# FEA of hyperelastic arteries in ANSYS APDL

• Killian Chellar
In summary: The large deformation may be activated when you solve the linear elastic case, but it may not be activated when you solve the Mooney-Rivlin case.2. You may apply the load all at once, or you may solve the problem several times in succession, starting from the solution for the previous load.3. You may try reducing the Mooney-Rivlin parameters so that the model is nearly linear, solving that problem, then increasing the Mooney-Rivlin parameters, starting with the solution for the previous set of parameters.4. You may try doing the above two tricks with both the load and the material parameters at the same time.

#### Killian Chellar

Hi all,

I am attempting to model an artery under internal pressure in ANSYS APDL.. This is my current attempt..

1. select solid 8 node 183 element type (and specify thickness)
2. select 5 parameter Mooney-Rivlin (for which I have constants)
3. create quarter area model dimensions
4. map mesh with quad area elements
5. Apply symmetry Boundary Conditions to artery inner cut lines
6. Apply pressure load on internal area line
7. Activate large deformation (NLGEOM,ON)
8. Solve using static analysis

This approach works fine for linear-elastic materials, but I cannot understand why it yields no results in this situation?

Hi Killian Chellar. Welcome to Physics Forums!

I don't have any direct experience with FEA, but I have lots of experience with numerical analysis. I have some thoughts and some questions.

My understanding is that you are solving a large set of non-linear algebraic equations. You experienced no problems when you considered cases of linear elastic behavior, but could not get any meaningful results when you switched to Mooney Rivlin.

Questions:
1. Was the large deformation description activated when you solved the linearly elastic case.
2. Do you apply the load all in one shot, or do you solve the problem completely several times in succession using small increments in the applied load, starting from the solution for the previous load?
3. Have you tried cutting back on the Mooney-Rivlin parameters so that the model is nearly linear, solving that problem, then increasing the Mooney-Rivlin parameters, starting with the solution for the previous set of parameters.
4. Have you tried doing the above two tricks with both the load and the material parameters at the same time.

What I'm saying is that, with the Mooney-Rivlin parameters, maybe the equations may be too non-linear, and you haven't been using a good enough initial guess to converge to a solution. One way of getting around this is to sneak up on the load, and another way is to sneak up on the material properties, and another way is to sneak up on both.

Chet

Incidentally, this sounds like a 1D problem, with only one independent variable, the radial location. So the equations should be expressible as ODEs, and can be solved by ODE methods. Is it correct that you are just dealing with a tube made out of material that behaves according to the Mooney-Rivlin equation, and you are just applying internal pressure to the tube? If so, then such a problem is much easier to solve than by using finite element.

Chet

## 1. What is FEA and how is it used in the analysis of hyperelastic arteries in ANSYS APDL?

Finite Element Analysis (FEA) is a computational method used to analyze the behavior of structures under different loading conditions. In the context of hyperelastic arteries, FEA can be used to simulate the mechanical response of arterial walls to various physiological conditions, such as blood pressure changes. ANSYS APDL is a software program commonly used for FEA, and it offers specific tools and capabilities for analyzing hyperelastic materials.

## 2. What are the benefits of using FEA for studying hyperelastic arteries?

FEA allows for a detailed and accurate analysis of the mechanical behavior of hyperelastic arteries. It can provide insights into the stress and strain distribution within the arterial walls, as well as the impact of different material properties and loading conditions. FEA also allows for the simulation of complex geometries and boundary conditions, which may not be possible with traditional experimental methods.

## 3. What are the main challenges of using FEA for hyperelastic arteries?

One of the main challenges of using FEA for hyperelastic arteries is accurately capturing the material behavior. Hyperelastic materials have nonlinear stress-strain relationships, which require specialized material models and careful calibration. Additionally, selecting appropriate boundary conditions and meshing strategies can also be challenging, as it can significantly impact the accuracy of the results.

## 4. How do you validate the results obtained from FEA of hyperelastic arteries?

Validation of FEA results for hyperelastic arteries can be done through comparison with experimental data. This can include measurements of arterial stiffness, strain, and displacement under different loading conditions. Additionally, sensitivity analyses can also be performed to assess the impact of different material properties and boundary conditions on the results.

## 5. What are some potential applications of using FEA for hyperelastic arteries?

FEA of hyperelastic arteries has many potential applications in the field of cardiovascular research and medical device design. It can be used to study the effects of different disease states, such as atherosclerosis, on arterial mechanics. FEA can also aid in the development and optimization of medical devices, such as stents and stent grafts, by simulating their interaction with hyperelastic arterial tissues.