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

AIM

The main aim of this project is to get familiarized with the idea of implicit analysis in FEA. The project aims to calculate the stretch ratio vs nominal stress of a cube with various element formulations using the hyperelastic material Ogden material model.

EXPLANATION

In this project a hyperelastic material model is given .A uniaxial tensile test simulation is to be done on a block of 10mm*10mm*10mm dimension, with the hyperelastic material model applied as its material.Then the stretch ratio is to be calculated and plotted with the corresponding engineering stress obtained for the element formulations -2,-1,1 and 2. The resulting plot is to be compared with the original plot obtained from real world tests. Stretch raio is defined as the ratio between the final length`L` and the initial length`L_0` of the component.

`lambda =1+epsilon_e`

Since the output values that we obtain after simulation from LS- dyna is the true stress and strain values ,we have to use the equation`epsilon_t=ln(1+epsilon_e)=ln lambda`for calculating stretch ratio and `sigma_t=sigma_e*(1+epsilon_e)` for calculating engineering stress.

Here implicit analysis is used for calculating the behaviour of the model as theoretical tensile test assumes that all the points of the model remain at equlibrium at all times and the extension happens at a very slow rate.

CASE SETUP

The input that we have is a hyperelastic material model. We first need to create a block of 10mm*10mm*10mm dimension. Before that the units are changed to gm,mm,ms units by using the *CONTROL_UNITS card. The cube is made by using the shape mesher tool from mesh options . Box solid is selected as the entity and the cube is created.

Here we are conducting the tensile test in the y direction. So using the *BOUNDARY_PRESCRIBED_MOTION_SET ,we give displacement to the nodes on the face of the cube in the y direction by giving DOF=2 and VAD=2.

Also, using *SPC_SET we constrain the nodes on nuetral axis in the x and z direction on the opposite face of the cube where we intent to pull for tensile test.

Now we define a curve for *BOUNDARY_PRESCRIBED_MOTION_SET using *DEFINE_CURVE for giving the displacement to the nodes along y-direction.

The curve is defined for 0 to 5.1ms with displacement ranging from 0 to 42mm.Eventhough we only need upto 5ms, we have defined the curve for an extra 0.1ms so that no errors are made by the software.

Using *SECTION_SOLID card we give the element formulations as -2 for the 1st simulation.*PART_PART keyword is used to assign the correct section and material to the model we made.

*CONTROL_TERMINATION is used for specifying the termination time of 5ms.

*CONTROL_IMPLICIT GENERAL with IMFLAG=5 is given to assign implicit solver with DT0=0.05 ms.

*CONTROL_IMPLICIT_AUTO is also given with IAUTO=1 and ITEOPT=11, ITEWIN=5 and DTMIN=5e-04 and DTMAX=5.

*CONTROL_IMPLICIT_SOLUTION is also applied with ILIMIT=25 and MAXREF=15.

*CONTROL_IMPLICIT_SOLVER is also applied.

*DATABASE_EXTEND_BINARY is given and STRFLG is activated to get the strain data. *DATABASE_ASCII_option is used with GLSTAT and MATSUM activated.

Also, *DATABASE_BINARY_D3PLOT card is also added.

The model is then run for simulation in LS run application. After the first simulation is done we change the element formulation to -1 with other parameters remaining the same and then run the simulation again to obtain the results for the second element formulation and so on for all the four element formulations.

The keyword setup done for the first element formulation is attached.

RESULT

The results of the simulation of various element formulations is given as an excel file attachment. The plots obtained are also included in the excel attachment. It can be observed that all the values of stretch ratio and stress obtained are very similar for all the element formulations .Also, the obtained plot is similar to the original plot given in the assignment.

The only difference observed for the different element formulations are the time taken to complete the simulation. Although in our case it is almost the same with a variations of almost two seconds. This could be since ,some element formulation may use more integration points for calculation.