This contribution presents a homogenization of the elastic properties of trabecular structures used in modern implantology. Trabecular structures can be characterized as spatial truss structures composed of beams. Their numerical modeling and precise three-dimensional discretization by finite elements usually lead to a huge number of degrees of freedom. One of the possible solutions of this problem can be a homogenization approach based on a two-level analysis, where the specimen, the implant, is discretized by a coarse mesh at the macro-level, and the elements of the trabecular structure are represented by effective (homogenized) material properties obtained from a representative volume element at the meso-level. The application of this multi-scale procedure is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.

Topics
Elasticity, Micromechanics, Numerical methods, Computer simulation
1.
A.
 
Jíra
,
P.
 
Hájková
, and
L.
 
Řehounek
, “
Trabecular structures as efficient surface of dental implants
,” in
EAN 2019, 57th Conference on Experimental Stress Analysis
(
2019
).
Google Scholar
 
2.
M.
 
Šejnoha
 and
J.
 
Zeman
,
Micromechanical analysis of random composites
, CTU Reports, Vol.
6
(Czech Technical University in Prague,
2002
).
Google Scholar
 
3.
J.
 
Zeman
 and
M.
 
Šejnoha
,
Modelling and Simulation in Materials Science and Engineering
 
325
–
335
(
2007
).
https://doi.org/10.1088/0965-0393/15/4/S01
Google Scholar
 
4.
J. C.
 
Michel
,
H.
 
Moulinec
, and
P.
 
Suquet
,
Computer Methods in Applied Mechanics and Engineering
 
172
,
109
–
143
(
1999
).
https://doi.org/10.1016/S0045-7825(98)00227-8
Google Scholar
Crossref
Search ADS
 
5.
P.
 
Vakrčka
,
Trabecular structure as the basis for modern implants
, Master's thesis,
Faculty of Civil Engineering, Czech Technical University in Prague
(
2019
).
Google Scholar
 
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