Supplementary Information: Nanoscale heterogeneity promotes energy dissipation in bone

1. Effect of Surface Roughness and Topography The possible role of surface roughness in influencing the nanoscale energy dissipation in bone was investigated both experimentally and computationally. The peak-to-valley heights of the topographical features measured from the tapping mode atomic force microscopy (AFM) images shown in Figs. 2a,d of the main manuscript (presumably mineral particles) were measured to be ~ 11.5 ± 9.1 nm and the average root mean square (rms) roughness was calculated to be ~ 11.5 nm over 2 μm × 2 μm scan areas. Hence, the average indentation depth was ~ 3× greater than the average topographical feature peak-to-valley height and rms surface roughness. Approximately 3000 AFM-based nanoindentation experiments (tetrahedral probe tip end radius, Rtip ~ 15 nm, equivalent cone angle 23.5o, measured by scanning electron microscopy and shown in Fig. 1 of the main manuscript) were carried out over a large range of the ratio, hmax/rms surface roughness (~2-16). Here, hmax was the depth at maximum load for a particular indent and the rms surface roughness was measured directly at each nanoindentation position (before nanoindentation) directly by tapping mode AFM imaging over a 100 nm × 100 nm square region. This point-by-point nanoscale rms surface roughness measurement taken at the exact position of nanoindentation and over the approximate size of the indent area is more accurate than employing a mean rms surface roughness value for the entire surface. Elastic modulus data (calculated using the commonly used Oliver-Pharr model at each position) were separated into equal bins of 1 hmax/rms surface roughness and the data that fell within in each bin was used to calculate a coefficient of variation (COV = ratio of standard deviation to the mean). Fig. 1 is a plot of COV versus hmax/rms surface roughness for the AFMbased nanoindentation data (black square symbols). These data show that the COV stays within 0.3-0.4 for the entire range of hmax/rms surface roughness and is in fact statistically independent of hmax/rms surface roughness. An ANOVA variance test was performed using the O’Brien method to test for homogeneity of variances between the different COV groups relative to one another. Using this analysis, it was shown that the assumption for homoscedasticity was met (F = 1.0113, p > 0.05), i.e. that there was no overall statistically significant trend for the dependence of the COV on hmax/rms surface roughness. Fig. 1 also compares AFM-based experimental nanoindentation data with experiments carried out on similar samples with an instrumented nanoindentor (Hysitron, Inc.) and Berkovich probe tip (square pyramidal, Rtip ~ 180 nm, included angle 142.3o). In this case, the Rtip was iteratively determined through a series of FEA simulations compared to experimental indentations on fused silica. These data show an increase in the COV for hmax/rms surface roughness < 5. It is unclear whether this effect is a surface roughness effect or is convoluted by a length-scale dependent homogenization effect due to the hierarchical nanostructure of bone (i.e. the response of local, nanoscale mechanically differing regions which are averaged into a more continuum-like response at larger contact areas). To determine the origin of the increased COV at smaller hmax/rms surface roughness values for the instrumented indentation data, further theoretical work is needed which would take into account the nanoscale structure of the material, the probe tip geometry and size, and the maximum load and depth (such research is ongoing and beyond the scope of this manuscript). As described in the main manuscript, the increased COV of the AFM-based experiments compared to the larger length scale instrumented indentation data is attributed to the exceedingly sharp probe tip which is able to feel local nanoscale heterogeneities for example, nanoscale interfaces and the effect of individual nanoscale constituents. A twodimensional indentation modulus map for hmax/rms surface roughness >10 is shown in Fig. 2 which shows a COV of 0.34, which is consistent with Fig. 1.