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

CALCULATING THE STRETCH RATIO AND COMPARING THE ELFORM(-2,-1,1,2)WITH OGDEN MATERIAL MODEL USING LS-DYNA

AIM:

1. To create a block of 10mm*10mm*10mm dimension with 10 elements each direction and use the material card attached.(ogden_material.k).
2. To use appropriate boundary conditions to simulate uniaxial tensile behaviour of 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 material is a hyperelastic material model that can be used for predicting the nonlinear stress-strain behaviour of materials 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 0ring and seal.Even though the ogden model is a hyperelastic material model,its strain energy function is expressed by the stretch ratio.

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

PROCEDURE:

• The given Ls-Dyna keyword file is opened.
• Import the ogden_material_card in the file.
• The FE model of a solid block of 10mm*10mm*10mm dimension with 10 elements for each dire ction is crreated as shown below.

PART DEFINITION:

Section properties:

The section properties of the FE model created is assigned as solid elements with different ELFORM such as,

Case(1).ELFORM=1,Constant stress solid elements.

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.

Note:The simulation has to bee executed for each case seprately.

Material properties:

Keyword manager>mat>077_OGDEN_RUBBER

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

NOTE:The unit of μ in the material defination is in MPa and α is a dimension less quantity.

Part defination:

BOUNDARY CONDITIONS:

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

The mimimum load to be applied in x-direction on the moving surface to attain a stretch ratio 5,is calculated by using following relations.

we kown that Engineering strain means change in length divided by original lengh.

εe=δl/l

stretch ratio

λ=1+εe

5=1+δl/10

δl=40mm,

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

Curve is defined between displacement and time.

motion set card:

BOUNDARY_PRESCRIBED_MOTION_SET Card is used to apply the boundary condition on the moving surface.

• To perform the uniaxial tensile test on the specimen.the nodes of one of the faces are fixed along x-axis
  

• Then we fix the vertical middle nodes along z-direction and x-dircetion

• Then we fix the horizantal middle nodes along x and y direction.

CONTROL FUNCTION:

CONTROL_IMPLICIT_AUTO Card is used for automatic timestep controlduring implicit analysis.input value for Automatic time step control flag=IAUTO=1

CONTROL_IMPLICIT_GENERAL Card is used to activate implicit analysis and define associated control parameters.this keyword is used for implicit analysis.

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

DTO=initial time step size for implicit analysis=0.01

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

CONTROL_IMPLICIT_SOLVER is used for implicit calculation.

DATABASE:

• BINARY_D3PLOT
• EXTENT_BINARY
• ASCII(ELEOUT,NODOUT,MATSUM,GLSTAT)

RESULT:

• From the above simulation we will get true stress and true strain graph as a result.
• with the resultant data we will have calculated engineering stress and engineering strain by formula.

ELFORM1

It is a constant stress solid element(default),it has hourglass control for large deformation.it is accurate and has low computational cost than others.

ELFORM-1

Fully integrated solid intended solid for elements with poor aspect ratio with efficient formulation.

ELFORM2

Fully integrated solid elements with reduced stiffness matrix.

ELFORM-2

Fully integrated solid intended solid for elements with poor aspect ratio with accurate formulation.

CONCLUSION

The result between Engineering Stress and Stretch Ratio is ploted for different formulation there is no much changes expect the computational time.The tensile test of a cube is very small simulation the difference can be noticed for big problems.

From the simulation ELFORM1 has less simulation time.