Study Different material models available in Radioss workbench. Apply that material cards on the body (part ) and study the behavior of that body (part) due to the respective material card.

Aim:- Study Different material models available in Radioss workbench. Apply that material cards on the body (part ) and study the behavior of that body (part) due to the respective material card.

Objective:-

1) Set the model under different LAW (Material IDs) and run the simulation for that.

2) Collect data in the form of videos and graphs.

3)Compare the OUT file (Engine output file) of each case and find out the Total number of cycles, Energy error, mass error, and simulation time.

 

In this assignment, I had got a .rad file named "FAILURE_JOHNSON_0000" and "LAW_27" contained one plate and Rigid ball. For this, I had Set 8 different cases and in the further report, I am gone go through all those cases. In this section, we will be seeing the different behavior of the plate when applying for different material cards.

                                FIG 01

The above image you can see the Different material cards under the card image also the properties related to the cards. Different Card has different sort of properties or input requirement so you can find different option get activated each time you select the different material card.

The Radioss Platform provides us a huge gallery of the material card/ LAWs of each sort of material existed, but we are going through only a few of them that are used in the daily application based simulation,

1)LAW-1 / M1_ELAST:- Elastic material

2)LAW-2 / M2_PLAS_JOHNS_ZERIL:- Elasto-Plastic material

3) LAW 27 / M27_PLAS_BRIT:- Brittle material

4)LAW 36 / M36_PLAS_TAB :- Elasto-Plastic material

Of all four of them, LAW 2 and LAW 36 are mostly used.

1)LAW1:-

-It defined the isotropic linear material behavior under the Hooks law. means material behavior within its elastic limits.

-It's applicable for truss, beam, shell as well as a brick (3d element). Mostly purely elastic material.

-If we applied this material card/ model to any 3D model (FE model) its behaves as ideal elastic means it will not show any teardown or rupture even after it crosses its max stress limit.  

-The Key parameters in this LAW are

`rho` = Density of the material

E= Youngs Modulus

`mu` = Poisons Ratio

G= Modulus of rigidity

-Mostly used for vibration and static types of analysis

2)LAW-2 / M2_PLAS_JOHNS_ZERIL:- Elasto-Plastic material

-This LAW represents an Isotopic Elasto-Plastic Material using the Johnson-Cook material model.

b= represents how the curve after the yield bends

n=how quickly the curve can bend.

-LAW 2 express material as a function of strain, strain rate, and temperature as you can see in the above formula. In most of the crash test scenario where strain rate and temperature data is hard to obtain or not available we can avoid that terms,

`sigma = (a + b *epsi^n)`

 [Determine Johnson Cooks parameters a,b, and n 

    To calculate these terms we need the true stress-strain values and we can calculate them from the Engineering Stress-strain curve data.

   -The True Yield stress is approximately equal to the Engineering Yield stress.  

   - True strain is equal to the natural log of one plus Engineering strain.

      `epsi_T = ln (1+epsi_E)`

   -True stress equal to the product of Engineering stress and exponent of the True strain

       `sigma_T = sigma_E * exp (epsi_T)`

       `sigma_T = sigma_E * (1+ epsi _E)`

    - From these true stress, strain, and Yield stress values we can easily calculate the Johnson Cooks parameter

       `a = sigma_y`

       `n = (sigma_T * epsi_T) / (sigma_T- sigma_y)`

       `b= (sigma_T) / (n* epsi_T^(n-1))`    ]

-The Johnson cook model comes with one failure method named "failure johnson" it will give more accurate results during the compression test as it contains a special option that allows cracking representation. But it only applicable for shell elements. If we only have data about D1, D2, D3 parameter instead of EPS_p_max we can very well perform the simulation using the failure card parameters.

The Key parameters of the LAW 2 material Card.

