Assignment 4-RADIOSS Material Laws Challenge

Assignment 4-RADIOSS Material Laws Challenge

Aim :

To run crash analysis on the given model by applying different materials laws available in Radioss and post-process the results

Objective :

To carry out simulations of the given starter files and compare the results. There shall be 7 cases (according to given parameters) and they are to be compared primarily via animations and plots. The files to be worked on are the FAILURE_JOHNSON_0000.rad file and the LAW27_0000.rad file. The cases are as follows:

1. Law 2 (file: FAILURE_JOHNSON_0000.rad) - base simulation.
2. Law 2 (file: FAILURE_JOHNSON_0000.rad) with Ifail_sh = 1, Dadv = 1, and Ixfem = 1.
3. Law 2 (file: starter file for case 2) with fail/JOHNSON card deleted.
4. Law 2 (file: starter file for case 3) with EPS_p_max value deleted
5. Law 1 (file: FAILURE_JOHNSON_0000.rad) with fail/JOHNSON card deleted and values for density, E, nu assigned
6. Law 27 (file: LAW27_0000.rad) with recommended shell properties
7. Law 36 (file: LAW27_0000.rad) with recommended shell properties and given reference curve.

Theory :

• The accuracy of the simulation depends on the material chosen.
• Choosing the right material and providing the reliable material data in performing a simulation is very important.
• RADIOSS has multiple material properties and wide variety of material library like concrete, foam, rubber, composites etc.,
• Some of the commercially used material laws are:

1. Law 1: Elastic (Isotropic Elasticity)
2. Law 2: Johnson-cook (Isotropic Elasto-plastic)
3. Law 27: Elastic-plastic brittle
4. Law 36: Elastic-plastic tabulated
5. Law 42: Ogden (visco hyperelastic)
6. Law 70: Foam

Isotropic Elasticity - Law 1

• Isotropic means that a material will have the same material properties in all directions. Under isotropic elasticity, RADIOSS provides two types of elasticity.
• Linear elastic: LAW1 elastic
• Hyperelastic: LAW69 Tabulated hyperelastic, LAW82 Ogden
• The RADIOSS elasticity law follows the hook’s law of elasticity i.e a linear relationship between the stress and starin.
• It is available for truss, beam, shell, and solid elements.
• As mentioned earlier, it is exclusively for elastic materials.
• The material stiffness is determined by Young’s modules of elasticity (E) and Poisson’s ratio (n).
• The sheer modulus G is calculated by G=E2(1+V)G=E2(1+V)

Limitations :

• Elastic materials cannot be used for large deformation cases such as blow molding etc.,
• In the case of large deformation, law 2 johnson-cook material with high yield can be used.

Isotropic Elasto-Plastic

• RADIOSS provides various types of elasto-plastic material laws. It has all the material models based on von mises hardening without damage, von mises hardening with ductile damage, von mises with visco-plastic flow.
• Here, we are going to look at Johnson-cook/JOHNS and tabulated piece-wise linear/PLAS_TAB.

(PLAS_JOHNS) Johnson-cook material- Law 2

• This law represents an isotropic elasto-plastic material using the johnson-cook material model.
• The model expresses material stress as a function of strain, strain rate, and temperature.
• In the material card, we have an option called EPS_max which is nothing but plastic strain at failure. Failure of the element happens when 1 integration point reaches EPS_max.
• Now if failure is only based on EPS_max, there can be instances where the EPS_max gives out unrealistic results. To avoid this, we have the option called /FAILS/JOHN.
• /FAIL/JOHN card provides the user with more control over the failure of the johnson-cook strain.

LAW36-PLAS_TAB Elastic plastic piecewise linear material

• The LAW36 material law helps in modelling isotropic elasto-plastic material using user defined functions for the work hardening portion of the stress-strain curve for different strain rates.
• The curve defined is nothing but the stress-strain curve after the yield point. The yield point is set to 0.
• This material law is available for both brick and shell elements.
• If the work hardening portion is defined by the user, then its elastic portion is taken from the inputted young’s modulus and poisson’s ratio.
• Any number of stress-strain curves can be defined.
• The important part is that the strain rate curves must not intersect with each other

• The plastic strain curve should start with 0.
• The user also has option to input yield stress with respect to pressure using fct_Idp.

Procedure :

Case 1 :

Running the model as it is given in challenge, observing simulation, discussing number of cycles it takes, energy error,mass error and plotting energies graph, naming it as law2_epsmax_failure.

