Heterogeneous directions of orthotropy in three-dimensional structures: finite element description based on diffusion equations
| Autor: | Rachele Allena, Christophe Cluzel |
|---|---|
| Přispěvatelé: | Institut de Biomecanique Humaine Georges Charpak, Université Paris 13 (UP13)-Arts et Métiers ParisTech, Laboratoire de Mécanique et Technologie (LMT), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Arts et Métiers ParisTech-Université Paris 13 (UP13) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
[PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] Numerical Analysis Basis (linear algebra) 0206 medical engineering Mathematical analysis ingénierie bio-médicale [Sciences du vivant] 02 engineering and technology 021001 nanoscience & nanotechnology Orthotropic material 020601 biomedical engineering Finite element method Stress (mechanics) [PHYS.MECA.MEMA]Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph] Computational Mathematics Matrix (mathematics) Unit vector [SDV.IB]Life Sciences [q-bio]/Bioengineering Boundary value problem [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph] 0210 nano-technology Orthonormality Civil and Structural Engineering |
| Zdroj: | Mathematics and Mechanics of Complex Systems Mathematics and Mechanics of Complex Systems, International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS),University of L’Aquila in Italy, 2018, 6 (4), pp.339-351 |
| ISSN: | 2326-7186 2325-3444 |
| Popis: | International audience; Heterogeneous materials such as bone or woven composites show mesostructures whose constitutive elements are all oriented locally in the same direction and channel the stress flow throughout the mechanical structure. The interfaces between such constitutive elements and the matrix are regions of potential degradations. Then, when building a numerical model, one has to take into account the local systems of orthotropic coordinates in order to properly describe the damage behavior of such materials. This can be a difficult task if the orthotropic directions constantly change across the complex three-dimensional geometry as is the case for bone structures or woven composites. In the present paper, we propose a finite element technique to estimate the continuum field of orthotropic directions based on the main hypothesis that they are mainly triggered by theexternal surface of the structure itself and the boundary conditions. We employ two diffusion equations, with specific boundary conditions, to build the radial and the initial longitudinal unit vectors. Then, to ensure the orthonormality of the basis, we compute the longitudinal, the circumferential, and the radial vectors via a series of vector products. To validate the numerical results, a comparison with the average directions of the experimentally observed Haversian canals is used. Our method is applied here to a human femur. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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