is removed(eps_max).

fig 5.38

After removing the value for plasic strain, the material card appears as shown in fig 5.39.

fig 5.39

Then the simulation is runned using radioss. After running the obtained animation files stored in the specified location appears as shown in fig 5.40.

fig 5.40

Then the obtained 0001.out file is opened. In order to view the obtained results in the form of values. The obtained values for last cycles are shown in fig 5.41.

fig 5.41

The obtained last cycle values are:

energy error = 1.1%

Internal energy = 0.3879E+05 KJ

Kinetic energy = 3.931 KJ

External work = 0.3838E+05 KJ

Mass error = 0

elapsed time = 141.41 s

Total number of cycles = 49304

Then the obtained h3d file is imported in the another window, In order to view the simulation. The obtained simulation in terms of von-mises is shown in below animation. As the eps_max value (plastic strain) is zero, the elements will not break.

The elements are not getting deleted.

Post processing:

The obtained rigid wall force graph appears as shown in fig 5. 42. The rigid wall force increases & decreases gradually. And reshes to the peak value at the last moment of collision & decreases.

fig 5.42

Then the internal energy is plotted, it appears as shown in fig 5.43. This will be some what similar to the previous cases.

fig 5.43

The obtained kinetic energy is plotted as shown in fig 5.44. And is similar to that of previus cases.

fig 5.44

fig 5.45

The obtained total energy graph appears as shown in fig 5.46. The total energy follows the internal energy & kinetic energy. So, there will be an increase in total energy.

fig 5.46

Case 5(Changing the material card to law 1):-

In this case, the material law is changed to law 1, which possess only the elastic behavior. Before changing the material law, it was in material law 2, as shown in fig 5.47.

fig 5.47

After changing the material card, it appears as shown in fig 5.48. And the values of E, `rho`, `mu` will remain the same.

fig 5.48

Then the simulation is runned. After running the smulation, the obtained animation files appears as shown in fig 5.49.

fig 5.49

Then the obtained 0001.out file is opened, inorder to view the energy errors, mass errors. The obtained values are shown in fig 5.50.

fig 5.50

The obtained values for last cycle are:

energy error = 1.3%

Internal energy = 0.8632E+06 KJ

Kinetic energy = 1677 KJ

External work = 0.8568E+06 KJ

Mass error = 0

elapsed time = 107.94 s

Total number of cycles = 47969

Then the obtained h3d file is imported in the another window, In order to view the simulation. The obtained simulation in terms of von-mises is shown in below animation. The elements will not even split during the collision. Because, the law 1 is assigned to the circular plate. So, it possess the elasticity (i.e., abitlity to regain its original size & shape).

Post-processing:

Then the graphs are plotted to view the results. The total resultant force of the rigid wall force increases gradually till the end. Because, there is no plastic behavior seen in this case. The obtained rigid wall force graph appears as shown in fig 5.51.

fig 5.51

Then the internal energy graph is obtained, as shown in fig 5.52. Internal energy also increases gradually. But the graph will be some what dissimilar to that of the previous cases.

fig 5.52

Then the kinetic energy is plotted, appears as shown in fig 5.53. Initially, the kinetic energy is constant. And it varies when the rigid sphere hits the circular plate & it reaches to the peak value when the elements absorbs the more energy at the end of collision.

fig 5.53

fig 5.54

Total energy increases with the increase in internal energy & kinetic energy. The obtained total energy appears as shown in fig 5.55. And it keeps on increasing just similar to the internal energy. And the graphvaries when compared to the other cases.

fig 5.55

Case 6(Changing the material card to law 36 & parameters in the properrty card):-

In this case, the material card is changed to law 36(possess elasto-plastic piecewise linear material). And the shell parameters in the property card are changed to the recommended properties. Before changing the parameters, the property card appears as shown in fig 5.56.

fig 5.56

After changing the values, the material card appears as shown in fig 5.57.

fig 5.57

While defining the material card as law 36, a function should be represented to define the curves. Initially, there will be some curves are defined. But a new curve is defined, the values are given by the user as shwon in fig 5.58. A curve will be generated based on the given values.

fig 5.58

Higher the curve---> Higher the strain rate---> But earlier the failure takes place.

The process of creating the curve is: create---> curve---> New---> assign a name---> proceed---> shows the curve with values & graph.