STEP 1 : Open Hyperworks in Radioss solver.

STEP 2 : Import Solver desk FAILURE_JOHNSON_0000.rad file

STEP 3 :

• Analysis>Radioss>save as input FAILURE_JOHNSON_0000.rad file
• Save path as --case1/law2_epsmax_failure_0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 4 : Switch to Hyper view

STEP 5 : Select local model and result law2_epsmax_failure.h3d file

• In this case, we can change the result type to 'Von Mises' and change the averaging method to simple. Doing so creates the Von Mises stress contours as shown below

STEP 6 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 49380
• Energy error = 0.8%
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 100.52 s

STEP 7 : Switch to Hypergraph 2D, upload law2_epsmax_failure.T01

Case 2 :

In Fail/Johnson collector changing ifail_sh=1, dadv=1, Ixfem=1 and running the model name as law2_epsmax_crack, observing simulation, discussing number of cycles it takes, energy error and plotting energies graph.

STEP 1 : Import Case 1 Solver desk law2_epsmax_failure_0000.rad file

STEP 2 : Change Failure_Johnson collector as per given challenge.

• Analysis>Radioss>save as input law2_epsmax_failure_0000.rad file
• Save path as --case2/law2_epsmax_crack0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 3 : Switch to Hyper view

STEP 4 : Select local model and result law2_epsmax_crack.h3d file

• Von-mises stress contours :

STEP 5 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 49217
• Energy error = 4.1%
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 102.34s

STEP 6 : Switch to Hypergraph 2D, upload law2_epsmax_crackT01 file

Case 3 :

Deleting Fail/Johnson card, running the model name as law2_epsmax_nofail , observing simulation, discussing the number of cycles it takes, energy error, mass error and plotting energies graph.

STEP 1 : Import Case 2 Solver desk law2_epsmax_crack_0000.rad file

STEP 2 : Delete Failure_Johnson collector as per given challenge.

STEP 3 :

• Analysis>Radioss>save as input law2_epsmax_nofail.rad file
• Save path as --case3/law2_epsmax_crack0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 5 : Switch to Hyper view

STEP 6 : Select local model and result law2_epsmax_nofail.h3d file

• Von-mises stress contours :

STEP 7 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 49408
• Energy error = 0.8 %
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 101.84s

STEP 8 : Switch to Hypergraph 2D, upload law2_epsmax_nofailT01 file

Case 4 :

Deleting the value of esp_p_max_, running the model name as law2, observing simulation, discussing the number of cycles it takes, energy error, mass error and plotting energies graph.

STEP 1 : Import Case 3 Solver desk law2_epsmax_nofail_0000.rad file

STEP 2 : Delete value of esp_p_max_ from material collector as per given challenge.

STEP 3 :

• Analysis>Radioss>save as input law2_epsmax_nofail.rad file
• Save path as --case4/law2_0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 5 : Switch to Hyper view

STEP 6 : Select local model and result law2.h3d file

• Von-mises stress contours :

STEP 7 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 48737
• Energy error = 3.0 %
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 99.95s

STEP 8 : Switch to Hypergraph 2D, upload law2T01 file

Case 5 :

Converting the material model to law1 elastic with same density, E, Nu, observing simulation, checking the number of cycles it takes, energy error, mass error and plotting energies graph.

STEP 1 : Import FAILURE_JOHNSON_0000.rad file

STEP 2 : Converting the material model to lawas per given challenge.

STEP 3 :

• Analysis>Radioss>save as input law1_0000.rad file
• Save path as --case5/law1_0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 5 : Switch to Hyper view

STEP 6 : Select local model and result law1.h3d file

• Von-mises stress contours :

STEP 7 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 48851
• Energy error = - 9.6 % (negative)
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 100.79s

STEP 8 : Switch to Hypergraph 2D, upload law1T01 file

Case 6 :

Opening Law27_0000.rad, changing the shell properties to recommended shell property, running that model with law27 material card, observing simulation, checking the number of cycles it takes, energy error, mass error and plotting energies graph

STEP 1 : Import Case 6 Solver desk law36_0000.rad file

STEP 2 : Changing the shell properties on our own which can results best

STEP 3 : Convert the material model to law27 (M27_Plast_Brit) and edit the parameters which can results best in our own.

