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Keywords = SAFEM-3D

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32 pages, 14106 KiB  
Article
On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method
by Simon Essongue, Guillaume Couégnat and Eric Martin
Appl. Mech. 2023, 4(4), 1140-1171; https://doi.org/10.3390/applmech4040059 - 14 Nov 2023
Cited by 2 | Viewed by 1955
Abstract
The augmented finite element method (AFEM) embeds cracks within solid elements. These cracks are modelled without additional degrees of freedom thanks to a dedicated static condensation process. However, static condensation can induce a lack of constraint problem, resulting in singular stiffness matrices. To [...] Read more.
The augmented finite element method (AFEM) embeds cracks within solid elements. These cracks are modelled without additional degrees of freedom thanks to a dedicated static condensation process. However, static condensation can induce a lack of constraint problem, resulting in singular stiffness matrices. To address this issue, we propose a new method called the stabilised augmented finite element method (SAFEM), which produces non-singular stiffness matrices. We conducted 2D experiments involving stationary traction-free cracks and propagating cohesive discontinuities to compare the performance of the SAFEM with the AFEM. The SAFEM outperforms the AFEM in modelling traction-free cracks. Full article
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27 pages, 10392 KiB  
Article
Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites
by Monica Tapia, Y. Espinosa-Almeyda, R. Rodríguez-Ramos and José A. Otero
Appl. Sci. 2021, 11(4), 1867; https://doi.org/10.3390/app11041867 - 20 Feb 2021
Cited by 7 | Viewed by 2641
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Nanotechnology and Applied Nanosciences)
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