Christian Hellmich

Abstract:

Many biological systems integrate inorganic, mineral components which are also used by nature in a geological context. This provides a fascinating avenue for interdisciplinary work at the “bio/geo-interface”. The present lecture will cover 20 years of research concerning works that translate and adopt concepts from poro-micromechanics, a theory having originally arisen in geoengineering, to move towards the deciphering of the mechanics of complex biological systems. In this context, particular emphasis will be laid on the use of the Mohr-Coulomb failure criterion, one of the most fundamental theoretical concepts in geomechanics. This criterion is within the framework of multiscale continuum micromechanics, so it allows prediction of the strength of bone from elastic and strength properties of the material’s elementary components: hydroxyapatite crytals, type I collagen, and water with non-collageneous organics.
In this context, the following theoretical steps, all carefully implemented numerically and tested by very many biomechanical, biophysical, and biochemical experiments, are the following: the hierarchical sequencing of traditional homogenization schemes such as the two-phase Mori-Tanaka and self-consistent scheme [1,2,3], the extension from two-phase to multi-phase systems [4,5], and the consideration of eigenstrains and their upscaling characteristics [6], which paved the way towards a unified vision of bone multiscale biomechanics, encompassing poro-elasticity, poro-plasticity [7,8], and creep [9].

[1] A. Fritsch, Ch. Hellmich, J Theor Biol 244, 597-620, 2007.
[2] Ch. Hellmich, J.-F. Barthélémy, L. Dormieux, Eur J Mech 23A, 783—810, 2004.
[3] V. Vass, C. Morin, S. Scheiner, Ch. Hellmich, CISM Vol. 578, 175-229, 2018.
[4] Ch. Hellmich, J. Celundova, F.-J. Ulm, J Eng Mech 135, 382-394, 2009.
[5] C. Morin, Ch. Hellmich, Ultrasonics 54, 1251-1269, 2014.
[6] B. Pichler, Ch. Hellmich, J Eng Mech 136, 1043-1053, 2010.
[7] A. Fritsch, Ch. Hellmich, L. Dormieux, J Theor Biol 260, 230-252, 2009.
[8] C. Morin, V. Vass, Ch. Hellmich, Int J Plast 91, 238-267, 2017.
[9] L. Eberhardsteiner, Ch. Hellmich, S. Scheiner, Comp Meth Biomech Biomed Eng 17, 48-63, 2014.