Stretch Ratio of an model by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.

Aim:-

To Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k), And Simulate Using appropriate boundary conditions, and Compare the results of the simulation with ELFORM = 1, 2, -1, -2 by plotting Engineering Stress vs Stretch Ratio up to stretch ratio 5. With Necessary 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's model has introduced Ogden in 1972. The Ogden model has been frequently used for the analysis of rubber components like O-ring and seal. Even though the Ogden model is a hyperelastic material model, its strain energy density function is expressed by the principal stretch ratio.

Procedure:-

The given LS-Dyna keyword file is opened in LS-PrePost using the option File>Open>LS-Dyna Keyword File. The imported keyword file consists of only the Ogden material card.

1. Modeling Cube:-

For Modelling Cube Open Mesh > Shape Mesher, IN the Shape Mesher Choose Box solid As Entity > Dimensions as 10*10*10

2. Section Creation:-

1. For Defining Section Go to Keyword manager > All > Section > Shell

2. For the Box, Section_Solid is created

3. Four different Element Formulations Are used To Solve the Problem, Element formulations(-1, -1, 2, -2) Are used Individually.

4.In this Case ELFORM=1 is Used ELFORM=-1, 2, -2 is used Consecutively for the Next cases.

Case (1). ELFORM = 1, constant stress solid element.

Case (2). ELFORM = -1, Fully integrated S/R solid intended for elements with poor aspect ratio, efficient formulation.

Case (3). ELFORM = 2, Fully integrated S/R solid

Case (4). ELFORM = -2, Fully integrated S/R solid intended for elements with poor aspect ratio, accurate formulation.

3.Assigning Materials:-

For Defining materials go to Keyword Manager > All> MAT > Select the Material card. Here The Material MAT_077_O-OGDEN_RUBBER Is given in the keyword file so it is assigned to the Box

4.Specifying the Material and Section ID to the respective part IDs.

1. In parts, we basically assign material and sections with their proper ID for every part individually.

2. Assign the Section Id and Material of the box in the Part.

5.Boundary conditions:-

Tp perform Uniaxial Tensile Test On the specimen The Nodes Of One of the Faces Are fixed Using SPC as shown below,

Select The Nodes in the Middle And Dof's are given According To the Deforming Consideration.

6. Prescribed Motion:-

A Set Of Nodes are created Along with the Face Of the Box opposite to the Fixed Face And Named As Displacement Nodes

Displacement is Given To the Node set Created Using Prescribed Motion Set By Boundary > Prescribed Motion set

The Load to be Applied On the Moving face to attain stretch Ratio is calculated

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)

`lambda`=1+`epsilon_e`

Engineering Strain `epsilon_e`= `( deltaL)/L`

`lambda=5,L=10`

`5=1+(deltaL)/10`

`deltaL=40mm`

For the safer Side, The Displacement is given as 50mm

A curve is defined with the Displacement of 50mm

The Displacement curve is assigned to the set of Displacement Nodes created.

As the Material, we use here is 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. In the Implicit method, displacement loading is recommended rather than Force load to achieve a more stable load. So this Problem is Solved using Implicit.

7. Control cards:-

As the LS-Dyna is explicit software in General, Some Control cards must be defined For switching to Implicit

1.Control_implicit_Auto:-

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

2.Control_Implicit_General:-

CONTROL_IMPLICIT_GENERAL card 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:-

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

4.Contol_Implicit_Solver:-

CONTROL_IMPLICIT_SOLVER card is used for implicit calculation.

5.Control_Termination:-

Termination time defined by using *CONTROL_TERMINATION card, Set Model and Part > Keyword Manager >Control> Termination to 1ms

8. Output Requests:-

1. To view the results of Simulations Following Steps are Specified.

2.The time interval between the outputs is 0.01 is defined in D3plot

3. Go to Keyword Manager > Database > ASCII select GLSTAT with DT 0.01

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

Run the Simulation:-

1. Save The Keyword Elform_(1, -1, 2, -2) Individually And Run the Simulation in LS Run

2.Open The D3Plot to Plot the Results.

Von mises Stress:-

Effective strain:-

From The Contour, We can see that The Stress values are 5.025, 5.024, 5.029,5.029.

The Respective Strain Values are 1.79, 1.79, 1.79,1.79

The Value Of strain is equal in all cases where there is a slight change in the Stress value but it's almost the same in all cases.

Calculation of Engineering Stress, Strain and Stretch Ratio:-

The Output Stress and Strain Obtained From The Post-processing are Noted as True Stress and Strain values,

We know that,

True stress, σt=`σe(1+epsilon_e)`

Engineering stress, σe=`sigma_t/(1+epsilon_e)`

Similarly,

True strain, ϵt=`ln(1+epsilon_e)`

Engineering strain, ϵe=`e^(epsilon_t)-1`

Stretch ratio, λ=`1+epsilon_e`

An element is selected as random In the Box and its value of Stress and Strain Are Plotted.

ELFORM_1:-

ELFORM_-1:-

ELFORM_2:-

ELFORM_-2:-

From The Results, we can find that hyperelastic materials exhibit the same Stretch ratios of 5.9 at 0.8 Mpa

Since It is a small analysis there is No nodal Displacement occurred and the element formulations Don't exhibit different Properties, whereas in the Industrial scenario working with large elements might show changes in termination time, accuracy based on the element Formulations Used.

Conclusion:

• The tension test was simulated for a cubical box modeled with Hexa elements and hyperelastic Ogden material model. The test was performed with ELFORM 1, -1, 2, and -2.
• The true stress and strain values were used to calculate the engineering stress and strain values.
• The stretch ratio was calculated for all the cases and a plot of Engineering stress vs stretch ratio curves was created and compared.
• An implicit method was used to solve this tension problem as the rate of displacement imposed on the model was very low and thus, it was similar to a quasi-static analysis on a hyperelastic elastic non-linear material.