Influence of experimental constraints on micromechanical assessment of micromachined hard-tissue samples

Continuing technological advancement of mechanical characterization at the microscale has enabled the isolation of micron-sized specimens and their direct mechanical characterization. Such techniques, initially developed for engineering materials and MEMS, can also be applied on hard biological materials. Bone is a material with a complex hierarchical structure ranging from the macro- all the way down to the nanoscale. To fully understand bone tissue mechanics, knowledge of the mechanics of all structural elements i.e. at every length scale is necessary. Particularly, the mechanical properties of microstructural elements, such as bone lamellae are still largely unknown. In the last decade, testing protocols have been devised to close this gap including bending and compression of micrometer-sized bone specimens. However, the precision and accuracy of results obtained have not been discussed. In this study, we aim to do exactly this: we validate microbeam bending by testing silicon microbeams with known mechanical constants, and evaluate the precision and sources of errors in both microbeam bending and micropillar compression by means of finite element (FE) modeling. Bending of Si-microbeams reproduced the expected value for the bending modulus within 17% accuracy, although the effect of geometrical uncertainties was estimated to result in relative errors of up to 50%. The deformation of constraining bulk material had a smaller influence, with relative errors of 11%, for microbeam bending and 25% for micropillar compression. For the latter this error could be sufficiently eliminated by the Sneddon correction. The tapering of micropillars had a negligible effect on overall apparent stiffness, but induced inhomogeneous stress state within micropillars may lead to superposed structural deformation mechanisms and be responsible for failure patterns observed in past studies.