Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Novel Implementation of Asymptotic Homogenization (NIAH) Applied to Frame-Like Periodic Materials
Submission Author:
Pablo Andrés Muñoz Rojas , SC , Brazil
Co-Authors:
Augusto Henrique dos Santos, Pablo Andrés Muñoz Rojas
Presenter: Pablo Andrés Muñoz Rojas
doi://10.26678/ABCM.COBEM2023.COB2023-1663
Abstract
Technological breakthroughs increasingly demand the development of materials capable of meeting multifunctional requirements. In order to reduce costs, industry is generally interested in materials that combine some specific property with low weight. Frame-Like Periodic Cellular Materials (FLPM), have gained prominence in this scenario especially since technical innovations as additive manufacture allow their fabrication even for complex base cells. As cellular metamaterials display heterogeneous properties within a typical cell, the prediction of their overall (macroscopic) behavior is frequently a challenge, which can be addressed using asymptotic homogenization (AH) coupled to the Finite Element Method (FEM). Aiming at computational efficiency, the base cell discretization is often performed using bar elements (pinned ends), although the use of frame elements (rigidly linked ends) would certainly render more reliable results because moments and torque are transmitted. In this work we use the “novel implementation of the asymptotic homogenization method (NIAH)” to obtain the homogenized elasticity tensors for FLPMs based on Euler-Bernoulli frame elements. The homogenized tensors provided by our implemented code are validated by comparison to published data. Numerical studies are carried out comparing the results obtained with bar and frame elements. As expected, for stretch dominated base cells, similar homogenized tensors are obtained. On the other hand, for bending-dominated base cells, the joints of bar elements act as hinges with free nodal rotations, which is unrealistic. The macroscopic behavior in this case is better described using beam elements in the base cell. One point of remark is that some base cells studied presented constitutive symmetry when modeled with bar elements. Often, this symmetry is lost when replacing bars by beams. The work also shows a systematic procedure to define the geometry of the base cell in order to obtain enhanced results.
Keywords
NIAH, Asymptotic homogenization method, Cellular Materials, Space frame