`rho` = Density of the material             

E = Youngs Modulus                               

`mu` = Poisons Ratio

`sigma_y` = Yield stress

EPS_p_max = represents the maximum strain value after which material will fail(rapture point). The material will fail for strain when its value reaches or cross to the EPS_p_max value. It considers in percentage but represents in decimal value. e.g. if you want to set max strain value to 70% we will represent it as 0.7 in the property window. lower the value earlier the material will fail.

Sig_max =it is an indicator of the max stress value. The material will fail for Stress when its value reaches or cross to the Sig_max value.

The Key parameters of the LAW 2 Failure Johnson material Card.

D1, D2, D3 = This determines what strain mode is needed for element break. These are the ideal values that are got from the Lab test.

Ifail_sh = is set to be 2 so we get the tensor stress at each integration point equal to zero.

Dadv= Creation of Crack advancement. Only activated with Ixfem

Ixfem = this will allow the user to the defined mode of element/ material failure. it is more of a representation type of option, with this user can define if he wants Crack sort of representation or direct element deletion where they are failing. There are two options available in Ixfem,

0= Default (Without Ixfem formulation). Direct delete the elements which are failing.

1= With Ixfem formulation. Represent a Crack formation.

3) LAW 27 / M27_PLAS_BRIT:- Brittle material

-This is a special material card for Brittle Material. 

-As we know the brittle material will fail much quicker. This law combines the isotropic Elasto-plastic Johnson cook material model with an Orthotropic brittle failure model.

-This law only applies to shell elements.

-Key parameters

`epsi_t` = Strain at the Beginning of the tensile Failure.

`epsi_m`= max tensile strain at which the stress in the element is set to the value depend on d_max1.

d_max1 = Factor that accelerates the failure of the elements.

`epsi_f` = Max tensile strain of element Deleteation.

4)LAW 36 / M36_PLAS_TAB :- Elasto-Plastic material

- This is the most commonly used material model after LAW2 for Elaso plastic material.

-It gives the result closed to the actual lab data at different strain rates.

-This Law model an isotropic elsto-plastic material using the user-defined function for the work hardening portion of the stress-strain curve and the elastic portion of the material defined by Young's modulus and poisons ratio.

 - Users take the lab data of material under different strain rates. This data may be a value or a simply stress-strain curve. we put this lab data at various strain rate under user-defined function while creating this LAW 36/ M36_PLAS_TAB model

-Users can very well use the Johnson failure model in this.

-Key parameters,

 

Let's discuss the cases in short first so you will gate rough idea,

CASE1:- Run Simulation with the LAW-2 material model by keeping the "Johnson Failure card" of pre-assign values along with the Jonhson card.

CASE2:- Run Simulation With the same LAW2 material card With Johnson Failure card by altering some properties/ values from the Failure card.

CASE3:- Run Simulation with only Johnson material card (LAW 2). Delete the Failure johnson card.

CASE4:- Run Simulation with only Johnson material card (LAW 2). set the  Eps_max value =0 with Failure johnson card.

CASE5:- Run Simulation with only Johnson material card (LAW 2). set the  Eps_max value =0 with No Failure johnson card activated.

CASE6:- Run Simulation with only LAW 1 (ELAST) material card.

CASE7:- Run Simulation with only LAW 27 (BRIT) material card. (Different card file is available for this simulation)

CASE8:- Run Simulation with only LAW 36 (PLAS_TAB) material card. (Same rad file use as used in 1-6 cases)

 

Recommended Shell properties,

QEPH prevents Hourglass formulation by Using the Physical Stabilization / Stiffness method.

For the good and accurate simulation results, along with material properties shell property must be defined by considering the element used for the meshing and Hourglass control during the simulation.

These Shell properties will be followed through all the defined cases (1-8)

 

         

CASE 1:- Run Simulation with the LAW-2 material model by keeping the "Johnson Failure card" of pre-assign values along with the Jonhson card.

- First step in case one is to set up Shell properties to the recommended one and save as "LAW2_Epsmax_Failure"

-After that, I had created a material card and Failure card using Johnson cook / LAW 2 model for the simulation as per the given data.

