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**Rudolf Bötticher www.rudolf-boetticher.de **

Comparison of EFG and Standard Elements for the Rubber Membrane in a Biomedical Valve in LS-DYNA Rudolf Bötticher Introduction This talk features the meshless Element Free Galerkin (EFG) method. This is a talk about LS-DYNA EFG as is in The EFG method is not explained the EFG implementation in LS-DYNA is not highlighted My interest lies in coupled simulations. Therefore, I chose a fluid structure interaction (FSI) problem. (Only solid EFG elements are possible with 5434.) For the EFG elements to have a chance I chose a problem with large element distortions and hourglass likelihood: the bending of nearly incompressible rubber membrane. I wanted to try out, whether a analysis of the interaction of multiple fluids with a structure out of EFG solids is possible. It is possible. I compare with standard Lagrangian solid elements: this means reduced integration and hourglass control type 6. The type is on the rise in LS-DYNA. Implicit prefers type 6. So let`s look at the pro and cons of EFG. .

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**Motivation Assess whether EFG with FSI and MMALE is possible.**

Compare the results with standard elements. Assess whether EFG is more robust. And I use an example that originates from LSTC`s FSI_Tutor.. I piece of mild steel is compressed between two rough cylinders. A small slice is modelled, because no axisymetric MMALE is possible. Dresden,

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**EFG is easy! *CONTROL_EFG *SECTION_SOLID_EFG 5,41 1.5,1.5,1.5**

$ in 970 EFG and (dormant) IMPLICIT cards are not tolerated $ in the same deck $ implicit and axisymmetric EFG not implemented! *SECTION_SOLID_EFG 5,41 $ the non-default bigger support helps to have consistent $ EFG simulations for *MAT_MOONEY-RIVLIN_RUBBER 1.5,1.5,1.5 Dresden,

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**MM-ALE is easy, if you got a working deck to refine!**

*ALE_MULTI-MATERIAL_GROUP Proceedings Dresden,

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**FSI: Tweaking of *CONSTRAINED_LAGRANGE_IN_SOLID**

3854, 5434 and newer beta versions deliver different results for identical decks! TSSFAC NADV METH CTYPE DIREC PFAC ILEAK Dresden,

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***EOS_GRUENEISEN ELFORM=11 *MAT_NULL *EOS_IDEAL_GAS AET=4**

*MAT_MOONEY-RIVLIN_RUBBER *EOS_IDEAL_GAS The next slide shows the detailed setup of the biomedical prototype duct. This is an axisymmetric structure, But, because there are no axisymmetric multi-material ALE elements in LS-DYNA, a 3D slice is modeled. Three fluids are in the system. This rubber membrane separates a water and an air domain, which are both at atmospheric pressure. The system is triggered by an ambient pressure source here. The rubber membrane is modeled with *MAT_MOONEY-RIVLIN_RUBBER. Here is the domain, where we will compare EFG and standard elements. The fluids` domain is modeled with multi-material ALE solids ELFORM=11. The water has an *EOS_GRUENEISEN and the air an *EOS_IDEAL_GAS. Above is the 30bar uniform ambient pressure source. The parameter AET is set to 4 on *SECTION_SOLID_ALE to model this. The system has constrains to model the outer wall and symmetry axis.. Dresden,

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**Why LS-DYNA for this problem?**

Curiosity Code is at your disposal Expect the same efficiency as for parallel crash simulation Rely on the advanced material modeling There are various reasons for using LS-DYNA for this problems apart from curiosity. Among them are …….. On the ANSYS conference here I do not claim that LS-DYNA is suited best for this problem: CFX may be better. CFX may be better Dresden,

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**Membrane covered with null shells Filling with *MAT_VACUUM**

Dresden,

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**CTYPE=4 CTYPE=5 DIREC=3 PFAC=0.1 www.rudolf-boetticher.de**

Dresden,

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**near incompressibility and mm dimensions require tiny time step**

