Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.
Aim:
The aim of the project is compare the different types of element formulation of the solid element by tensile test analysis and calculate the stretch value of the model using hyperelastic material.
Hyperelastic Model:
Hyperelastic materials are designed for modeling rubber or rubber-like materials in which the elastic deformation can be extremely large.
Hyperelastic materials use something called a strain energy density function to derive the relationship between stress and strain. This allows them to model the relationship between stress and strain accurately even when the strain is between 100% to 700%, depending on the exact hyperelastic model that is used.
Various hyperelastic models are accurate over different range of strains. You must choose the model to use depending on the expected range of strains, the computational expense of the formulation and the amount of data that you have to define in the stress-strain relationship.
Ogden Material:
Here we are using the ogden material model to simulate the tensile test. This model is a hyperelastic material and used to describe the non-linear stress–strain behaviour of complex materials such as rubbers, polymers, and biological tissue. The model was developed by Raymond Ogden in 1972.The Ogden model, like other hyperelastic material models, assumes that the material behaviour can be described by means of a strain energy density function, from which the stress–strain relationships can be derived.
Solver:
In the field of CAE based on the type of analysis we will use the solver. There are two types of solver which plays a vital role in the field of CAE. They are Explicit and Implicit solver.
Explicit Solver:
At each node point, internal and external forces are summed and accelerating at the nodes is computed using F=ma. By integrating acceleration in time, velocity or displacement are calculated and the solution can be advance with respect to time. It is conditionally stable and capable to solve extreme non- linear problem. Good for short duration and highly transient problems.
Implicit Solver:
A global stiffness matrix is computed and inverted and applied to the nodal out of balance force to determine the displacement (F=ku). It is unconditionally stable and good for long duration problem.
Tensile Test:
Tensile test analysis mostly used to find the tensile behaviour and strength of the material. The tensile test experiment are conducted in a very slow manner and the readings are noted. From this data we will format the data to get the accurate result. For doing analysis in LS-Dyna it is better to use implicit analysis which helps to calculate the stress value more accurately compare to the explicit solver.
Simulation:
The above figure shows the model which created by using shape mesher of the dimension 10mm X 10mm X 10mm . This model is used to do the tensile test analysis by using the implicit solver and the material type is ogden.
Boundary Condition:
To capture the real time experiment, i am using the two spc and one prescribed motion.
The above figure shows the spc which constrain only in y translational.
The above figure shows the spc which constrain all degree of freedom except in y translational. The reason to give like this is, because if we constrain all degree of freedom in left end and we will give tensile force in right end there is a chance of compression happened in the left end. But in real time experiment it is not possible. So to avoid this compression effect we will give this kind of single point constrain.
In right end we will give displacement prescribed motion by defining the load curve.
To run the analysis by using the implicit analysis, we need to use control implicit general and control implicit auto.
Element Formulation:
This box is a solid box, so we need to define the section as solid and specify the element formulation. Element formulation deals with the mathematics and assumptions that drive the development of the displacements for different finite element types. Insights gained from displacements of the elements help determine the strain, stresses and nodal forces for that type of element which based on the integration of the nodes and the element shape.
Here we are comparing Elform -2,-1,1,2.
EQ.-2: fully integrated S/R solid intended for elements with poor aspect ratio, accurate formulation.
EQ.-1: fully integrated S/R solid intended for elements with poor aspect ratio, efficient formulation.
EQ.1: constant stress solid element (default),
EQ.2: fully integrated S/R solid,
Element Formulation -2:
The above figure shows the console memory for the elform -2 and the step , iteration of the simulation.
The above figure shows the equivalent stress value by using the element formulation -2. The stress shows in the above figure is accurate and predictable value of the tensile test analysis.
The above figure shows the uniaxial plot of the true stress strain curve of the tensile test behaviour for the ogden material. This curve file clearly shows that the value of youngs modulus is very less because the linear curve is very small.
In ls dyna we will get the true stress and strain curve.
Conversion of true curve and engineering curve:
For true stress and strain curve we are considering actual cross sectional area(instant) and in engineering stress and strain we calculating final cross sectional area.
True strain= ln(1+engineering strain)
True Stress= eng Stress(1+ eng Strain).
Stress strain plot are captured by using excel sheet from the above plot and stretch ratio is calculated.
Stretch Ratio:
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)
The above figure shows the curve of stretch ratio and nominal stress. Compared to the uniaxial plot, the curve matches approximately.
Element Formulation -1:
The above figure shows the run console for the element formulation -1.
The above figure shows the uniaxial stress value( elongation is x direction).
True Stress Strain Curve :
The above figure shows the true stress and strain value of this analysis. This curve data import in excel sheet and calculate the engineering stress and strain value to get stretch value.
Stretch ratio and Engineering Stress Plot:
The above figure shows the stretch ratio in x axis and stress in y axis which is plotted by using excel sheet.
Element Formulation 1:
The above figure shows the run console for the element formulation 1 tensile test.
Stress :
The above figure shows the stress value for the element formulation1.
True Stress and Strain Plot:
Stretch Ratio and Stress Plot:
Element formulation 2:
Stress:
True stress and True strain Plot:
Stretch ratio and Engineering stress plot:
Comparision of the Element Formulation -2,-1,1,2:
In run console, it is clearly shows that element formulation affect the iteration steps and computational time. In some cases these element formulation causes the hourglass effect. There is a slight variation in the stress value. If we compare the stress data in excel sheet it will shows the stress value differences clearly.
Similarly for stretch ratio plot, we will get the most accurate results compared to the uniaxial plot of the ogden material which showns clearly in the above figures.
For solid, element formulation 2 is best compared to other elform. It shows the elform 2 is less computational time and lss steps and also results are more accurate than the elform -2,-1,1,2.
Conclusion:
Different element formulation is compared by using the tensile test behaviour. The results are compared with uniaxial test and we get the most similar curve. The only difference stress and strain value is slightly differe because of the shape function which is integrated to get the result.
More integrated points will get to increase the accuracy of the results. For solid elform 2 is most recommend and for shell element elform 6 is recommended.