Compressive strain measurements in porous materials using micro-FE and digital volume correlation

Abstract

A local Digital Volume Correlation (DVC) based measurement of displacements and strains of synthetic bone samples under an ex-situ compression using the time-lapsed imaging procedure was performed in the present study. Micro Finite Element (µFE) model was used to simulate the compression of synthetic bone samples with experimental-based ( ExBC), and DVC interpolated displacement boundary conditions ( IPBC). The obtained µFE nodal displacement data compared with DVC. A good match of displacement patterns and correlation values of R2 = 0.85–0.99 and RMSE ≤ 12 µm was observed for the IPBC predicted displacements against DVC displacements. However, the ExBC provided a good correlation of transverse displacements only (U: R2 = 0.85–0.99 and V: R2 = 0.77–0.99). The average axial displacement of ExBC matched well with DVC, and a qualitative and quantitative understanding of the axial displacement was possible with ExBC. A moderate agreement of axial strain patterns was observed between DVC and IPBC, even though a good agreement on displacement was observed. The ExBC showed a higher axial strain compared to DVC in all samples. The transverse strains varied between the same extreme values for both boundary conditions and within the DVC range.

Evaluation of compressive behaviour of porous structures under large deformation using micro‐CT, DVC and micro‐FE

“…The DC approach sums all possible shifts associated with a subvolume, and the final displacement is determined by achieving the highest correlation value ( C norm ) using a normalised cross‐correlation function (eq. A1‐1 in Kunnoth et al 39 ). The DVC parameters used for CCF and OCF samples are given in Table 2…”

“…The rigid body motions of the samples were extracted from the FFT results using polar decomposition. The rigid body motion corrections (RBCs) were implemented on the deformed image volume in integer values of voxels only 39,49 for all compression stages. It was also verified that non‐integer values of RBC do not make any significant difference in the displacement patterns and values 39 …”

“…In sectional comparison, the displacements on an x‐y plane are compared between DVC and micro‐FE, where the section represents a set of subvolume whose z coordinates are the same (Figure 5). 39 The sectional displacements consisted of fewer subvolume data (CCF ~ 530; OCF ~ 72). The normal strain components were also compared at section and volume levels.…”

“…A statistical comparison of the displacements was also performed to identify the significance of the predicted displacements. However, limited studies have performed the micro‐FE analysis with the experiment‐based boundary conditions with porous structures for the above mentioned strain range 35,39 . A poor prediction capability of experimental boundary conditions was observed by Chen et al, 35 whereas a better agreement of predicted displacement was obtained by Kunnoth et al 39 The experimental boundary conditions were successful with whole bone samples, such as the human femur, where the fracture strain and the failure locations were predicted well.…”

“…However, limited studies have performed the micro‐FE analysis with the experiment‐based boundary conditions with porous structures for the above mentioned strain range 35,39 . A poor prediction capability of experimental boundary conditions was observed by Chen et al, 35 whereas a better agreement of predicted displacement was obtained by Kunnoth et al 39 The experimental boundary conditions were successful with whole bone samples, such as the human femur, where the fracture strain and the failure locations were predicted well. The FE model of the femur that does not incorporate the microstructures of the trabecular bone samples was developed using Computed Tomography (CT) 40 .…”