Comparison of linear and nonlinear stepwise μFE displacement predictions to digital volume correlation measurements of trabecular bone biopsies. (February 2023)

• Record Type: Journal Article
• Authors: Stefanek, Pia; Synek, Alexander; Dall'Ara, Enrico; Pahr, Dieter H.
• Is Part Of: Journal of the mechanical behavior of biomedical materials. Volume 138(2023)
• Publication Date: 2023-02
• Subjects: Micro finite element model -- Materially nonlinear simulation -- Digital volume correlation -- Displacement -- Trabecular bone biopsies; Biomedical materials -- Periodicals; Biomedical materials -- Mechanical properties -- Periodicals; Biomedical materials; Biomedical materials -- Mechanical properties; Periodicals; Electronic journals; 610.28
• DOI: 10.1016/j.jmbbm.2022.105631
• Languages: English
• ISSNs: 1751-6161

Abstract

Abstract: Digital volume correlation (DVC) enables to evaluate the ability of μFE models in predicting experimental results on the mesoscale. In this study predicted displacement fields of three different linear and materially nonlinear μFE simulation methods were compared to DVC measured displacement fields at specific load steps in the elastic regime ( Step El ) and after yield ( Step Ult ). Five human trabecular bone biopsies from a previous study were compressed in several displacement steps until failure. At every compression step, μCT images (resolution: 36 μm) were recorded. A global DVC algorithm was applied to compute the displacement fields at all loading steps. The unloaded 3D images were then used to generate homogeneous, isotropic, linear and materially nonlinear μFE models. Three different μFE simulation methods were used: linear (L), nonlinear (NL), and nonlinear stepwise (NLS). Regarding L and NL, the boundary conditions were derived from the interpolated displacement fields at Step El and Step Ult, while for the NLS method nonlinear changes of the boundary conditions of the experiments were captured using the DVC displacement field of every available load step until Step El and Step Ult . The predicted displacement fields of all μFE simulation methods were in good agreement with the DVC measured displacement fields (individual specimens: R 2 >0.83 at Step El and R 2 >0.59 at Step Ult ; pooled data: R 2 >0.97 at Step El and R 2 >0.92 at Step Ult ). At Step El, all three simulation methods showed similar intercepts, slopes, and coefficients of determination while the nonlinear μFE models improved the prediction of the displacement fields slightly in all Cartesian directions at Step Ult (individual specimens: L: R 2 >0.59 and NL, NLS: R 2 >0.68; pooled data: L: R 2 >0.92 and NL, NLS: R 2 >0.94). Damaged/overstrained elements in L, NL, and NLS occurred at similar locations but the number of overstrained elements was overestimated when using the L simulation method. Considering the increased solving time of the nonlinear μFE models as well as the acceptable performance in displacement prediction of the linear μFE models, one can conclude that for similar use cases linear μFE models represent the best compromise between computational effort and accuracy of the displacement field predictions. Graphical abstract: Image 1 Highlights: Stepwise compression until failure of 5 human trabecular bone biopsies. Digital volume correlation to measure elastic and ultimate point displacements. Comparison of different linear and materially nonlinear μFE simulations. μFE models accurately predict elastic and ultimate point displacement fields. Linear μFE is the best compromise between accuracy and computational effort.