ABSTRACT
Micro-Finite Element analysis (µFEA) has become widely used in biomechanical research as a reliable tool for the prediction of bone mechanical properties within its microstructure such as apparent elastic modulus and strength. However, this method requires substantial computational resources and processing time. Here, we propose a computationally efficient alternative to FEA that can provide an accurate estimation of bone trabecular mechanical properties in a fast and quantitative way. A lattice element method (LEM) framework based on the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) open-source software package is employed to calculate the elastic response of trabecular bone cores. A novel procedure to handle pore-material boundaries is presented, referred to as the Firm and Floppy Boundary LEM (FFB-LEM). Our FFB-LEM calculations are compared to voxel- and geometry-based FEA benchmarks incorporating bovine and human trabecular bone cores imaged by micro Computed Tomography (µCT). Using 14 computer cores, the apparent elastic modulus calculation of a trabecular bone core from a µCT-based input with FFB-LEM required about 15 min, including conversion of the µCT data into a LAMMPS input file. In contrast, the FEA calculations on the same system including the mesh generation, required approximately 30 and 50 min for voxel- and geometry-based FEA, respectively. There were no statistically significant differences between FFB-LEM and voxel- or geometry-based FEA apparent elastic moduli (+24.3% or +7.41%, and +0.630% or -5.29% differences for bovine and human samples, respectively).
ABSTRACT
Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and ⟨100⟩ dumbbell interstitials in Ni-Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy's non-monotonic behavior. In contrast, the difference between formation energies of Ni-Ni, Ni-Fe, and Fe-Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition-based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one-is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.
