User-Materials in ANSYS Holzapfel-Model l lfor Soft Tissues Prof. Dr.-Ing 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 awider range of applications. An extensive description can be found in the ANSYS documentation, which is provided for download at the ANSYS customer portal. For UPF, the following manual is essential: Programmers Manual for ANSYS: Part I: Guide to interfacing with ANSYS Part II: Guide to ANSYS User Programmable Features 1 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
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. Manipulate various types of loads: BF or BFE loads, temperatures, pressures, convections, heat fluxes and so on. Create 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 2 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Programming language ANSYS UPF subroutines are written in FORTRAN90 with some extensions (e.g. Cray-style pointers). However, most of the example subroutines are still written in FORTRAN77 Thus, you can choose your favorite language. 3 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
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 subfolder Platform Details you will find the information needed: E.g. on a 32-bit Windows XP platform you currently (ANSYS v12) need the Intel Fortran v10.1 1and MS Visual Studio 2005 compilers! 4 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
License prerequisites: The use of the ANSYS customization tools is only possible for certain types of licenses. These are (complete list): ANSYS Multiphysics ANSYS Mechanical ANSYS Structural ANSYS PrepPost ANSYS Emag ANSYS S Academic Associate ANSYS Academic Research ANSYS Academic Teaching Advanced ANSYS Academic Teaching Mechanical 5 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
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 the use of UPFs in Workbench also! Compile 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 that does the linking! 6 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Motivation for Holzapfels model: Arterial 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 wall mechanics. (M) Media: Muscle cells, elastin and collagen fibrils. Well-defined concentrically fiber-reinforced layers. Contributes significantly to wall stiffness at low pressures. (A) Adventitia: Consists of fibroblasts/fibrocytes (matrix) and thick kbundles of f collagen fibrils, il arranged in helical structures. Contributes significantly to the wall stiffness at higher pressure levels. 7 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
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 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: ( C, a01, a02) iso( C) aniso( C, a01, a02) The fiber directions a 01, a 02 ( a 01 = a 02 = 1) are incorporated as structural tensors and are defined as A 01 a 01 a 01, A a a 02 02 02 [1] Holzapfel, G.A.; Gasser, T.C.; Ogden, R.W.: A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. of Elasticity, vol. 61, p 1-48 (2000). 8 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Constitutive model For the anisotropic part of the strain-energy, Holzapfel proposed the following ansatz: aniso ( I k k 2 2 1 1 4, I6) e 1 2k 2 i 4,6 I i For the isotropic part of the strain-energy function, a small extension to Holzapfels ansatz was made. This allows the material model to be used also in non-biological applications (e.g. industrial reinforced tubes). Implemented is iso 3 ( I 1, I 2 ) ci 0 I 1 3 c 01 I 2 i 1 i 3 9 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Constitutive model Please note, that according to I T 4 C, a01 C A01 C a01 a01 a01f F a01 2 1 the two invariants i I 4 and I 6 are the squares of the fiber stretches t and therefore have a clear physical meaning! Furthermore, 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 aniso Ii 2 S fi Ii C, Ii 1 i 4, 6 0, I 1 i 10 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Constitutive model Although soft biological tissues can be always treated as incompressible, ANSYS USERMAT interface only allows for a nearly incompressible modeling. Therefore avolumetric (ANSYS-)part has to be added: vol 1 2 ( J ) J 1, J d det F d is a material parameter and can be identified with the initial bulk modulus K=2/d. Finally, the implemented strain-energy function is ( 6 C, A01, A02, J ) iso( I1, I2) aniso( I4, I ) vol ( J ) 11 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Example: Fiber stresses 12 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
Example: Fiber angles 13 ANSYS Conference & 28. CADFEM Users` Meeting 2010, Aachen
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Seminar notes of CADFEM GmbH CADFEM GmbH 2009 These seminar notes are in copyright. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of CADFEM GmbH. -3-
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