     

                              FIG 02 (a)                                                                                              Fig2(b)

-After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows

-From the above data you can see that Internal energy increase with respect to time also the mass error is zero means we can state that there is no addition or removal of mass to stabilize the strain/ simulation.

- Energy error gets started from -ve value and increase within the simulation time up to 0.8%. As per the standards of the simulation Energy error in between +5 to -15% is acceptable, so it is in the acceptable range. This 0.8% energy error indicates there is energy generated as we are using the QEPH element to avoid Hourglass formulation.

-The total Run time is 4.02 sec and the Number of the cycles is 49380.

     

                                             FIG 3(a)                                                                                          Fig3 (b)

- This animation showing how the impact of the ball gets absorbed by the plate. Here I had created an animation file to represent Von Mises stresses on the plate. If you see the animation window it is showing the Max stress value of 275.2 Mpa. Our Max stress failure value is 425 and as per the data getting from the animation, I can say that non of the elements are undergoing such a huge force still plate get damaged or rapture. The reason behind this is the Plate is failing for the strain value. We have set the Max failure strain to 15% so all that element you are seeing gets deleted are failing for Max strain failure value also the Johnson failure parameters D1, D2, and D3 is responsible for this result as they all are strain related parameters.

-Here you are directly seeing that element deletion and not a crack representation its because we set Ixfem to zero. The Fi3 (b) showing the Energy formulation in the body. At approx 3.8ms the graph showing a horizontal movement this is because at this point numbers of elements which are come in contact with the ball are get deleted due to strain failure and now there is very less or no element is there in contact with the ball so energy transformation is very less. Up until this point, the Internal Energy increases as material try to absorb the deformation. You can see that the Internal energy and total energy are approximately the same. Hourglass energy is zero though there is some Kinetic energy in the system.   

CASE2:- Run Simulation With the same LAW2 material card With Johnson Failure card by altering some properties/ values from the Failure card

-set up Shell properties to the recommended one and save as "LAW2_Epsmax_Crack"

-Run Simulation With the same LAW2 material model With the Johnson Failure model by altering some properties/ values from the Failure card.

-The Only changed value in the Johnson Failure Model is Ixfem and Dadv. The benefit of Ixfem is it will represent the Crack formation before deleting the element.

                      Fig 4

-After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows

           

-The total run time is 2.13 sec with total numbers of the cycle of 49217. If you compare it with the result of CASE 1 you can see that the numbers of cycle increases but the simulation time decreases. Also, the Energy Error generate to compensate the Hourglass formulation is also High. This sort of high value in acceptable but not consider a good one because the limit is +5 to -15 and  +4.1% is too closed to the rated value. Internal Energy developed by the body to oppose the deformation is significantly higher than the CASE1. the mass error is zero means we can state that there is no addition or removal of mass to stabilize the strain.

-The results I got after the simulation are not that much different than the CASE1 as we only change the Johnson failure model Ixfem Property. The result is more smoother and realistic than the previous one as we can see the cracks before elements get deleted.

  

                                           Fig5(a)                                                                                                                           Fig 5(b)

-You can clearly see the Crack formation before the element gets deleted. The Max stress is 295 Mpa also higher than CASE1 as Crack propagation is carried out and delays the element failure time. This crack propagation before the element gets deleted is possible because of the Ixfem option.

-There is one significant change in the Energy graph if you compare it with Case1 the linearity of the curve is followed much longer in case2 than Case 1. This sort of behavior is due to the fact that elements are cracking before getting deleted that's responsible for the delay in the small hike and drop you can witness after approx 4.5 ms in case2 and approx 3.8 ms in Case1. 

                                                Fig5(c)

- in this image, you can able to see that small hike and drop clearly. The Difference between Internal and total energy is very less and Internal energy is trying to match the Total energy. At this point, the ball has already shattered the plate and there is no much contact area available in between the ball and plate that's why the graph is in a horizontal  line at the end of the simulation.

