MATEC Web Conf.
Volume 310, 20204th International Scientific Conference Structural and Physical Aspects of Construction Engineering (SPACE 2019)
|Number of page(s)||9|
|Published online||05 March 2020|
Homogenization of trabecular structures
Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 16629 Praha 6, Prague, Czech Republic
* Corresponding author: firstname.lastname@example.org
Numerical modeling of implants and specimens made from trabecular structures can be difficult and time-consuming. Trabecular structures are characterized as spatial truss structures composed of beams. A detailed discretization using the finite element method usually leads to a large number of degrees of freedom. It is attributed to the effort of creating a very fine mesh to capture the geometry of beams of the structure as accurately as possible. This contribution presents a numerical homogenization as one of the possible methods of trabecular structures modeling. The proposed approach is based on a multi-scale analysis, where the whole specimen is assumed to be homogeneous at a macro-level with assigned effective properties derived from an independent homogenization problem at a meso-level. Therein, the trabecular structure is seen as a porous or two-component medium with the metal structure and voids filled with the air or bone tissue at the meso-level. This corresponds to a two-level finite element homogenization scheme. The specimen is discretized by a reasonable coarse mesh at the macro-level, called the macro-scale problem, while the actual microstructure represented by a periodic unit cell is discretized with sufficient accuracy, called the meso-scale problem. Such a procedure was already applied to modeling of composite materials or masonry structures. The application of this multi-scale analysis is illustrated by a numerical simulation of laboratory compression tests of trabecular specimens.
© The Authors, published by EDP Sciences, 2020
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