Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.

OBJECTIVE:

To run the simulation with different element formulation 1,-1,2,-2 and compare the stretch ratio vs Stress for all the cases

Steps carried out:

• Initially open the LS Dyna keyword file which is containing only the ogden material card, like shown in below image
  
• Now we have to create a cube of 10*10*10 mm cube with 10 elements on each face
• inorder to create the cube go to element and mesh>shape mesher>box solid
  
• Create a section card for solids with element formulation=1, -1, 2,-2 for case1,2,3,4 respectievely
  
• Now assign the section card and material card to cube
• To perform a tensile test we need to fix the cube on one side and apply the displacement load on the other end
• Create few node sets as defined below
• Select the nodes from one face and restrict them in global x direction
  
• Now select the nodes in global z direction and constrain the DOF in y direction
  
• Now select the nodes in global Y direction and constrain the DOF in Z direction
  
• Now create node set id for prescribed motion set like shown in below image
  
• We know that the stretch ratio should be 5
  Stretch=1+engg strain
  5=1+(Change in displacement/10)
  Displacement=40mm
• We have to specify the displacement as 40mm, in order to give the displacement define a load curve
• Go to keyword manager>Define>curve
  
• Now assign this load curve to prescribed motion set card
• Now inorder to solve this problem using implicit solver, we need to create few implicit cards mentioned below
• go to keyword manager>controls>create Implicit_auto, Implicit General, Implicit solver,Implicit solution cards
  
  
  
  
  
  
• Create a termination card in order to run the simulation till 2 second
  
• Now create database cards like ASCII and Binary to get the required output
• Create Binary extenet card and set the STRFLG=1 as mentioned above in challenge
  

Output:

Case 1(ELFORM=1):-

• X-stress
  
  

Case 2(ELFORM=-1):-

• X-stress
  
  

Case 3(ELFORM=2):-

• X-stress
  

Case 4(ELFORM=-2):-

• X-stress
  
• The output what we get in post fringe are True stress and True strain values
• Inorder to calculate the stretch ratio we need to caluclate Engg stress and strain using the formulas
  True Stress:- `sigmat`=`sigmae`*(1+`epsilone`)
  Engg stress:- `sigmae`=`sigmat`/(1+`epsilone`)
  True Strain:- `et=ln(1+epsilone)`
  True Stress:- `epsilone=((exp epsilont)-1)`
  Stretch ratio:- `lamda=1+epsilone`
• Initially from history, plot the graph for an element true X-stress and strain(lower ipt X-strain) to all the cases(plot the graph for same element to all the cases)
• Save the plot with required interpolate points
• import the true stree and strain value to an excel sheet and calculate Engg stress and strain and Stretch ratio
• The graphs Engg stress VS Stretch ratio is shown in below images
• Case1
  
• Case2
  
• Case3
  
• Case4
  

CONCLUSION:

• Usage of different formulations will effect our computational time, in this because we do not have much variation.
• If the model would have been large or complicated we could have seen the computational time difference for each element formulations