A=500MPa no implicit, no time step split between rubber/ALE domain, no mass scaling! A=100MPa PR=0.49 Dresden,

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**5831 beta version delivers different results.**

However, problem not solved. FSI not robust against artificial shortening of time step. No difference between EFG and standard elements. Now comes the key graph for the comparison of EFG and standard elements. Shown is the displacement of the membrane tip in time for the simulation we just have seen. The pint is displayed in the picture in the corner. We see two bands of curves: one for the weak and one for the strong rubber. We first concentrate on the strong rubber. Curves E and G show the results for a Poisson`s ratio of 0.49 and EFG and standard elements. Standard elements means reduced integration with hourglass control type 6. Hourglass control type 6 is on the rise in LS-DYNA. Implicit prefers hourglass control type 6. Therefore I use it. EFG needs no hourglass control. These two curves are nearly identical: EFG shows the same behaviour as standard elements. If we now raise the Poisson's ratio to we reach curve A. At first glance we would attribute this change to the change of material properties. However, if the Poisson’s ratio is raised, the bulk modulus is raised, and the time step is shortened. If we shorten the time step artificially to the same value for the Poisson's ratio 0.49 simulation by setting TSSFAC on *CONTROL_TIMESTEP to a small number of about 0.3 we get curve C, which is nearly identical to A. We now have to state two facts: Firstly, the fluid structure interaction in LS-DYNA is not robust against artificial shortening of the time step. We cannot investigate the effect of the Poisson's ratio. Secondly, EFG and standard elements deliver nearly identical results. If we now look at the curves for the weaker rubber, we see that even the steady state value reached at the right side is dependent on time step. Testing the new beta versions one get different results. However, the problem is not solved. Further investigation and development is necessary. The joint behavior of *ALE_MULTI-MATERIAL_GROUP and *CONSTRAINED_LAGRANGE_IN_SOLID must be clarified. Dresden,

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Robustness It proves difficult generating an extreme situation where EFG works but standard elements do not! EFG may be superior preventing hourglass modes. In the second part of my talk I want to compare the robustness of EFG and standard Elements. It proves difficult generating a situation in which the solver aborts for standard elements but continues for EFG elements. The standard elements are pretty robust. Therefore, I want to focus on another important feature of EFG. The EFG method does not need a hourglass control. EFG does not introduce non-physical energy in the system to control these hourglass modes . This is hinted in the picture that shows a typical hourglass pattern. Dresden,

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**EFG performance lack: 10% elements switched, CPU time +20% ELFORM=1 **

*HOURGLASS,6 EFG This simulation uses a weaker rubber and a higher pressure step. On the left the results for standard elements are animated; this means reduced integration and hourglass control type 6. Despite this hourglass control a hourglass pattern emerges. The animation on the right side displays the results with the EFG method. The displacements are smoother. They show no hourglass problem. Apart from that, EFG does not introduce non-physical energy to control hourglass modes. However, this advantage comes at a price to the user. Though, only 10% of the elements are switched to EFG the solution time raises by 20%. Most elements are in the ALE domain and remain the same. There is a performance lack of the EFG method. This has to be bettered in the future. Dresden,

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Conclusions FSI simulations with MMALE and structural EFG solids are possible in LS-DYNA. Here no real advantage of EFG over standard elements. EFG may be better in hourglass prevention. Time step dependence of FSI needs further investigation! I now come to my conclusions. Well, you can mix it all, all advanced features. Fluid-structure interaction with multi material ALE elements and EFG solids is possible in LS-DYNA: Here, no real advantage of EFG over standard elements has been found. EFG may be better in preventing hourglass modes. However, this requires more CPU time. The time step influence on the fluid structure interaction in LS_DYNA needs further investigation and development for the multi-material ALE elements. This is important, because the time step is small for high Poisson`s ratio and small dimensions. At the end, I want to mention once again the decks in the proceedings and on my website. Thank You for your patience on this late afternoon. Dresden,

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