User-Materials in ANSYS

H l f l M d l f S ft TiHolzapfel-Model for Soft Tissues

Prof. Dr.Prof. Dr.--Ing A. FritschIng A. Fritsch

Possibilities of user programming

ANSYS User Programmable Features (UPF) are capabilities you can use to write your own subroutines. This extents the usage of ANSYS to a wider range of applicationsto a wider range of applications.

An extensive description can be found in the ANSYS documentation, p ,which is provided for download at the ANSYS� customer portal. For UPF, the following manual is essential:

Programmer�s Manual for ANSYS:Programmer s Manual for ANSYS:

Part I: Guide to interfacing with ANSYSPart II: Guide to ANSYS User Programmable Features

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Possibilities of user programming

There are different possibilities using UPF. Here are some examples (excerpt):

Read into or fetch information from the ANSYS database Write your own commands.yManipulate various types of loads: BF or BFE loads, temperatures, pressures, convections, heat fluxes and so on.C b l lid lCreate your own beam, plane, solid� user element.Modify and monitor existing elements.

Routines to customize material behavior for

Plasticity, Hyperelasticity, Creep etc.

most general routine therefore is USERMAT

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most general routine therefore is USERMAT

Programming language

ANSYS� UPF subroutines are written in

FORTRAN90FORTRAN90

with some extensions (e.g. Cray-style pointers). However, most of the example subroutines are still written in

FORTRAN77FORTRAN77

Thus, you can choose your favorite language.Thus, you can choose your favorite language.

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Compiler prerequisites:

For the compilation process you need the appropriate compilers and compiler versions. The necessary information is given in the ANSYS� Help Installation and Licensing Documentation In the subfolderHelp Installation and Licensing Documentation. In the subfolder �Platform Details� you will find the information needed:

E.g. on a 32-bit Windows XP platform you currently (ANSYS v12) need th I t l F t 10 1 d MS Vi l St di 2005 il !

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the Intel Fortran v10.1 and MS Visual Studio 2005 compilers!

License prerequisites:

The use of the ANSYS customization tools is only possible for certain types of licenses. These are (complete list):

ANSYS MultiphysicsANSYS MultiphysicsANSYS MechanicalANSYS StructuralANSYS PrepPostANSYS Emag

S S dANSYS Academic AssociateANSYS Academic ResearchANSYS Academic Teaching AdvancedANSYS Academic Teaching AdvancedANSYS Academic Teaching Mechanical

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Compiling and Linking

Since ANSYS v12 you do have the choice between two compiling options (Windows):

Link your routines into shared libraries (as discussed later). This will create a dynamic linked library *.dll. This option allows y y pthe use of UPFs in Workbench also!

Compile and link your custom routines into the ANSYS programCompile and link your custom routines into the ANSYS program itself. This will create a new ANSYS executable (ansys.exe). You may need superuser or root privileges to run the procedure h d h l kthat does the linking!

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Motivation for Holzapfels� model: Arterial wall mechanics major componentsArterial wall mechanics, major components

Major components of a healthy elastic artery:

(I) Intima: single layer of endothelial cells. For young individuals, it has only an insignificant contribution to y gwall mechanics.

(M) Media: Muscle cells, elastin and collagen fibrils Well-definedcollagen fibrils. Well-defined concentrically fiber-reinforced layers. Contributes significantly to wall stiffness at low pressuresstiffness at low pressures.

(A) Adventitia: Consists of fibroblasts/fibrocytes (matrix) and thi k b dl f ll fib ilthick bundles of collagen fibrils, arranged in helical structures. Contributes significantly to the wall stiffness at higher pressure levels

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stiffness at higher pressure levels.

Constitutive model (Holzapfel et al. [1])

In [1], Holzapfel proposed a hyperelastic potential, which models each layer (media and adventitia), according to its histological information (e g fiber directions) as a fiber reinforced compositeinformation (e.g. fiber directions), as a fiber-reinforced composite. Each layer consist of two families of (collagen-) fibers which are arranged in symmetrical spirals.

The isochoric part of the proposed strain-energy function is as follows:

The fiber directions a01, a02 (||a01 || = ||a02 || = 1) are incorporated as structural

),,()(),,( 02010201 aaCCaaC anisoiso

01, 02 (|| 01 || || 02 || ) ptensors and are defined as

aaAaaA

[1] Holzapfel, G.A.; Gasser, T.C.; Ogden, R.W.: A new constitutive framework for arterial wall mechanics

020202010101 , aaAaaA

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and a comparative study of material models. J. of Elasticity, vol. 61, p 1-48 (2000).

Constitutive model

For the anisotropic part of the strain-energy, Holzapfel proposed the following ansatz:

642

164 1e

2),(

212

ianiso

iIk

kkII

For the isotropic part of the strain-energy function, a small extension to

6,42 i

Holzapfels� ansatz was made. This allows the material model to be used also in �non-biological� applications (e.g. industrial reinforced tubes). Implemented is s

33)( 2011

3

021 IcIcII i 33),( 20111

021 IcIcIIi

iiso

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Constitutive model

Please note, that according to

2T

th t i i t I d I th f th fib t t h d th f

210101010101014 , aFFaaaCACaC TI

the two invariants I4 and I6 are the squares of the fiber stretches and therefore have a clear physical meaning!

Furthermore due to the wavy structure of the collagen fibers the anisotropicFurthermore, due to the wavy structure of the collagen fibers, the anisotropic part only contributes to the mechanical response if the fibers are extended. Therefore we have

641 , 2 iIII i

ianiso

fi CS 6,4 1 , 0

iI

Ii

ifi CS

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Constitutive model

Although soft biological tissues can be always treated as incompressible, ANSYS� USERMAT interface only allows for a nearly incompressible modeling Therefore a volumetric (ANSYS ) part has to be added:modeling. Therefore a volumetric (ANSYS-) part has to be added:

Fdet,11)( 2 JJJl

d is a material parameter and can be identified with the initial bulk modulus

Fdet , 1)( JJd

Jvol

K=2/d. Finally, the implemented strain-energy function is

)(),(),(), , ,( 64210201 JIIIIJ volanisoisoAAC

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Example: Fiber stresses

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Example: Fiber angles

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Seminar notes of CADFEM GmbH

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