CASE 3:- Run Simulation with only Johnson material card (LAW 2). Delete the Failure johnson card.

-set up Shell properties to the recommended one and save as "LAW2_Epsmax_Nofail"

-Run Simulation With the same LAW2 material model Without the Johnson Failure model. For this simulation, I had deleted the Failure Johnson model.

-So now the material behavior depends on LAW 2 key parameters only. which are having the same values as you can see in Fig2(a).

- After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows,

 ___________________START

___________________Intermidiate

___________________END

-from the above data you can get the idea about Run time and the Total Numbers of the cycle. The time taken by simulation is Slight higher than CASE1 (4.02) but significantly larger than CASE2 (2.13) 

-The value of Energy Error is keep on fluctuating through the Simulation from -0.6% to max +1.2% so it is in the acceptable range. At the end of the simulation, I get an Energy error of 0.8%. energy error indicates there is energy generated as we are using the QEPH element to avoid Hourglass formulation.

--From the above data you can see that Internal energy increase with respect to time also the mass error is zero means we can state that there is no addition or removal of mass to stabilize the strain.

 

                                Fig 6 (a)                                                                                           Fig 6 (b)          

   

                                                                                        Fig 6 (c) 

- From fig 6 (a) and (b) you can see that we are getting the approximately same result as the CASE1 study. Also, you can see the drastic deformation/rapture in the body at approximately the same point.

-The Fig6 (c) showing the detail about that small hike and drop value we are getting after the badly rapture point. As you can see the elements which are undergoing more strain are getting deleted immediately, the same happens here as the element near the marking witness more strain that its neighboring element and get deleted from the midway and we are getting shattering effect. This behavior is the same for all three cases up until this point. After this point, energy transformation is showing a horizontal line as lesser elements are available for energy absorption.

CASE4:- Run Simulation with only Johnson material card (LAW 2). set the  Eps_max value =0 with Failure johnson card.

-set up Shell properties to the recommended one and save as "LAW2_NoEpsmax_failure"

-Run Simulation With the same LAW2 material model With putting the value of EPS_p_max is zero. IF we set the EPS_p_max value= 0 than it will take a Default value of `10^30`. Which gave the material Ideal elastic property as the EPS_p_max represents the maximum plastic strain value for material failure. But at the same time, we are Keeping the Failure Johnson Model which also contains the Strain parameters D1, D2, D3 which will eventually provide the material the failure strain value and stop the material from behaving as an ideal elastic material.

 

-We are keeping Ixfem = 0 so no more Crack formulation before deleting the element.

- After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows,

_____________________START

______________________Intermediate

______________________END

-from the above data you can get the idea about Run time and the Total Numbers of the cycle. The time taken by simulation is approximately equal to the CASE2.

-Same sort of energy error to dampened the hourglass formulation. Energy error in this case also fluctuating from -0.6 to +1.2%. The 1.2% is that max Energy error I had noted in this case.

-Also you have noticed the Failure representation in the Intermediate section showing the Headline "FAILURE (JC)" means failure Johnson cook model. 

                                       Fig7 (a)                                                                                                                   Fig7 (b)

-The failure you are noted here is because of the Failure Johnson card. As you can see the max stress noted here is 245 Mpa which is less than the set value od 425 Mpa so there is no way that these materials are failing for the Stress value. The Only affecting Factor here is the values of the Johnson failure strain values. which are the cause of the failure

-You can see the failure is not ended with midway rapture. The energy distortion is also linear here. If we study the graph in Fig 7(b) there is no Horizontal line or sudden hike and drop, The graph is increasing linearly. Also, KE is very small here. This Result showing perfect energy transformation / Dissipation as there is no non-linearity in the graph until the end. But the problem is that we only have to rely on the Failure Johnson model. the strain parameter values we added here is Lab generated and it is not possible to obtain such data for every simulation.

-Though the End results, in this case, are pretty good compared to the other three. The Total energy is matching with the sum of Internal energy and Kinetic Energy.

