Assignment 4

Objective: Here we are going to compare the given 7 types of cases which are:

1. Law 2 material (with failure johnson card)
2. Law 2 material (with failure johnson card) with XFEM formulation
3. Law 2 material (without failure card)
4. Law 2 material without failure card nor a maximum plastic strain value
5. Law 1 material card
6. Law 27 material ( brittle type)
7. Law 36 material card

We are going to compare the energy plots; observe the manner of crack formation and element deletion in each of the cases.

Case Setup and Execution:

For case 1:

• Go to Import > import solver deck > select the Failure_johnson_0000.rad > import.
• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law2_epsmax_failure_0000.rad > click RADIOSS to run.

For case 2:

• Go to Import > import solver deck > select the Failure_johnson_0000.rad > import.
• Go to failure card > change Ifail_sh to 1, Dadv to 1, and Ixfem to 1.

• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law2_epsmax_crack_0000.rad > click RADIOSS to run.

For case 3:

• Go to Import > import solver deck > select the Failure_johnson_0000.rad > import.
• Go to failure card, right-click, and delete failure card.
• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law2_epsmax_nofail_0000.rad > click RADIOSS to run.

For case 4:

• Go to Import > import solver deck > select the Failure_johnson_0000.rad > import.
• Go to failure card, right-click, and delete failure card.
• Go to the material card > right-click aluminum select edit > remove the value of esp_max.
• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law2_0000.rad > click RADIOSS to run.

For case 5:

• Go to Import > import solver deck > select the Failure_johnson_0000.rad > import.
• Go to failure card, right-click, and delete failure card.
• Go to the material card > Select card image > Change it to law 1.
• Set the value of Rho_initial = 0.0028, E = 71000.00, nu = 0.33.

• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law1_0000.rad > click RADIOSS to run.

For case 6:

• Go to Import > import solver deck > select the Law27_0000.rad > import.
• Go to properties > this is to set shell properties. Ishell=24, Ismstr=2, Ish3n=2, N=5, Ithick=1, Iplas=1.

• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law27_0000.rad > click RADIOSS to run.

For case 7:

• Go to Import > import solver deck > select the Law27_0000.rad > import.
• Go to curves and add a new curve, name it plastic_true_stress_strain curve. The data in this curve is obtained from the Material 7 video.

• Go to properties > this is to set shell properties. Ishell=24, Ismstr=2, Ish3n=2, N=5, Ithick=1, Iplas=1.
• Go to materials > change card image to M36_PLAS_TAB.
• To run the analysis, go-to analysis > check include connectors > set options as -nt 4 > save as Law27_0000.rad > click RADIOSS to run.

Results and Discussion:

Case 1: Here the obtained results depend on the failure card. The default settings for this case are Ishfail=2, Dadv=0, and Ixfem =0. This card does not use crack formation in the depiction of the results. Thus the results obtained do not show elemental crack formation but only the deletion of the elements as Xfem=0 and Dadv=0. However, they check for crack formation and if there is a crack formation in the element then it is deleted.

Here the total energy is seen to increase linearly up to 4sec and then the rate of increase drops till it reaches 27500 at the end of 5sec. An observation of a sudden increase in kinetic energy is made at 4sec due to the splitting of material from the parent body.

Case 2: Here the results are slightly different than what we see in case 1. The input value of Ifail_sh=1, Dadv=1, and Ixfem=1 cause changes in the results obtained. The elements that have undergone crack are not deleted. If an element undergoes crack twice only then it is deleted. Here the crack in an element is observed. In the contour below we can observe a cracked element at the center.

This leads to a different plot in energy. The total energy is seen to rise at the same rate up to 4.5s then it becomes constant till 5s reaching the maximum value of 31000, .i.e. greater than the previous case. We notice that at 4.5 sec the kinetic energy increases as the elements are separated from their parent body.

Case 3: Here the Failure/Johnson Card is deleted. This is done to observe the effect on results without the failure card. Now, in the absence of a failure card the element deletion is performed on the basis of the eps_p_max (failure plastic strain). Thus when the ball hits the plate the elements that undergo deformation that exceed the eps_p_max value are deleted. In this case the eps_p_max value is 0.151, so if an element reaches this value, it is considered to be a failed element and it is deleted. No crack formation is shown in this case.

Here the Total energy variation is the same as in case 1 and reaches a similar value of 27500 at the end of 5 s with an increase in kinetic energy around 4s marking the splitting of an element from its parent body.

Case4: Here the Eps_p_max value is deleted. Now when the eps_p_max value is deleted then the default becomes 10^30 as it is Law 2 material card which we know is for an elastoplastic material. Thus an increase in the eps_p_max value increases the force absorption of the material and the elasticity of the material. As the default eps_p_max value is so high, it behaves as an elastic material. So there is no deletion of elements nor there are any crack formations observed in the animation up to 5seconds.

Here we observe a steep increase in the total energy reaching a maximum value of 70000. The kinetic energy is zero as the elements do not split from the parent body.

Case 5: Here the plate is considered to be completely elastic as no plastic strain is recorded in the simulation. Also, von misses stress is observed to be extremely high compared to the LAW2 condition. No fracture, deletion, failure, or cracking of elements is observed in this case.

Here the total energy of the plate is extremely high and reaches up to 900000. As the element shows no failure at this high energy it shows that the plate material is extremely elastic.

Case 6: This case used Law27 which is for brittle material. Here we notice the entire separation of the plate from the center. The material here is not completely brittle as it bends in the beginning before breaking ultimately. Here the elements that have failed are deleted. This is also seen with the elements at the boundary of the plate. After 4 seconds the elements at the boundary fail and are deleted from the model.

Case7: Here the material deformation and failure are according to the plastic true stress-strain curve that has been included in the law 36 material card. Here the material showed less bending when the object strikes. There is no cracking in the elements observed. The elements that have failed are deleted from the model. Here we observe that there is a hole formation that has the same size as the of the object striking it. Another observation is that less plastic strain is experienced throughout the material compared to the other case.

As the strain in the body increases the total energy increases at a constant linear rate, then after 3 sec due to element failure the energy in the object stops to increase as it has reached it maximum strain value and the energy change is zero till the end of 5sec.

Based on the results this case would show the on-field scenario as it obeys the true stress-strain curve is calculating the deformation of the object. Also, the manner in which the object deforms is similar to the on-field scenario.

COMPARISON TABLE:

CASE	No. of Cycles	Mass Error	Max Energy Error(%)
Law2_espmax_failure	49480	0	1.10%
Law2_espmax_crack	49497	0	5.8%
Law2_espmax_nofail	49405	0	1.20%
Law2	48737	0	3.00%
Law1	47969	0	4.00%
Law27	49536	0	1.10%
Law36	53151	0	-1.50%