Week-6 Calculate the Stretch Ratio by comparing the ELFORM (-2,-1,1,2) with Ogden_Material Model.
AIM:
To perform a uni-axial tensile simulation of a solid block (10mmX10mmX10mm) upto stretch ratio of 5 using ogden material card with different element formualtion (1,2,-1,-2).
PROCEDURE:
1.Import the given material file.
2.Create a block with given dimension.
3.Generate a solid mesh using mesh tools with elemental length of 1.
4.Create a solid section with 4 differnet element formualtion 1,2,-1,-2.
5.Assign the material id and section id to the part id.
BOUNDARY CONDITIONS:
1.Create entity > spc > select all the nodes on one side.
2.Create node set for all the nodes on the opposite side.
3.Create Prescribed motion set and define the LCID there as an input for displacement.
4.Now we need to define the LCID For that we deduce how much dispacement is to be given,
We require stretch ratio to be 5,
(1+ε) = λ
[1+(L+δ)/L] = 5,
By solving this we get
L=10 and δ=30.
Solver:
1.We are giving our input as a displacement and thus this simulation acts as static or quasi static problem.
2.Control Implict General keyword to activate the implict solver.
3.Now we are using odgen material we need to consider the non-linearity and thus we need to activate nonlinear solver.
4.Implict solver solves the problem using matrix inversion of stiffness matrix.
5.Control termination is set to 10.
Database:
1.We only require the d3plot to obtain the result. Dt=0.05.
OUTPUT:
1.Whatever data we recieve fromt the solver is the true stress and true strain. But we require the data in term of engineering stress and stretch. So we will take the data and convert them in required terms using formula,
ε(t) = ln[1 + ε(e)]
The equation implies,
ε (e) = exp[ε(t)] – 1
λ = 1 + ε(e)
σ(t) = σ(e) * [1 + ε(e)]
The equaiton implies,
σ(e) = σ(t) / [1 + ε(e)]
1.Using the following relations, we got a plot of Stress vs Stretch for all 4 case. These plots are
as follow.
2.Below figure shows that the result remain almost constant irrespective of the elemental
formulation.
ELFORM=1:
ELFORM=2:
ELFORM=-1:
ELFORM=-2:
STRESS VS STRETCH:
RESULT:
Thus the uni-axial tensile simulation of a solid block (10mmX10mmX10mm) upto stretch ratio of 5 using ogden material card with different element formualtion (1,2,-1,-2) is performed sucessfully.