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# Equations used in LS Dyna

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(@nitin_kumar)
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Which equations are used in LS Dyna for bullet hitting the fabric. Following is the link

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(@negativevolume)
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Hi @nitin_kumar,

What exactly do you mean by equations? Are you specifically talking about the material equations of the fabric? Or something else like the contact between the fabric and the bullet and the breaking of the fabric?

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Topic starter
(@nitin_kumar)
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I need stress-strain consecutive equations, FEM equations and how friction coefficients are calculated

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(@negativevolume)
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@nitin_kumar

This is quite a broad question so I'm going to refer you to the LS-Dyna theory manual to start. Everything that you mention is explained there. If you have any other specific questions feel free to ask.

http://ftp.lstc.com/anonymous/outgoing/jday/manuals/DRAFT_Theory.pdf

(@nitin_kumar)
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@negativevolume

I have read the theory manual but I am confused:

1) For fabric 4-node rectangular shell element, whether to use Belytschko-Lin-Tsay or Hughes-Liu shell element?

2) For bullet 8-node solid element, whether to use 8-node hexahedron solid element or something else?

Thanks

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Topic starter
(@nitin_kumar)
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Hi,

In LS Dyna, I have defined bullet as a solid element. As shown in the attached file/picture N9 and N10 are 0, so the solid element will be 8-node or 10-node element.

Thanks

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(@negativevolume)
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@nitin_kumar

1.) When you say "fabric" do you mean that you are using *Mat_Fabric? Because if so then you can use Belytschko-Tsay. It is the default and I normally start here and change if I run into issues. If you are using a material that is not *Mat_Fabric but you still want a fabric-like response, then you can try  Belytschko-Tsay membrane. This will make reduce bending stiffness so that the part behaves like a fabric.

https://www.dynasupport.com/tutorial/ls-dyna-users-guide/elements

2.) You say 8-node hexahedrals but the picture you attached is tetrahedral elements which are defined with 4 nodes, so I'm confused here. Your tetrahedrals should not be defined with 8 nodes. I think the issue is that you saved your mesh out with the option of "ten nodes format" so it filled nodes 5,6,7,8 with the same id as node 4.

I never use the ten nodes format so I would just re-save your model with that option un-checked. I may have to get back to you on how to convert this but it should still work fine as you currently have it if you want to proceed with your project.

(@nitin_kumar)
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@negativevolume

I have rectangular shell elements in the fabric, so should I use Belytschko-Lin-Tsay shell element as it is not rectangular shell or something else?

For bullet solid elements, should I use four node tetrahedron element or something else?

Thanks

(@negativevolume)
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@nitin_kumar

I just watched back through the video. Since they are using *Mat_Plastic_Kinematic for the fabric, you will need to use ELFORM 5 Belytschko-Tsay membrane or ELFORM 9 Fully integrated Belytschko-Tsay membrane. The fully integrated version will take longer to simulate but may be more accurate.

The bullet is fine as 4 node tetrahedrals.

What is that picture of that you are showing? The fabric in the video is modeled as two layers like a weave so it's a little complicated.

(@nitin_kumar)
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Dear @negativevolume thank you very much.

I have purchased the vedio .k file for testing my LS dyna and modelling the same. I am following the same paper( https://www.tandfonline.com/doi/full/10.1080/09243046.2012.690298 ).  In this paper(page 180) it is mentioned:

Figure 4 shows how the total fabric sample was modeled by using rectangular cross sections of shell elements to represent the interwoven yarn comprising each of the four fabric layers.

So I think Belytschko-Tsay shell is used for fabric. the above picture is two layer fabric solid elements(shrunken element mode with messing)

I am confused whether bullet mess is four node tetrahedron element or nodal pressure tetrahedron or Fully Integrated Tetrahedron Element With 24 Degrees of-Freedom.

Thanks

(@negativevolume)
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@nitin_kumar

So fabric within LS-Dyna means that there is not bending stiffness of the elements. So think of a blanket on a bed how it forms to the shape of the bed. It's up to you to determine whether or not that is what you want to use. So either use Belytschko-Tsay or Belytschko-Tsay Fabric.

The bullet mesh, as in the actual elements that make up the bullet, are four node tetrahedron.

Within FEA, your modeling process is should go like this:

Geometry -> Determine element type needed (3D: tetrahedral or hexahedral, 2D: tria or quad, 1D: beam) -> Mesh the geometry with the elements that you want -> Assign a section property to the mesh which is where you define the element formulation (ELFORM) which would be something like Belytschko-Tsay for example -> Assign a material model to that mesh and define the needed inputs for the material like density, elastic modulus, poisson's ratio -> Then finally assemble the model using contacts, control cards, constraints ect.

I hope this helps!

(@nitin_kumar)
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@negativevolume

Thanks for the suggestions, its helping me lot to clear my doubts.

1) which equations are used when coulomb friction is incorporated in shell and solid element?

2)which equations are used when we combine all shell elements(say 100) together in our simulation?

Thanks

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(@negativevolume)
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I will also mention that you can use the fully integrated versions of the element formations that I mentioned previously which would be elform 9 or 16. This can provide more accurate results than traditional under-integrated elements in certain situations.

(@nitin_kumar)
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@negativevolume

Thank you very much for the help

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