Hierarchical Biomechanics: Concepts, Bone as Prominent Example, and Perspectives Beyond

Abstract

The main motivation for “hierarchical biomechanics” is that the wide variability of mechanical properties encountered at the macroscopic scale may be traced back to just a few “universal” or invariant mechanical properties of elementary components at a sufficiently small scale (such as collagen, elastin, and water in case of soft tissues; complemented by hydroxyapatite in case of hard “mineralized” tissues such as bone), and to the nano-and microstructures which the latter build up. This challenging task requires a physically rigorous and mathematically sound basis, as provided by Finite Element and Fast Fourier Transform methods, as well as by continuum micromechanics resting on (semi-)analytical solutions for Eshelby-type matrix-inclusion problems. Corresponding numerical and analytical mathematical models have undergone diligent experimental validation, by means of data stemming from a variety of biophysical, biochemical, and biomechanical testing methods, such as light and electron microscopy, ultrasonic testing, and scanning acoustic microscopy, as well as physicochemical tests associated with dehydration, demineralization, decollagenization, ashing, and weighing in air and fluid. While elastic scale transition and homogenization methods have attained a high maturity level, the hierarchical nature of dissipative (i.e., viscous or strength) properties is still a vibrant field of research. This applies even more to hierarchical approaches elucidating the interface between biological cells and extracellular matrices (“mechanobiology”), to cells interacting in complex biofluids such as blood, and to the intricate and highly undiscovered mechanics unfolding within biological cells.