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

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

Aim:

To compare the results obtained from simulation of solid block using elform -2, -1, 1, 2. The solid block parameters are given below.

1. To create solid block of dimensions 10mm*10mm*10mm with 10 elements for each direction.
2. To attach the given material model Ogden_Material.k extension file
3. To choose a type of solver (explicit/implicit) and justifying the chosen solver.
4. To create an excel sheet with proper conversion and calculation of stress/strain and stretch ratio for all the elform.

Software used :- Ls prePost(R) V4.7.17

Problem statement :-

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:

1. Open LS-Dyna Project Manager>>Start LS Prepost>>Import the given material file Ogden_Material.k
2. Go to Element and Mesh option>>Shape Mesher>>Enter the values shown below in the popup. This would create a solid box of dimensions 10mm*10mm*10mm with 10 elements in each direction.

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

Note: For the different cases of simulation select different values of ELFORM from the drop-down and save it as a different extension file and run the analysis. The definitions of various ELFORM is shown in the above figure.

4. The given material card is shown in the figure below.

5.Go to Keyword Manager>>Part>>Rename the part accordingly and assign the section and material card to the part ID.

6.Go to create Entity >> Arrest the nodes in the origin plane (along y-z plane) from all rotational degree of freedom and translation along x-axis.

This will ensure that the nodes does not move along different axes when the load is applied along the x-axis.

7. Select the midsection of nodes along z-axis and y-axis and arrest the translation of the nodes along their respective axes to arrest the lateral movement when displacement is applied. This is shown in the figure below.

8. Go to Keyword Manager>>Define>>Curve. The curve is defined as shown below.

The scale factor is assigned in the boundary condition card.

9. Go to Keyword Manager>>Boundary Condition>>Select the nodes on the y-z plane and assign the curve ID defined in step 10 as the displacement value. This is shown in the figure below.

10. Create *CONTROL_IMPLICIT_GENERAL and *CONTROL_IMPLICIT AUTO cards from the control card in the keyword manager. This is shown in the figure below.

11. Create *CONTROL_IMPLICIT_SOLUTION and *CONTROL_IMPLICIT_SOLVER cards as shown in the figures below.

Create a total *CONTROL_TERMINATION of 1ms.

12. The following output requests are placed.

13. Save the file with a suitable name with .k extension and run the simulation.

RESULTS :-

Case 1: ELFORM 1 element formulation

The X-Stress and X-Strain contours are shown in the figures below.

Case 2: ELFORM 2 element formulation

The X-Stress and X-Strain contours are shown in the figures below.

Case 3: ELFORM -1 element formulation

The X-Stress and X-Strain contours are shown in the figures below.

Case 4: ELFORM -2 element formulation

The X-Stress and X-Strain contours are shown in the figures below.

From the results, it is observed the maximum value of X-Stress and X-Strain are same for all the element formulation and the values are 4.5 MPa and 1.7 respectively.

True stress and strain curves have been plotted and saved in.csv format and then graph has to be plotted for engineering stress and stretch .for this it is required to convert true stress and true strain to engineering stress and engineering strain and engineering strain is converted to stretch using these formulae.

ɛ_t = ln(1+ɛ_e)=ln λ

to find engineering strain natural log when taken to the other side the engineering strain is the (exponential of true strain - 1).

ɛ_e = Exp(ɛ_t) - 1

ɛ_e =Exp(1.33E-02) - 1

to find stretch 1 is added to engineering strain

λ = 1+ɛ_e

finally engineering stress is obtained by dividing the true stress with stretch

σ_t = σ_e * (1 + ɛ_e)

σ_t = σ_e * λ.

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

Case 1: Elform 1 element formulation

Case 2: Elform 2 element formulation

Case 3: Elform -1 element formulation

Case 4: Elform -2 element formulation

From the stretch ratio plots, it can be inferred that there is a huge deviation from the actual plot given in the problem statement. The plots for various element formulation is almost the same. It is due to the simplicity of the model. If there is a complex geometry involved, then significant change can be observed in the results. Here, the actual test-up might not be given as the boundary conditions for the problem. For example, temperature plays a significant role during the test. Also, the rate of application of load highly varies in actual when compared to simulated results thereby causing deviation in the obtained results.

CONCLUSION:

The case setup was done as per the objective and the corresponding output requests are obtained. Implicit solver is used for the simulation because the effect of strain rates are minimal.

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