 

CASE5:- Run Simulation with only Johnson material card (LAW 2). set the  Eps_max value =0 with No Failure johnson card activated.

 

-set up Shell properties to the recommended one and save as "LAW2_NoEpsmax_NOfail"

-Run Simulation With the same LAW2 material model With putting the value of EPS_p_max is zero and Deleting the Failure Johnson Card. IF we set the EPS_p_max value= 0 than it will take a Default value of `10^30`. Which gave the material Ideal elastic property as the EPS_p_max represents the maximum plastic strain value for material failure.

In this CASE, we are also deleting the Failure Johnson card which contains the Strain parameters D1, D2, D3, and will eventually provide the material the failure strain value and stop the material from behaving as an ideal elastic material. So now my material dependent on the default strain value for the Strain failure. 

-from the above data you can get the idea about Run time and the Total Numbers of the cycle. The time taken by simulation is very less as compared to the other four CASES.

-Also the Energy error is Lineraly increasing here, not like the other CASES where Energy error is fluctuating as simulation goes on. The reason behind this is the Elastic behavior of the material. But due to this, you can see the Max Energy error 3.0% at the end of the result. If we run the simulation for more time than it will keep showing you a higher value of the Energy error as the material won't fail because of the High strain value we put when defining the Material card.

 

                                     Fig8 (a)                                                                                                          Fig8 (b)

-In the above animation you can see how the plate is behaving as its made up of ideal elastic material. Though we defined the Max Stress value 425Mpa the simulation didn't cross that limit as you can witness the Max stress developed in the body is 425.7 Mpa which is a little bit less than the max stress failure value. But at the same time, you can see that Energy is spreading over the body in a linear manner. That indicates the Energy Equilibrium is getting maintained.

-The Graph also showing a gradual increase in energy with respect to time.

CASE6:- Run Simulation with only LAW 1 (ELAST) material card.

 

-set up Shell properties to the recommended one and save as "LAW1"

-Run Simulation With the same LAW1 material model. As we discuss in the earlier section this LAW is mean to be for Elastic material or the material in which Deformation takes place within its elastic limit.

-For LAW1 we only have to define the Material density, Young's modulus, and Poisson's ratio.

- After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows,

  

 

-The total Run time is 3.54 sec and the Number of the cycles is 47969.

- The Energy error is not consistent it keeps on fluctuating as you can see in the above data. The max Energy error noted is of +4%. So the Energy error is in an acceptable range. (Same for CASE 1-4).

-Because of the entire simulation is carried out on only three parameters the time taken by it is higher for fewer Numbers of a cycle of all Cases (CASE 1-5)

                                     Fig 9(a)                                                                                                               Fig 9(b)

-This LAW represents the ideal elastic material. you can see the Max stress developed in the plate is 10890 Mpa which is higher than all the cases we are studied up until now.

 

CASE7:- Run Simulation with only LAW 27 (BRIT) material card. (Different card file is available for this simulation)

 

-Imported the LAW27 rad file which is given and set up Shell properties to the recommended one.

-Run Simulation With the same LAW27 material model. As we discuss in the earlier section this LAW combines the isotropic Elasto-plastic Johnson cook material model with an Orthotropic brittle failure model.

-This model only applicable for Shell elements, also Failure Johnson Model is not available Under this LAW.

-Yield surface definition is the same as LAW2.

-For LAW27 we only have to define the Strain at the Beginning of the tensile Failure ('epsi_t`), max tensile strain if the failure (`epsi_m`), Max tensile strain of element Deleteation(`epsi_f`).

        

                                                            Fig 10

 

-These key parameter data obtained by the Lab test for that particular material.

- After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows,

____________START

______________Intermediate

______________END

-The total Run time is 1min 53 sec and the Number of the cycles is 49508. Internal Energy is Consistently increased w.r.t. time.

- The Energy error is not consistent it keeps on fluctuating as you can see in the above data. The max Energy error noted is of +1.1%. So the Energy error is in an acceptable range. (Same for CASE 1-4).

