Virtual simulation of same model with different material cards in Radioss

Objective:- In this challenge, we will study about the different material laws and will observe the different behavior of the given model with the different material card and will do the comparison as per the cases defined below:

Case 1: Changing the model name from Failure_johnson_0000 to Law2_epdmax_failure. and running the model as it is without changing the shell properties and modification in a material card.

Case 2: Change the material card properties Ifail_sh=1, Dadv=1and Ixfem1. and Run the model as Law2_epsmax_crack.

Case 3: In this delete the fail johnson card and run the model with new name Law2_epsmax_nofail.

case 4: In this case, we will change the value for EPS_p_max and run the model with the model name Law_2 and then compare the results of Case 3 & Case 4.

Case 5: In this case, we will convert the material model to Law1 with the same density, E and nu values and see the difference in the behavior of the elastic material.

Case 6: In this case, we will open the given model with law27_0000.rad which is for brittle material and change the shell properties to recommended shell properties

Case 7: In this last case we will change the material model to Law36(Plas_tab) and compare the results.

Case 1 & Case 2 Comparison

• Both the model is defined as Johnson cook material model. This model expresses material stress as a function of strain, strain rate, and temperature. A built-in failure criterion based on the maximum plastic strain is available.
• In first case EPS Max value is defined as 0.151 which means the material will fail at 15.1% and Ixfem =0 which means Elements will get deleted without cracking also, Dadv is inactive and automatically assume the zero value.
• In the second case, Ixfem =1 and Dadv=1 which means elements will first crack and then will get deleted also the stress produced on the plate are more in this case.

• When the ball hits the plate it begins to deform elastically and, in so doing, the internal energy which is nothing but elastic strain energy stored in the plate and that is progressively converted into Kinetic energy as we can see the rise in the kinetic energy graph at the same point where the internal energy stabilizes.
• We are seeing the early rise in Kinetic energy in Case 1 it is due to the No Crack advancement (Default Ixfem=0) and in case two there is crack then deletion happened in the elements as seen in the above figure. (Ixfem=1 & Dadv=1) for crack advancement.

Case 3 & Case 4 Comparison

• In the Case 3 Fail/Johnson card & EPS_p_max value is set to 0.151 is deleted that means if any elements reach a strain rate of 15.1% it will fail and get deleted.
• In the Case 4 EPS_p_max value is set to 0, Due to which element will go into infinite deformation without fail. Explanation for simulation below:

Case 3. Case 4.

Images of the value set for EPS_p_max

• As the EPS_p_max value is zero in Case 4, so the elements went through larger deformation as seen above and therefore the stress produced is larger in Case 4 than Case 3.

• As we can see the gradual increase of Internal energy in both the cases but in case 3 when elements reaching the EPS_p_max value of .151 they are getting deleted hence resulting in very less formation of internal energy after 3.6ms, but in the Case 4 there is No EPS_p_max value assigned and elements are undergoing larger deformation as compared to Case 3 so the exponential rise in Internal energy is visible in the graph.

Case 3 Case 4

• In Case 3 due to the rupture of the elements, there are sudden slopes in the graphs but in Case 4 the internal energy is stored in the plate as there is no failure of the elements seen.

Case 5 Analysis

• In this case, we have changed the material properties to Law 1 which is generally used for 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.
• Global integration approach is applied to LAW1 and shell elements when the number of integration points through the shell thickness is different from NP=1 (membranes).
• Note: Failure models are not available in the case of global integration. LAW2 and LAW27 with very high yield stress may be used as a substitution to LAW1 in these cases.

The explanation for simulation below:

• It is clearly observed from the above plotting that when the material is converted to elastic material it is trying to absorb as much kinetic energy produced by the sphere into internal energy of the plate without failing due to which stress value is increased to the maximum as compared to other cases.
• Also, the energy error is reached to 4.0% which is not acceptable.

Case 6 Analysis

• Epsilon t = Stress at the beginning of tensile failure.
• Epsilon m = Maximum tensile strain at which the stress in the element is set to valuable dependent on dmax1.
• Dmax = Maximum damage factor.
• Epsilon f = Maximum tensile strain for element deletion.

Dmax factor is the factor to accelerate the failure of the element.

The explanation for simulation below:

• In this case, model material properties are converted into Law 27 which is for brittle material. In this model, the material behaves as a linear-elastic material when the equivalent stress is lower than the plastic yield stress.

• It can be observed from the above image material damage is accounted for prior to failure. Failure and damage occur only in tension.
• Internal energy is not able to transfer to other elements(the other end part of the plate and can be seen no stress has been produced at the boundary of the plate) also the hourglass energy is visible in this particular due to the elements causing zero stress.
• the rupture of the elements occurs due to material properties which result in deletion of the elements due to which very less amount of kinetic energy has been recorded in the graph.

Case 7 Analysis

• This law models an isotropic elastoplastic material using user-defined functions for the work-hardening portion of the stress-strain curve (for example, plastic strain vs. stress) for different strain rates.

User-defined curve:

The explanation for simulation below:

• Once (plastic strain) reaches Eps_p_max, in one integration point, the element is deleted and when stress is not to reach the maximum range as seen in the image below.

• After the gradual increase in Internal energy, there is some noticeable distortion in the graph and the sudden rise in the kinetic energy just before 4ms that is due to the deletion of the elements.
• There is a slight delay in rupturing of the elements due to the low stress and strain rate value defined by the user.

Comparison of all cases

• In the case of using QEPH shell formulation (I_shell=24) or fully integrated elements, the Energy Error can be slightly positive since there is no Hourglass energy Except (law 27 case)and the computation is much more accurate. An error of +1% or +2% is acceptable.

In the above graph, only the case of Law_27 has shown the rise in hourglass energy value due to the brittle nature which causes zero stress and no strain in the elements due to which its simulation result is not suitable.

Conclusion:

• Total cycle for all the cases ranges between 49000 to 53000 except the case with Law 27 has taken 41000 cycle due to brittle in nature.
• As mentioned in Case 6 (Law 27) is for brittle material so it was showing energy error of -4.3% which is not recommendable.
• Case 5 is showing energy error of 0.1% to 4.0% (Not recommendable).
• Case 3 is the most suitable because the energy error is fluctuating between 0.3% to 1.2% and the stress produced is 270 N/mm2. (Recommendable)
• Case 7 Law 36 is showing the energy error between -1.2% to 0.1%.
• Case 1 is not showing the appropriate simulation result deleting without cracking but in Case 2 Simulation is ok but energy error has gone up to 3.7% which is not recommendable.

Below is the link for all the .hm files for all the cases.

https://drive.google.com/open?id=1XExdhsXKmfgYzcX2Me-bStfjRjrC-L4_