The pursuit of more representative numerical models for open-cell metallic foams requires the computation of volume and percentage porosity of geometries containing randomly distributed interconnected pores, which is one of the main characteristics that determines its mechanical properties. From a mathematical standpoint, the analytical definition of foam geometries forms a three-dimensional non-convex set. It is known that the volume computation of n-dimensional polytopes and sets is a P-hard problem. A common way to approach this problem is using the Monte Carlo techniques; however, efforts are oriented toward the treatment of convex polytopes and polyhedrons. In this article, the Direct Monte Carlo Simulation (DMCS) is used to compute the percentage porosity of three-dimensional non-convex sets. A single-thread Python code was implemented, and tests were run to estimate the percentage porosity of three-dimensional open-cell porous geometries. Measurements of percentage porosity and runtime requirements over cubical and cylindrical geometries containing from 100 to 4000 overlapping spherical pores showed high accuracy and consistency in non-convex three-dimensional sets, while the proposed algorithm achieved a significant reduction in computing time with respect to the currently available method. In the same manner, results from the proposed algorithm were compared with a similar software available, showing a gain in both performance time and accuracy.
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In this appendix, more detailed information regarding the computed percentage porosity for the data set obtained by means of the proposed algorithm and McVol after 20 independent runs are presented in Table 2.
In this appendix, more detailed information regarding the computed runtimes for the data set for the proposed algorithm and McVol after 20 independent runs are presented in Table 3.
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Campillo, M., Pérez, P., Daher, J. et al. Percentage porosity computation of three-dimensional non-convex porous geometries using the direct Monte Carlo simulation. Engineering with Computers (2019). https://doi.org/10.1007/s00366-019-00866-2
- Direct Monte Carlo simulation
- Percentage porosity
- Non-convex sets
- Metallic foams