STEP 4 :

• Analysis>Radioss>save as input law27_0000.rad file
• Save path as --case7/law27_0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 5 : Switch to Hyper view

STEP 6 : Select local model and result law27.h3d file

• Von-mises stress contours :

STEP 7 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 49501
• Energy error = 0.8 %
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 106.95 s

STEP 8 : Switch to Hypergraph 2D, upload law27T01 file

Case 7 :

Converting the card to law36 elasto plastic based giving data as per given in challenge, observing simulation, checking the number of cycles it takes, energy error, mass error and plotting energies graph.

(Fig-1)

STEP 1 : Import Case 5 Solver desk law1_0000.rad file

STEP 2 : converting the material model to law36 and edit the parameters as per given challenge (Fig 1)

STEP 3 : Create a new curve in curves collector and rename it.

STEP 4 : Give the X and Y coordinate as per given challenge(Fig 1)

STEP 5 :

• Analysis>Radioss>save as input law36_0000.rad file
• Save path as --case6/law36_0000.rad
• Checkbox include collectors
• Write (-nt 4) in options
• Click Radioss

STEP 6 : Switch to Hyper view

STEP 7 : Select local model and result law36.h3d file

• Von-mises stress contours :

STEP 7 : Checking the number of cycles it takes, energy error, mass error and simulation time.

• Number of cycles = 53164
• Energy error = - 2.3 % (negative)
• Mass error = 0.0
• Simulation time = Starter+Engine run time = 111.51s

STEP 8 : Switch to Hypergraph 2D, upload law36T01 file

Observations :

Case 1 :

• In this case, it has the Fail/JOHNSON card as well as EPS_p_max value assigned, with Ixfem value as 0. This means that the elements are deleted as soon as they cross the EPS_p_max threshold, which is what we can see in the above simulation
• Internal energy, as well as rigid wall forces, are reactions to the force generated by the sphere on the sheet. Energy increases linearly until many elements are deleted at around the 4ms threshold. This probably creates some vibrations and that results in a surge of kinetic energy at the same point.
• The rigid wall forces fluctuate when the elements are deleted, and when a large chunk of elements are deleted at 4ms, the graph drops, meaning there aren't many elements opposing the force of the sphere. Most of the elements in its path have been deleted at that point.

Case 2 :

• In Case 2 we have used Ifail_sh, Dadv, and Ixfem as part of the Fail/JOHNSON card. Ixfem is especially important here because it decides the way the elements react. With its value equal to 1 here, it means the elements will crack and fail. Along with Dadv, crack propagation can also be seen here, with elements being deleted only when the crack reaches them. As a result, this is a more realistic depiction.
• In this case, the rigid wall is moving. So, to move any object there should be some external force is applying to the object. So that is why the rigid wall forces start increasing from zero and when it collided with the plate, the energy got transferred to the elements, that's the reason the rigid wall forces get decreased again to zero.

Case 3 :

• With the Fail/JOHNSON card deleted in this case, the onus is on EPS_p_max to be the factor for element deletion. As we can see in the following screenshot, its value is 0.151, meaning elements will be deleted if the strain on any integration point within said elements reaches 15.1% of the plastic strain. The elements, in this case, fail rapidly when compared to the elements in case 2 due to XFEM crack formulation there.
• There is a linear increase in internal and total energy until a bulk of the elements are deleted from the model. This is expected since the energy absorbed by these elements go to waste due to their deletion.
• This also explains the sudden drop in rigid wall forces at the same timestamp due to most elements that were in contact with the sphere during collision being deleted. The rigid wall force is basically a measure of the opposing force generated by the metal sheet against the sphere. Fluctuations occur when elements are deleted. When there are no elements to oppose the incoming sphere, there won't be any rigid wall forces.

Case 4 :

• Law 2 (PLAS_JOHNS) expresses material stress as a function of strain, strain rate and temperature.
• The metal sheet is able to withstand a large amount of stress and avoid element deletion primarily due to the fact that the value for EPS_p_max was deleted. Since it was deleted, RADIOSS assigns it the default value of 10^30. In addition to that, the fail/JOHNSON card was deleted. The material behaves like a pseudo-elastic (also called elasto-plastic) material since it has a very high EPS_p_max threshold and elements cannot be deleted due to no failure cards.
• With the value of c (Strain rate coefficient) = 0, there is no strain rate (neither does temperature play a role here). As a result, the stress, in this case, is purely a function of strain generated in the material.
• Added, the kinetic energy generated in this case is almost negligible (2.5-4 mJ) compared to the internal (and total) energy here. The total energy increase is almost linear over time.

