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

CALCULATE THE STRETCH RATIO BY COMPARING THE ELFORM (-2, -1,1,2) WITH OGDEN MATERIAL MODEL

AIM: To model spot weld as beam and hexa elements and create a complete simulation file for crash analysis from the given FE model of assembly of parts and produce the following deliverables.

1. To Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k).
2. To Use appropriate boundary conditions to simulate uniaxial tensile behavior for the model.
3. Compare the results of the simulation with ELFORM = 1, 2, -1, -2 by plotting Engineering Stress vs Stretch Ratio up to stretch ratio 5.
4. To use a proper solver (Implicit/Explicit).

INTRODUCTION:

An Ogden model is a hyperelastic material model that can be used for predicting the nonlinear stress-strain behavior of material such as rubber or polymer. Ogden model was introduced by Ogden in 1972. Ogden model has been frequently used for the analysis of rubber components like O-ring and seal. Even though Ogden model is a hyperelastic material model, its strain energy density function is expressed by principal stretch ratio.

In this simulation a solid block is created and appropriate boundary conditions are applied to simulate uniaxial tensile behavior for the model and stretch ratio is calculated. The solver used for this simulation is implicit solver because the analysis is similar to a quasi-static analysis on a hyperelastic non-linear material with slow steady loading conditions.

PROCEDURE:

The given LS-Dyna keyword file is opened in LS-PrePost using option

File>Open>LS-Dyna Keyword File as shown

The imported keyword file consists of only Ogden material card. As shown above

THE FE MODEL OF A SOLID BLOCK OF10MMX10MMX10MM DIMENSION WITH 10 ELEMENTS FOR EACH DIRECTION IS CREATED AS SHOWN :

Step 1 – Model Creation

Open LS-PrePost > Element >Mesh >Shape Mesher

Step 2 – Part Definition

After the creation of the model, the material card is defined. for the creation of the MAT_OGDEN_RUBBER card the material properties are specified as given in the question.

SECTION_SOLID card is used to define the section. Since the problem is given to use different element formulations, the ELFORM will be changed respectively.

The different ELFORM used are,1, -1, 2, -2.

CASE 1 - ELFORM = 1 EQ.1: Constant stress solid element

SECTION PROPERTIES:

Keyword manager>SECTION>SOLID.

MATERIAL PROPERTIES:

The above material card is already provided as a keyword file and it is assigned to the solid block part.

The unit of μ in the material definition is in MPa and α is a dimensionless quantity.

Keyword manager>MAT>077_O-OGDEN_RUBBER

Part definition:

Keyword manager>PART

BOUNDARY CONDITIONS:

To perform uniaxial tensile test on the specimen, the nodes of one of the faces is fixed as shown in the following fig

ENTITY CREATION – NODE SET- FACE_YZ_PLANE_NORAML_Z

Nodes fixed in X-direction.

ENTITY CREATION – MIDDLE NODE SET- MIDDLE_NODE_XY_PLANE_Z_DIRECTION

Middle nodes along Z- direction fixed in Y-direction

ENTITY CREATION – MIDDLE NODE SET- MIDDLE_NODE_XZ_PLANE_Y_DIRECTION

Middle nodes along Y- direction fixed in Z-direction

Now Prescribed_Motion_Set card is used to define the displacement of the model.

• Stretch ratio l is defined as the ratio between the final length L and the initial length L0 of a component i.e., it is equal to (1 + engineering strain)
• Your boundary condition should be relatable with the real-time boundary condition

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

Engineering strain,

Hence, minimum value of 50mm is taken to define the load curve

BOUNDARY_PRESCRIBED_MOTION_SET card is used to apply the boundary condition on the moving surface

NODE SET FOR - BOUNDARY_PRESCRIBED_MOTION_SET

CONTROL FUNCTION:

Keyword manager>CONTROL>IMPLICIT_AUTO

KEYWORD CONTROL_IMPLICIT_AUTO card is used for automatic time step control during implicit analysis. Input value for Automatictime step control flag = IAUTO = 1.

KEYWORD CONTROL_IMPLICIT_GENERAL card is used to activate implicit analysis and define associated control parameters. This keyword is required for all implicit analyses.

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

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

KEYWORD CONTROL_IMPLICIT_SOLUTION card is used to specify whether a linear or nonlinear solution is desired. The default values areset as it is in the card.

KEYWORD CONTROL_IMPLICIT_SOLVER card is used for implicit calculation

Keyword manager>CONTROL>TERMINATION

The control termination function is enabled to specify the end time of simulation. The termination time is set for 1 ms to capture the effect of brackets striking the rigid wall.

DATABASE OPTION:

Keyword manager>DATABASE>BINARY_D3PLOT

The time step value of 0.01 ms is given for the BINARY_D3PLOT and 0.01 ms in the DATABASE_ASCII option for GLSAT, ELOUT.

Keyword manager>DATABASE>EXTENT_BINARY

DATABASE_EXTENT_BINARY card with STRFLG =1, is used to compute the elastic strain in the model.

Keyword manager>DATABASE>HISTORY_SOLID

DATABASE_HISTORY_SOLID card is used to compute the stress/strain of a 1630, 1035 node in the model.

The keyord file created is checked for errors using the option keyword manager>model check. The keyword file is saved using‘.k’ extension and is made to run in the solver by getting normal termination message for different cases of ELFORM.

RESULTS:

The D3plot output file is opened in LS-PrePost using option File>open>LS-Dyna binary plot.

The animation of Von-Mises stress contour is as shown below.

CASE 1

CASE 2

CASE 3

CASE 4

2. The animation of X strain contour is as shown below

CASE 1

CASE 2

CASE 3

CASE 4

It is observed from the stress contour that the maximum value of X-stress for case 1, 2, 3 and 4 are 5.029 MPa, 5.021 MPa,5.029 MPa, 5.029 MPa respectively. The maximum value of X-strain for case 1, 2, 3 and 4 are 1.7890, 1.788, 1.789, 1.7879respectively. There is a small variation in the stress value but the strain value is almost same for different cases.

Calculation of Engineering stress/strain and stretch ratio.

In LS-DYNA the output of stress and strains from Post Fringe Comp Stress/Strain is given as true stress and strains. To find the engineering stress/strain and stretch ratio following relations are used,

We know that,

True stress σt = σe(1 + ϵe)

Engineering stress, σe =

Similarly, True strain, ϵ_t = ln (1 + ϵe)

So, Engineering strain, ϵe = e^ϵt -1

From the graphs plotted for Engg. Stress vs Stretch Ratio for different cases, the Engg. stress value corresponding to a stretch ratio of 5 is 1.6 MPa approximately.

The output from different cases of ELFORMS gives approximately same results since the model and loading conditions are simple.

CONCLUSION

1. We can conclude that the stretch increases as the stress induced on the part model increases. We can notice a huge deformation in the hyper elastic material even after the yeild point while this cant be seen in other materials. We can aso visualize that the deformation occurs in an non-linear manner since the change in stress is not linear to the change in strain.
2. A FE model of solid block was created with ogden material to simulate uniaxial tension test for different cases of
3. ELFORM(1, -1, 2, -2)

4. The Engineering stress/strain and stretch ratio was calculated to plot a graph of Engg. stress vs stretch ratio up to stretch ratio 5

5. The Engineering stress value for a stretch value 5 from the simulation for different ELFORM was approximately equal to
6. 7 MPa, but from the actual graph it was equal to 1.8 MPa with a difference of 0.1 MPa

7. The uniaxial tension test was solved using implicit solver since the analysis is similar to a quasi-static analysis on a hyper elastic non-linear material with slow steady loading conditions.