ANSYS Mechanical software provides a vast library of material models that can help users simulate various kinds of behaviors such as elasticity, plasticity, creep and hyperelasticity, just to name a few. Although these models can be used to investigate the mechanical response of a large number of different materials such as metals, rubbers, biological tissues and special alloys, users may wish to incorporate their own material laws into ANSYS. This task can be accomplished by means of a user-programmable feature named USERMAT, a subroutine that allows users to write their own material constitutive equations within a general material framework using ANSYS’ current element technology. This presentation shows the use of USERMAT recently shown at the 2014 ANSYS Regional Conference in Eindhoven, The Netherlands.

1. / Department of Biomedical Engineering

2. Implementing a microstructure-enhanced
material model using ANSYS USERMAT
for the prediction of bone failure
Javad Hazrati, Bert van Rietbergen, Keita Ito
Materials Technology
Eindhoven University of Technology

4. Osteoporosis
• Osteoporosis is the most epidemic bone disease in elderly
populations.
• It is characterized by:
• low bone mass
• deterioration of bone micro-architecture
• compromised bone strength
• It leads to bone fragility and increased risk of fracture under
low loads.
Healthy Osteoporotic
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5. Motivation
Current diagnostic approach (DXA) is not
an accurate predictor of osteoporosis or
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bone strength
There is a need to have a better predictor
of bone strength
Image based patient specific mechanical
approaches using continuum finite
elements (FE) method are better predictor
of bone strength
The goal is to build micro-structure
enhanced continuum FE models
Dual Energy X-ray Absorptiometry (DXA)
Neck BMD
Age
g/cm2
1.22
0.98
0.74
0.50
*
20 40 60 80 100
Density
Image based patient specific FE modeling

6. Bone
• From a material point of view, bone tissue can be considered a
porous material with a varying degree of porosity:
1. Cortical bone: tube-like structure of high-density bone
2. Trabecular bone: porous type of bone
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• Trabecular bone can be
highly anisotropic:

7. Continuum FE models
• Building continuum FE models of bone relies on two essential
tools:
• ANSYS Mesh morphing tool
• Morphology analysis tool to measure local micro-structural
parameters.
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8. Mesh morphing
ANSYS Mesh morphing tool:
• Automation of subject-specific
FE model generation while
keeping surface regularity.
• Comparison of results sets from
two or more meshes (subjects)
since morphing generates
isotopological meshes.
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Lorenzo Grassi et al., Medical Engineering & Physics, 2011

9. Morphology analysis
Morphology analysis tool:
• Bone density distribution (ρ) and
Fabric tensor (M) are used to
calculate compliance tensor.
 
3 3
 M M 
M M
E E
 1 ,  1;

3
, 1;
1
,M
( ) ( )
1
( )
ij
i j i j
i i s i j i j i s
i j
i j i j ij s
M M
G


 

 
 




C
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(a)
(b)
a) Bone density distribution
b) Major fabric direction (major eigenvector)

10. Material behavior
• A validated anisotropic elastic-plastic damage model is used to
define bone mechanical behavior.
• The material model requires specific constitutive equations
which do not exist in ANSYS standard material library.
• Therefore, we need to use ANSYS user’s programmable
features to implement the material model in ANSYS (UserMat).
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Rheological model
Algorithmic stiffness

11. UserMat
• The UserMat subroutine is a tool for advanced users and allows
us to write our own material constitutive equations within a
general material framework.
• We use Fortran programming language to implement our
material model in ANSYS.
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Elastic-plastic damage model

12. A case study using ANSYS UserMat
A novel approach to estimate trabecular bone anisotropy using a
database approach.
FEM Database website: www.bmt.tue.nl/nl/fe_database/
doi:10.4121/uuid:4ae59365-92f0-480b-a899-ade34bc84a00
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13. A case study using ANSYS UserMat
• Problem: we can’t measure bone fabric information from
clinical CT scans because of the lack of resolution, which is
needed for such anisotropic fabric-elasticity relationships.
Database
Isotropic model Orthotropic model
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High resolution
Femur
low resolution
Human can’t be exposed to high
X-ray doses to obtain high
resolution images.
• Proposed solution:
Anisotropy is derived
from a database of
high resolution
images.
Mapping
anisotropy from
best matched
model in DB
Mesh Template

14. Study design
• To investigate if FE models with DB-derived anisotropy
produce similar stress and stiffness results as models based
on the actually measured bone fabric.
• To investigate if DB-derived models can provide more accurate
results than isotropic models.
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15. Materials
• 10 test femurs were used in this study.
• Loading conditions applied to the models represented a fall
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to the side configuration.

16. Results
Isotropic model DB-derived model
Gold standard
a) Von Mises stress distribution
b) Damage parameter distribution (user defined parameter in UserMat)
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17. Summary
• DB-derived FE models well reproduce the mechanical behavior
of models with anisotropy based on the actually measured
bone fabric.
• DB-derived FE models can provide more accurate results than
isotropic models.
• Database approach can be also used to obtain more
parameters than fabric such as Tb.Th, Tb.N and etc. for the
patient’s models.
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18. Acknowledgement
Funding from the European Union for
the osteoporotic virtual physiological
human project (VPHOP FP7-ICT2008-
223865) is gratefully acknowledged.
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19. Thanks for your attention!
Comments, questions or more informations?
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j.marangalou@gmail.nl
b.v.rietbergen@tue.nl