Abstract
Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.
Highlights
Porous materials are some of the most prospective advanced materials and have begun to be widely used in various engineering fields, utilizing their advantageous properties such as the light weight, heat adiabaticity, and sound and vibration insulation properties
A phase field model for investigating the three-dimensional space-filling structures that were typically observed in metal foam materials was presented
An additional term to balance the volume of every cell was introduced to the conventional multi-phase field model, and the stability of the obtained structures was investigated
Summary
Porous materials are some of the most prospective advanced materials and have begun to be widely used in various engineering fields, utilizing their advantageous properties such as the light weight, heat adiabaticity, and sound and vibration insulation properties. Porous materials are divided into two types: open and closed cells The latter, which is focused in this study, consists of many small cells separated by a wall made of the base material, and the cells are usually polyhedral with rounded corners. Lord Kelvin leaves his name in the Kelvin cell, which is known as a preferable candidate of the foam model and was long considered the best solution for the so-called Kelvin problem, “which shape of cells have the least surface area when the space is divided into cells having the same volume?,” before Weaire and Phelan found a better solution in 1994 [3]. The model is extended to a three-dimensional description, and the reproducibility of the stable structures is discussed
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
