CIMEC   24726
CENTRO DE INVESTIGACION DE METODOS COMPUTACIONALES
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Making Use of Symmetries in the Elastic Inverse Homogenization Problem
Autor/es:
CARLOS MÉNDEZ; ALFREDO HUESPE; SEBASTIAN TORO; JUAN MANUEL PODESTÁ; JAVIER OLIVER
Lugar:
Nueva York
Reunión:
Congreso; 13th World Congress on Computational Mechanics (WCCM XIII) and 2nd Pan American Congress on Computational Mechanics (PANACM II); 2018
Institución organizadora:
World Congress in Computational Mechanics (WCCM)
Resumen:
It is a known fact that even the highest symmetry (isotropic) of the elastic tensor can be achieved through topology design using a unit cell with arbitrary shape whose material distribution does not present any symmetry (think about a polycrystal or an amorphous material). However, it is also well known that an adequate choice of the unit cell and the symmetries imposed in the design process can significantly facilitate the finding of certain classes of composites (like Vigdergauz microstructures or new ones proposed by Sigmund [1]). In this work, we make a comprehensive analysis of the connection between the symmetry of the material distribution in the microstructure and the properties of the resulting elastic tensor. Considering periodic structures, we analyze all the possible Bravais lattices and all the plane (wallpaper) groups in order to study the way in which the symmetries of these patterns are reflected in the homogenized elastic tensor. For the unit cell we adopt Wigner-Seitz cells, which are primitive cells that preserve all the symmetries of the subjacent Bravais lattice and simplify the implementation of plane groups. Given an arbitrary elastic tensor, we propose a procedure for the inverse homogenization that allow us to choose the most convenient shape for the unit cell and to select the symmetries to be imposed that guarantee (during the whole optimization process) that the homogenized elastic tensor will have the same symmetry of the tensor to be designed. Concerning the design, several well established tools were used, such as algorithms for the rotation of the tensor to their material axes [2] and topology optimization methods based on SIMP [1] and topological derivative [3]. Some examples regarding the search of new classes of extreme materials are shown, where it can be seen how different composites classes emerge depending on the enforced symmetries. [1] O. Sigmund (2000). A new Class of Extremal Composites. Journal of the Mechanics and Physics of Solids, 48(2), 397-428.[2] N. Auffray and P. Ropars (2016). Invariant-based reconstruction of bidimensional elasticity tensors. International Journal of Solids and Structures, 87, 183-193.[3] S. Amstutz et al. (2010). Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures. International Journal for Numerical Methods in Engineering, 84(6), 733-756.