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