Some investigations on 3D homogenization of nano-composite/nano-porous materials with surface effect by FEM/XFEM methods combined with Level-Set technique

• Published in: Computer methods in applied mechanics and engineering Vol. 371; p. 113319
• Main Authors: Hachi, Brahim Elkhalil, Benkhechiba, Abdelfattah Elhadj, Kired, Mohammed Riad, Hachi, Dahmane, Haboussi, Mohamed
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2020; Elsevier BV
• Subjects: 3D homogenization; Anisotropy; Boundary conditions; Cracks; Elastic limit; Elastic properties; Finite element method; Homogenization; Level-Set; Nano composite; Nano void; Nanocomposites; Porosity; Porous materials; Shape effects; Simulation; Stiffness; Surface energy; Three dimensional composites; Two dimensional analysis; XFEM; Level-Set; Nano composite; Nano void; 3D homogenization; Surface energy; XFEM
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113319

Here, the problem of homogenization of medium containing heterogeneities (nanoinclusions, nanovoids and/or nano-cracks) with surface energy effects is numerically addressed within Matlab® code, by XFEM/FEM combined with the Level-set technique, for various forms of nanoheterogeneities in a full 3D context. The developed simulation tool is first validated by comparison with analytical and 2D numerical results from the literature, before being utilized to perform 3D numerical investigations accounting for the real 3D spherical and cylindrical shapes of the nanoheterogeneities in presence. The numerical simulations carried out enable us to study the global stiffness and the degree of the overall anisotropy of homogenized medium as a function of the shape ratio and the interface elastic properties of the nanoheterogeneities. The limit case of flattened or crack-like 3D nanovoids with surface energy compared to pure nano-cracks is also emphasized. Furthermore, the numerical simulations enable us to assess the slight effect of the adopted shape of the surrounding medium and the type of applied boundary conditions on the computed effective properties. Finally, and as a surprising output, which was also obtained in a 2D former work by the authors, it was numerically found that it is possible to tailor a nanoporous material that is stiffer than the parent medium provided the contribution of the surface energy of the nanopores is considered. In conclusion, the performed simulations show the predictive capability of the developed 3D simulation tool in capturing 3D features that are not attainable by 2D approach. [Display omitted] •Development of a 3D simulation code based on XFEM/FEM coupled with the LSM.•3D Homogenization of composites containing nano voids/inclusions with surface effect.•Size and surface properties effects of voids on effective behavior of nano composite.•Flattening effect of voids on the surface energy impact in term of effective behavior.•Comparison between nano voids extremely flattened and cracks of compared size.