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

AIM:-calculate the Stretch Ratio by comparing the ELFORM

OBJECTIVE:-

Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k) that is representative of the material properties from the above figure.

Use appropriate boundary conditions to simulate tensile behavior for the model and finally compare the results from your simulation to the plot above up to stretch ratio 5.

Only the uniaxial plot is to be compared.

Compare the results for the simulation using ELFORM = 1, 2, -1, -2

The unit of µ in the material definition is in MPa and α is a dimensionless quantity. Modify those quantities according to your unit systems.

Use a proper solver (Implicit/Explicit) and also explain the reason.

Procedure:-

- Open the given Ogden file > create a 10x10x10mm solid mesh using the shape mesher option.

Section Creation:

3/ The section properties of the FE model created are assigned as a solid element with different ELFORM such as,

Case (1). ELFORM = 1, constant stress solid element. [Under integrated constant stress; needs hourglass stabilisation; efficient and accurate.]

Case (2). ELFORM = -1, Fully integrated S/R solid intended for elements with poor aspect ratio, efficient formulation. [Similar to ELFORM 2, but shear locking is accounted for; efficient formulation (CPU time).]

Case (3). ELFORM = 2, Fully integrated S/R solid, [Reduced integrated; no hour glass stabilisation needed; slower than ELFORM 1; shear locking can occur.]

Case (4). ELFORM = -2, Fully integrated S/R solid intended for elements with poor aspect ratio, accurate formulation. [Similar to -1, more accurate, more computational cost.]

Go to Keyword Manager > Section > Solid > Enter the values as shown in the figure below.

Material:

4/ The material card given in the below image is already provided in the keyword file, the unit system followed is gm-mm-ms and it is assigned to the solid block part.

Assigning Material and Section to PART:

5/ The material and section properties are assigned to the solid part as shown in the image given below.

Boundary Conditions:

SPC_Set ->

6/ To perform the uniaxial tensile test on the specimen, the nodes of one of the faces are fixed along the X-axis.

7/ Then we fix the vertical middle nodes along the ‘Z direction’ fixed in the Y-direction.

8/ Then we fix the horizontal Middle nodes along the Y-direction fixed in the Z-direction.

Psecribed_Motion ->

9/ The minimum load to be applied on the moving surface to attain a stretch ratio of 5, is calculated by using the following relation,

True strain = ln (1+Engg.strain)

Stretch Ratio = 1+Engg.strain

5 = 1+ ( delta L / L )

delta L = 40 mm

Hence, the minimum value of 40mm is taken to define the load curve.

/ Define Curve: go to Keyword Manager > All > Define > Curve.

10/ The node-set and load curve IDs are assigned to the prescribed motion set so the selected nodes move along the X direction.

Control Cards:

11/ CONTROL_IMPLICIT_AUTO card as shown in the below image is used for automatic time step control during implicit analysis. The input value for the Automatic time step control flag = IAUTO = 1.

12/ CONTROL_IMPLICIT_GENERAL card as shown in the below image is used to activate implicit analysis and define associated control parameters. This keyword is required for all implicit analyses.

The input value for IMFLAG=Implicit/Explicit switching flag = 1 (implicit analysis)

DT0=Initial time step size for implicit analysis = 0.01.

3/ CONTROL_IMPLICIT_SOLUTION card as shown in the below image is used to specify whether a linear or nonlinear solution is desired.

The default values are set as it is in the card.

14/ CONTROL_IMPLICIT_SOLVER card as shown in the below image is used for implicit calculation.

15/ The control termination function as shown in the below image is enabled to specify the end time of the simulation.

The termination time is set for 1 ms.

Database:

16/ The time step value of 0.01 ms is given for the BINARY_D3PLOT as shown in the below image and the DATABASE_ASCII option for GLSAT and ELOUT.

7/ The DATABASE_EXTENT_BINARY card with STRFLG =1, as shown in the below image is used to compute the elastic strain in the model.

18/ The DATABASE_HISTORY_SOLID card as shown in the below image is used to compute the stress/strain of a 551 node in the model.

/ The keyword file is saved using the ‘.k’ extension and is made to run in the solver by getting normal termination messages for different cases of ELFORM.

Results:

/2/ Go to the destination folder & open True Stress/Strain vs time in Excel polt and then put 1,2,3 formula to converse in Engg Strain/Stress, Stretch ratio in Excel,

/3/ Finally, with Engg. Stress (Y-axis) & Stretch ratio (X-axis) we plot the graph in Excel > Insert > Chart.

he values of the stretch ratio obtained for all four cases are shown below.

Case 1: ELFORM ‘1’ element formulation

Case 2: ELFORM ‘2’ element formulation

Case 3: ELFORM ‘-1’ element formulation

Comparison:

• Since this is the uniaxial tensile test, we are getting similar results for different element formulations.
• Also, the deformation we have given to the cube was not so large for this type of hyperelastic material, so the difference cannot be observed.
• For different boundary conditions and different loading conditions, we can get different results with changes in element formulation type in a more efficient manner and clearly visible.
• Since the element formulation (1) is constant stress solid element, which defaults, a constant point element is invoked, which is good to propose the strain energy function.
• Element formulation (2) is a selectively reduced integrated solid element, which gives constant pressure throughout the element to avoid pressure locking, but type (1) is more accurate the type (2) for implicit problems.
• Element formulation types (-1) and (-2) are fully integrated elements intended for elements with poor aspect ratios. Among which type (-1) is more efficient and type (-2) is a more accurate formulation.
• Since Element formulation (-1) has some side effects related to some particular deformation modes, we can conclude that Element formulation (-2) is more accurate and mostly preferred for the solid elements in Implicit problems.

CONCLUSION:

The case setup was done as per the objective and the corresponding output requests are obtained.

An implicit solver is used for the simulation because the effect of strain rates is minimal.

The value of the stretch ratio is calculated for various element formulations.