-Time taken by simulation is low but not then we discuss in CASE 5. The Failure element gets noted as per the above image (Intermediate section)

                                      Fig 11 (a)                                                                                                                      Fig 11 (b)

-Here you can see the 

- From fig 10 a and b you can see that we are getting a Linear curve up until point 4.2ms approx. after that because for the rapture you can see the fluctuation in the graph,

-The Fig10 (b) showing the detail about that small hike and drop value we are getting after the bad rapture point. As you can see the elements which are undergoing more strain are getting deleted immediately.  After this point, energy transformation is showing a horizontal line as lesser elements are available for energy absorption.

-The material is breaking because of the Brittle nature we define in the material card, We have set the parameters like Beginning of the tensile Failure ('epsi_t`), max tensile strain if the failure (`epsi_m`), Max tensile strain of element Deleteation(`epsi_f`) at the start. These parameters are defining the strain property of a material in this case (Ref. Fig 10 ). Material behaving the same as the defined material card and breaks apart when exceeding the max strain value.

-You can clearly see in the graph after 4.2ms the energy behavior is suddenly changing due to the sudden breakage.

-One thing is to be noticed is that the behavior of the plate under the defined material card/model giving the approximately same result as we discussed in CASE 1 and CASE 3 where we had used LAW 2 with modification.

CASE8:- Run Simulation with only LAW 36 (PLAS_TAB) material card. (Same rad file use as used in 1-6 cases)

-set up Shell properties to the recommended one and save the given rad file as "LAW36"

-This Law model, an isotropic elsto-plastic material using the user-defined function for the work hardening portion of the stress-strain curve and the elastic portion of the material defined by Young's modulus and poisons ratio.

-This is the best suitable option for Elasto-plastic material because it gives the result close to the actual Lab data. The best thing about the PLAS_TAB / LAW36 material model is it will apply for both the shell and solid element.

-We can use the Failure johnson model along with the LAW 36 material model which will give us result in the form of crack. In this case study, we are not including the Failure johnson model.

  

-In this case, I had created a curve using the data point I had got in the form of LAB DATA as you can see in the above image. After that, I had defined this curve as a function inside the LAW 36 Material Card under fct_ID. Also defined given scale factor for the value

- After defining the material and shell property card I had RUN the simulation on Radioss workbench. End of the simulation I get the Output file from the simulation containing simulation data as follows,

-from the above data you can get the idea about Run time and the Total Numbers of the cycle. The time taken by simulation is approximately equal to we have found in CASE 2.

- The Energy error is not consistent it keeps on fluctuating as you can see in the above data. The range of fluctuations is from -1.3 to +0.6%. The max Energy error noted is of +0.6%. So the Energy error is in an acceptable range. 

 

-You can see the same rapture in the material as you witness in the previous cases but the rapture here is more aggressive as you can see it is happing way too early and also the KE increase in the system.

-The Von misses stress value is also higher of all CASEs 1267 Mpa except CASE6 (Ideal Elastic with LAW 1).

 

Conclusion:-

-Selecting the correct material model for the appropriate body is an important factor and the User must have well knowledge of imp material card so he can do analysis under that specific material model.

-Deploying the wrong material model will give the user a result but that result may or may not able to represent the actual situation when the body undergoes an actual physical test.

-The best result is that which can represent the actual behavior of the force on the body.

-LAW 1 is fro ideal plastic only. We can use this law only on the material that gives deformation under its Elastic limit.

-LAW 2 is very good for Elasto-plastic material and with the Failure Johnson card, we can get the CRACK formulation before the element gets deleted. But the only drawback is to define the key parameter like a, b, and n we have to calculate or obtain True stress-strain values.

-LAW 27 is only for Brittle material (Shell element).

-LAW 36 is very good for Elastoplastic material as it will give more realistic representation. We can use the Failure Johnson card with this model for crack based representation.