Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites
A three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nano...
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MDPI AG
2021-02-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/4/1867 |
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| author | Monica Tapia Y. Espinosa-Almeyda R. Rodríguez-Ramos José A. Otero |
| author_facet | Monica Tapia Y. Espinosa-Almeyda R. Rodríguez-Ramos José A. Otero |
| author_sort | Monica Tapia |
| collection | DOAJ |
| description | A three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nanowires (CNW). The nanocomposites are assumed to have isotropic or transversely isotropic inclusions embedded in an isotropic matrix. The SAFEM-3D approach is developed by combining the two-scale asymptotic homogenization method (AHM) and the finite element method (FEM). Statements regarding the homogenized local problems on the periodic cell and analytical expressions of the effective elastic coefficients are provided. Homogenized local problems are transformed into boundary problems over one-eighth of the cell. The FEM is implemented based on the principle of the minimum potential energy. The three-dimensional region (periodic cell) is divided into a finite number of 10-node tetrahedral elements. In addition, the effect of the inclusion’s geometrical shape, volume fraction and length on the effective elastic properties of the composite with aligned or random distributions is studied. Numerical computations are developed and comparisons with other theoretical results are reported. A comparison with experimental values for CNW nanocomposites is also provided, and good agreement is obtained. |
| first_indexed | 2024-03-09T00:41:46Z |
| format | Article |
| id | doaj.art-90c9326a5b334a01b9698abf487b2e7f |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T00:41:46Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj.art-90c9326a5b334a01b9698abf487b2e7f2023-12-11T17:45:39ZengMDPI AGApplied Sciences2076-34172021-02-01114186710.3390/app11041867Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic NanocompositesMonica Tapia0Y. Espinosa-Almeyda1R. Rodríguez-Ramos2José A. Otero3Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, State of Mexico 52926, MexicoInstituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, Alcaldía Álvaro Obregón, Mexico City 01000, MexicoFacultad de Matemática y Computación, Universidad de la Habana, San Lázaro y L, Vedado, La Habana 10400, CubaTecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, State of Mexico 52926, MexicoA three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nanowires (CNW). The nanocomposites are assumed to have isotropic or transversely isotropic inclusions embedded in an isotropic matrix. The SAFEM-3D approach is developed by combining the two-scale asymptotic homogenization method (AHM) and the finite element method (FEM). Statements regarding the homogenized local problems on the periodic cell and analytical expressions of the effective elastic coefficients are provided. Homogenized local problems are transformed into boundary problems over one-eighth of the cell. The FEM is implemented based on the principle of the minimum potential energy. The three-dimensional region (periodic cell) is divided into a finite number of 10-node tetrahedral elements. In addition, the effect of the inclusion’s geometrical shape, volume fraction and length on the effective elastic properties of the composite with aligned or random distributions is studied. Numerical computations are developed and comparisons with other theoretical results are reported. A comparison with experimental values for CNW nanocomposites is also provided, and good agreement is obtained.https://www.mdpi.com/2076-3417/11/4/1867asymptotic homogenization methodcarbon nanotubenanocompositesSAFEM-3Deffective elastic properties |
| spellingShingle | Monica Tapia Y. Espinosa-Almeyda R. Rodríguez-Ramos José A. Otero Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites Applied Sciences asymptotic homogenization method carbon nanotube nanocomposites SAFEM-3D effective elastic properties |
| title | Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites |
| title_full | Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites |
| title_fullStr | Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites |
| title_full_unstemmed | Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites |
| title_short | Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites |
| title_sort | computation of effective elastic properties using a three dimensional semi analytical approach for transversely isotropic nanocomposites |
| topic | asymptotic homogenization method carbon nanotube nanocomposites SAFEM-3D effective elastic properties |
| url | https://www.mdpi.com/2076-3417/11/4/1867 |
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