Case 5 :

• In this case, the plate is defined with a LAW-1 material which defines the basic properties of elastic material. This model considers only the elastic phase of the material, there is no plasticity involved which results in linear deformation.
• This case makes use of the M1_Elast card and as we can see, the metal sheet absorbs the full impact of the sphere. This material law is used to model purely elastic materials. This explains why there are no element deletions nor ruptures. Due to its elasticity, it also can absorb an extremely large amount of energy, which explains the peak at the end of the kinetic energy plot below. Absorbing a lot of energy also results in very high stresses - the maximum stress observed on the metal sheet is 10890 MPa, which is a massive value compared to the same in LAW 2.
• The kinetic energy gradually increases as the plate is stretched to the maximum limit for the applied load.
• Also, due to the elastic nature, the internal energy (and rigid wall forces) keep increasing exponentially. The internal energy of the metal sheet increases due to the absorption of the kinetic energy from the impacting sphere and drops down once the plate returns to the original shape.

Case 6 :

• In this case the use of the M27_PLAS_BRIT material card that is used for isotropic elastoplastic Johnson-Cook material model with an orthotropic brittle failure model. The sheet (compared to case 7) absorbs more force and resorts to more deformation before the elements are deleted (at around 4ms).
• With the loss of energy through deleted elements, we notice the graph plateaus at around the 4 ms mark.

• With several elements deleted and none to stop the incoming sphere, the rigid wall force graph drops at the same timestamp of 4ms. The spikes are formed when an element is deleted and is characterized by a trough and crest but with so many elements deleted, the trough is massive at the 4ms mark.

Case 7 :

• In this case, from the simulation, we can say that this material exhibits strong brittle behaviour. It does not bend as much in response to the applied force and immediately disintegrates. There seems to be not much cracking and the region of element deletion takes the shape of the sphere. Another thing that we can notice is that the stress concentration is localized around the region of impact and these stresses are not dissipated throughout the whole metal plate.

• There is an almost linear relation between internal energy and time till past the 3ms mark where many elements get deleted at once. When the elements are deleted, the energy on each element goes to waste, which results in the plateauing of the curve.
• On the topic of energy wastage and element deletion, it is more particularly visible in the rigid wall force graph. Each of the spikes is due to an element deletion. The resultant force gradually increases past the same 3ms mark which is when the sheet gives way and lets the sphere through. With not much of the sheet in the way, the rigid wall forces are drastically reduced, and that results in that drop at the 3ms mark. The first drop occurs when the sheet ruptures the first time.

Comparison of all 7 cases :

CASE	No. of cycles	Mass Error	Final Energy Error	Simulation Time	Condition of elements under excessive stress
Case 1 (Law2_epsmax_failure)	49380	0	0.80%	100.52	Deleted
Case 2 (Law2_epsmax_crack)	49217	0	4.10%	102.34	Elements undergo crack formation and then deletion
Case 3 (Law2_epsmax_nofail)	49408	0	0.80%	101.84	Deleted
Case 4 (Law2)	48737	0	1.10%	99.95	Cannot be deleted due to lack of failure card and high default EPS_p_max_value
Case 5 (Law1)	47969	0	1.30%	100.79	Cannot be deleted due to elastic card property
Case 6 (Law27)	49508	0	0.80%	111.51	Deleted
Case 7 (Law36)	53143	0	-1.80%	106.95	Deleted

Conclusion :

Selecting a correct material model plays a very important role in simulation. Selecting the wrong material model and doing simulation will also give result but it will not represent the actual situation.

Law 1 : is used to model purely elastic materials or materials that remain in the elastic range. To model this we require Poisson's ratio and Young's modulus. This law represents a linear relationship between stress and strain.

Law 2 : In this law, the material behaves as linear elastic when equivalent stress is lower than the yield stress. For a higher value of stress, the material behaves like plastic. Failure can be captured better with the help of an optional Fail_Johnson card.

Law 27 : Used for brittle materials.

Law 36 : The elastic-plastic behavior of isotropic material is modeled with user-defined functions. The stress-strain curve is modeled using E and Poisson's ratio. Therefore, it is the best card because we cannot know the exact failing condition of the material in the other cases, but we can define the stress-strain curve, and then we can decide where the material is failing.

Learning Outcome :

• Learned about different type of material cards.
• Learn about the failure card in hypermesh.
• Learn about contact energy, kinetic energy, hourglass energy, rigid wall forces.
• Learned about different simulation results we get using different settings.