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

OBJECTIVE:

• Perform a uniaxial tensile simulation of a solid block (10x10x10 mm) upto stretch ratio of 5 using Ogden material card with different element formulation (1,2,-1,-2)
• Compare the uniaxial plots for all element formulation.

PROCEDURE

Defining the geometry

• Open the given keyword file containing the Ogden Material.
• Create a block of 10 x 10 x 10
• Generate the solid mesh using mesh tools with elemental length of 1.

• Now create a solid section with 4 different element formulation i.e. 1, 2, -1 and -2

• Assign the material id and section id to the part id.

Boundary conditions

• Since we are exercising the tensile test, we will keep one side fixed and will give displacement on the other.
• Create entity -> spc -> select all the nodes on one side
• Create node set for the all the nodes on the opposite side
• Create Prescribed motion set and define the LCID there as an input for displacement

• Now we need to define the LCID. For that we will deduce how much displacement is to be given
• Now we know we require stretch ratio to be 5.
• So (1 + ε) = λ
  [1 + ( L +δ)/L ] = 5, L = 10
  δ = 30
• Using this we will define the LCID as below

Solver

• We know that the explicit solver is used for the high speed dynamic simulation whereas implicit is more suitable for static/ quasi static loading condition.
• Here we are giving our input as a displacement and thus this simulation acts as static or quasi static problem. Considering that we will use the implicit solver for Ls-Dyna. Here time is a parameter which defines the evolution of loading
• We use Control_Implicit_General keyword to activate the implicit solver. Tag IMFLAG = 1 and define DT0
• Now since we are using Ogden material, we need to consider the non-linearity and thus we need to activate nonlinear solver. For this we use Control_Implcit_Solution and change the value of NSOLVR
• Control_Implicit_Auto – This keyword is used to define the no of iterations ( ITEOPT & ITEWIN )and minimum and maximum timestep size ( dtmin & dtmax )
• Implicit solver solves the problem using matrix inversion of stiffness matrix. For this Control_Implicit_Solver is used to select the solver type using LSOLVR card
• Control_Termination is set to 10

Database

• We only require the d3plot to obtain the result in our case as in implicit problem we do not require energies. Dt = 0.05
• To ensure that we get the true values of strain, we will use Database_Extend_Binary and set STRLFG to the required value

RESULTS

• We defined the steps of solving the problem in above section. 4 different simulations were done using different element formulation.
• Here we have extracted the Z stress (direction of displacement) and plastic strain for our further study using history plot for element 1067.
• Whatever data we receive from the solver is the true stress and true strain. But we require the data in term of engineering stress and stretch. So we will take the data and convert them in required terms using following formula.

• ε(t) = ln[1 + ε(e)]
  => ε (e) = exp[ε(t)] – 1

• λ = 1 + ε(e)

• σ(t) = σ(e) * [1 + ε(e)]
  => σ(e) = σ(t) / [1 + ε(e)]

• Using the following relations, we got a plot of Stress vs Stretch for all 4 case. These plots are as follow.
• Below figure shows that the result remain almost constant irrespective of the elemental formulation.

CONCLUSION

Based on our study, we conclude that the stress vs stretch is almost constant for our simpler problems. But this may not be the case in complex problems and thus suitable element formulation needs to be selected depending on the type of problem.

We learnt the use of implicit solver by this exercise.

Link:

https://drive.google.com/drive/folders/1AJsFgxvIz2ue1qv17ji1KnFClqPnGCpR?usp=sharing