Then the simulation is runned, by using radioss. After running the simulation, the 0001.out file is opened to view the obtained results in the form of values, as shown in fig 5.59.

fig 5.59

The obtained values for last cycle are:

energy error = 1.4%

Internal energy = 0.4326E+05 KJ

Kinetic energy = 159.4 KJ

External work = 0.4426E+06 KJ

Mass error = 0

elapsed time = 121.3s

Total number of cycles = 53202

Then the obtained h3d file is imported in the another window, In order to view the simulation. The obtained simulation in terms of von-mises is shown in below animation.

In this case also the elements will break. Beacuse, the material card assigned possess both elastic & plastic material.

Post-processing:

The rigid wall forces obtained are shown in the form of graph as shown in fig 5.60.

fig 5.60

The obtained internal energy in the form of graph appears as shown in fig 5.61. The internal energy increases gradually same as in previous case.

fig 5.61

Then the obtained kinetic energy graph is plotted, shown in fig 5.62.

fig 5.62

fig 5.63

Total energy increases with the increase in internal energy & kinetic energy. The obtained total energy appears as shown in fig 5.64. And it keeps on increasing just similar to the internal energy.

fig 5.64

Case 7(Changing the material card to law 27):-

In this case, the material card is changed to law 27(Which possess brittleness) & to change the parameters in the property card with the recommended values. For example: like aluminium & glass etc. This law combines the elasto-plastic johnson-cook material with an orthographic brittle failure model. Before changing the parameters, the property card appears as shown in fig 5.65.

fig 5.65

After changing the parameters in the property card, it appears as shown in fig 5.66.

fig 5.66

Then the simulation is runned. After running the simulation, the obtained animation files in the specified location appears as shown in fig 5.67.

fig 5.67

Then the 00001.out file is opened, inorder to view the energy errors, mass errors. The obtained values are shown in fig 5.68.

fig 5.68

The obtained values for last cycle are:

energy error = 0.7%

Internal energy = 0.2936E+05 KJ

Kinetic energy = 53.59 KJ

External work = 0.2927E+05 KJ

Mass error = 0

elapsed time = 112.75 s

Total number of cycles = 49468

Then the obtained h3d file is imported in the another window, In order to view the simulation. The obtained simulation in terms of von-mises is shown in below animation. Here the elements will break due to its brittle property.

Post-processing:

The obtained rigid wall forces graph appears as shown in fig 5.69. The rigid wall forces will reach a peak value at the time of impact and decreases gradually.

fig 5.69

Then the obtained internal energy is plotted, as shown in fig 5.70.

fig 5.70

The obtained kinetic energy is plotted, shown in fig 5.71.

fig 5.71

fig 5.72

Total energy increases with the increase in internal energy & kinetic energy. The obtained total energy appears as shown in fig 5.73. And it keeps on increasing just similar to the internal energy.

fig 5.73

Comparsion of 7 cases:

Basis of comparsion	case 1	case 2	case 3	case 4	case 5	case 6	case 7
energy error(%)	0.8%	0.2%	0.8%	1.1%	1.3%	1.4%	0.7%
Internal energy(KJ)	0.2730E+05	0.2708E+05	0.2744E+05	0.3879E+05	0.8632E+06	0.4326E+05	0.2936E+05
Kinetic energy(KJ)	67.81	113 .6	87.08	3.931	1677	159.4	53.59
External work(KJ)	0.2721E+05	0.2721E+05	0.2736E+05	0.3838E+05	0.8568E+06	0.4426E+06	0.2927E+05
Mass error	0	0	0	0	0	0	0
elapsed time(S)	112.27	114.38	112.73	141.41	107.94	121.3	112.75
Total number of cycles	49380	49217	49408	49304	47969	53202	49468
Elements deletion	will be deleted	will be deleted	will be deleted	will not be deleted	will not be deleted	will be deleted	will be deleted
Material law used	Law 2 with a, b,n values	Law 2 by changing the value in failure card	Law 2 by deleting the failure johnson card	Law 2 by removing plastic strain(eps_max) value	Law 1	Law 36	Law 27

6. Conclusion:

Applied the various cases as mentioned in the above question on the given failure johnson cook material.
Plotted the graphs(Post-processing) with respect to the obatined values from those cases.
Finally, compared the obtained results from those cases.

Assignment 4-RADIOSS Material Laws Challenge

Ship work like this
in your own course.

Talk to a career counsellor

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.