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概要

MAT TOOLBOX 2018

What makes biologicalmaterials so special?Bones can absorb large strain energies by sacrificing their integrity.Crustacean shells achieve extreme impact resistance by reorientingtheir fibres. Sea-cucumbers and starfishes move around bychanging the stiffness of their bodies. My research aims at explainingwhy with mathematical models.Anders Poulsen, (https://commons.wikimedia.org/wiki/File:Sea_cucumber_at_Pulau_Redang.jpg), https://creativecommons.org/licenses/by-sa/3.0/legalcodePaul Shaffner, (https://commons.wikimedia.org/wiki/File:Starfish_08_(paulshaffner).jpg), https://creativecommons.org/licenses/by/2.0/legalcodeFig. 1: Left: sea cucumber(Thelenota ananas); right:Unknown Starfish species,Lazy Lagoon, near Bagamoyo,Tanzania.Viscoelastic creep ofmutable collagenous tissuein echinodermsEchinoderms (like sea-cucumbersand starfishes, Fig. 1) modify the stiffnessof the interfibrillar matrix chemically,by releasing stiffening reagents.This alternate stiffening and softeningcauses the locomotion of the limbswithout the need of a central nervoussystem. My colleagues (Dr Gupta andco-workers) measured the viscoelasticcreep of the tissue. Through synchrotronmeasurements, they werealso able to measure the viscoelasticcreep on the fibril. They repeated themeasurements for tissues in artificialStress [MPa]1.210.80.60.40.2seawater (as a reference) and in watersolutions with different solvents,known to trigger stiffening and softeningof the matrix. I used mathematicalmodels known as“Hill self-consistent”and“Eshelby tensor”to obtain theviscoelastic creep of the interfibrillarmatrix in these three conditions (Fig. 2).The results confirmed that in a solutionwith decreased calcium ions, the matrixis softer than the one in artificialseawater; in a solution with potassiumions, the matrix is, instead, stiffer thanthe matrix in seawater.Energy Absorptionin Cyclically Loaded Antler BoneWho doesn't love the deer in Nara(Fig. 3)? Male deer have antlers thatMatrix - Artificial SeawaterMatrix - Ca 2+ solutionMatrix - K + solutionFig. 2: Viscoelastic creepof the interfibrillar matrixof a sea cucumber inartificial water and twodifferent ionic solutions.Fig. 3: A male deer near T?dai-ji, in Nara.are very resistant to impacts becausethey can absorb a significant amount ofenergy. They act like natural bumpers.Through experiments and mathematicalmodels at the microscale, my colleaguesand I found out why. The ingredientsfor the energy absorption arethe staggered arrangement of the fibrils(Fig. 4, top), the different mechanicalresponse of each fibril (elastic andplastic) and, paradoxically, the weaknessof some of the bonds between thefibrils. The principal building-blockof bone is a Type-I collagen fibril. Thedisposition of the fibrils is a staggeredarrangement. Some of these fibrils deformelastically, and the rest insteaddeform plastically. Also, some of theinterfaces between fibrils are damageable(they break easily), others insteadare undamageable. These three ingredientscause the viscoelastic stress-strainresponse of the bone under uniaxialcyclic loads (Fig. 4, bottom). The areaunder the hysteretic loops is a measureof the absorbed strain energy: the widerthe loops, the higher the dissipatedenergy.00 50100 150 200 250 300 350 400 450 500Time [sec]8非線形物理