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Aim : Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k) that is representative of the material properties from the above figure. Use appropriate boundary conditions to simulate tensile behavior for the model and finally compare…
abhijeet dhillon
updated on 22 Dec 2021
Aim :
Create a block of 10mmx10mmx10mm dimension with 10 elements for each direction and use the material card attached (Ogden_Material.k) that is representative of the material properties from the above figure.
Use appropriate boundary conditions to simulate tensile behavior for the model and finally compare the results from your simulation to the plot above up to stretch ratio 5. Only the uniaxial plot is to be compared.
Compare the results for the simulation using ELFORM = 1, 2, -1, -2
The unit of µ in the material definition is in MPa and α is a dimensionless quantity. Modify those quantities according to your unit systems.
Use a proper solver (Implicit/Explicit) and also explain the reason.
Solution :
First we will discuss a set of new cards as shown below :
1.Cross Section Database Card : This card is used to find out the the cross sectional forces in x and y direction at any connectors or section of the component that helps us to find out the at which force will the connector break .In order to use it a set of nodes or shell element is defined and later on used in this card.
Now we will discuss implicit and explicit solvers :
For all nonlinear and non-static analyses, incremental load (also known as displacement steps) are needed. In more simplistic terminology, this means we need to break down the physics/time relationship to solve a mathematical problem. To do this, we form two groups: either time-dependent or time-independent problems. To solve these problems, we commonly use ‘implicit’ and/or ‘explicit’ methods.
We refer to problems as ‘time-dependent’ when the effects of acceleration are pronounced and cannot be neglected. For example, in a drop test, the highest force occurs within the first few milliseconds as the item decelerates to a halt. In this case, the effect of such a deceleration must be accounted for.
In contrast, when loads are slowly applied onto a structure or surface (i.e., when a monitor is placed onto a table) the loading can be considered ‘quasi-static’ or ‘time-independent’. This is because the loading time is slow enough that the acceleration effects are negligible.
All of these implicit vs explicit problems are expressed through mathematical partial differential equations (PDE’s). While today’s computers can’t single-handedly solve PDE’s, they are equipped to solve matrix equations. These matrix equations can be linear or nonlinear. In most structural problems, the nonlinear equations fall into 3 categories:
One method of solving for the unknowns {x} is through matrix inversion (or equivalent processes). This is known as an implicit analysis. When the problem is nonlinear, the solution is obtained in a number of steps and the solution for the current step is based on the solution from the previous step. For large models, inverting the matrix is highly expensive and will require advanced iterative solvers (over standard direct solvers). These solutions are unconditionally stable and facilitate larger time steps. Despite this advantage, the implicit methods can be extremely time-consuming when solving dynamic and nonlinear problems.
Explicit analyses aim to solve for acceleration (or otherwise {x´´}). In most cases, the mass matrix is considered as “lumped” and thus a diagonal matrix. Inversion of a diagonal matrix is straightforward and includes inversion of the terms on the diagonal only. Once the accelerations are calculated at the nth step, the velocity at n+1/2 step and displacement at n+1 step are calculated accordingly. In these calculations, the scheme is not unconditionally stable and thus smaller time steps are required.
Now we will discuss how to use implicit solver in ls dyna :
For this we use the following card :
1.Control Implicit General :
This card is used to activate the implicit solver so that the solution can be obtained implicitly . To activate we need the Iflag which is defined as 1 .The timestep in this is called the load step.
Imflag = 1 activates the implicit solver.
In implicit solver there is one load step which has a number of iterations within it . These iterations go on until convergence is achieved .
2.Control Implicit Auto :This is used to control the timestep or load step of the solver.
3.Control Implicit Solver : This keyword is linear solver parameter that is responsible for inverting the matrix .
4.Control Dynamics Solver : This is used to for simulating the dynamic problems .
Now we will discuss the material used in implicit anaylsis :
Since implicit analysis usually deals with linear part of the material law it is important to put the non linear segment as a linear input into the solver which will help it solve it . In order to do this we use the log of the non linear part which converts into linear part that helps it solve the problem.
This approach is used in the mat power law elasticity that helps to compute the material linearly .
Now we will discuss the contact used in implicit analysis :
Sometimes the contacts can lead to a lot of noise which might not lead to the accurate amount of force acting on the model .
In order to solve this problem we will use mortar contact that helps us to remove this problem.
Now we will solve a problem using the same theory as shown below :
Using the mesh elements present we have created a block of 10 by 10 by 10 mm as shown above .
Now we will define the material card as shown below :
Now we will use the implicit control cards that will help us define the implicit analysis :
1.Implicit Control General : This keyword helps us to make sure the analysis starts in implicit .
2.Control Implicit Auto : This helps us to define a strategy to control the timestep by making it or less depending on the problem .
3.Control Implicit Solver : This is the card that is responsible for inverting the stiffness matrix and solving the linearity of the problem.
4.Control Implicit Solution : This is the card that is responsible for solving the non linearity of the problem .
We have used the following cards as shown below :
The intial timestep should be end time by 100 .
Now we will define other basic cards such as :
Now we will set up the boundary conditions as shown below :
We have applied spc on a single face as shown
Now we will apply the intial velocity as shown below :
Now in order to view the strain we will introduce the following card :
So we have the following set up ready as shown below :
Now we will simulate for different element formulations :
We get the following :
COULD NOT FINISH
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