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

Aim:
To perform the simulation using ELFORM- 1,2,-1,-2 and calculate a stretch ratio

Objective:

• To Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k) with given properties
• Use appropriate boundary conditions to simulate tensile behavior for the model and finally compare the results from your simulation using engineering stress vs stretch ratio
• Use a proper solver (Implicit/Explicit)

Procedure:
Creating solid mesh

• The solid block of 10mmx10mmx10mm dimension with 10 elements for each direction is crested using Shape Mesher from Mesh option

Section

• The Solid_section is created by section option using a different type of ELFORM such as,

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

Material

• The material card has been provided in the keyword file, the unit system followed is gm-mm-ms and it is assigned to the solid block part

Part

• The material and section properties are assigned to the solid part

Boundary condition

• To perform the uniaxial tensile test on the part, the faces of one of the nodes are constrained along the X-axis

• Then creating the vertical middle nodes along Z- direction, to get Y- direction constrained

• Finally creating the horizontal middle nodes along Y- direction, to get Z-direction constrained

Prescribed motion

• The minimum displacement to be applied on the moving surface model to attain a stretch ratio of 5, is calculated by using the following relation,
  λ=1+εe
  Engineering Strain, εe=δL/L
  λ=5,L=10
  5=1+(δL/10)
  δL=40mm
• Hence, the minimum value of 40mm is taken to define the load curve

Generally in LS pre-post, the solver worked as an explicit method. To perform an Implicit solver the following keywords are needed to switch from implicit to explicit

Control Cards

• CONTROL_IMPLICIT_AUTO is used for automatic time step control during implicit analysis. The input value for the automatic time step control flag, IAUTO= 1 is used to activate the implicit method

• CONTROL_IMPLICIT_GENERAL is used to activate implicit analysis and define associated control parameters
  The input value for IMFLAG=Implicit/Explicit, switching flag = 1 (implicit analysis). DT0 refers to the Initial time step size for implicit analysis = 0.01

Database

• The time step value of 0.01 ms is given for the BINARY_D3PLOT, DATABASE_ASCII for GLSAT

Results

Von Mises

Calculation of Engineering stress/strain and stretch ratio

• In LS-DYNA always the output of stress and strains I get from the Post fringe comp Stress/Strain are given as true stress and strains
  To find the engineering stress/strain and stretch ratio following relations are used,
  I know that True stress, σt=σe(1+ϵe)
  Engineering stress, σe=σt / (1+ϵe)
  Similarly, True strain, ϵt=ln(1+ϵe)
  Engineering strain, ϵe=eϵt−1
  Stretch ratio, λ=1+εe
• Using excel I calculated our Engineering Stress (ϵe) and Stretch Ratio (λ) using the above relations

Conclusion:

• A FE model was understood and created a solid block with Ogden material to simulate a uniaxial tension test for different cases of ELFORM (1, -1, 2, -2)
• The Engineering stress/strain and stretch ratio was calculated to plot a graph of Eng. stress vs stretch ratio up to stretch ratio 5
• The uniaxial tension test was solved using an implicit solver since the analysis is similar to a quasi-static analysis on a hyperelastic non-linear material with slow steady loading conditions