Buckling And Fracture Analysis Of Biological Composite Materials

Biological materials such as bone, tooth and nacre are hierarchichal nanocompositematerials with excellent mechanical properties, and the mineral crystals are arranged in astaggered manner in protein matrix at nano-scale. In the first part of this paper, we analyzedthe local buckling behavior of staggered structure of biological materials at larger scaleusing a beam-spring model by finite element method, where the mineral was modeled byEuler beam while the matrix by distributed elastic spring, and considers the free-staggeredmodel, pinned-staggered model and continuous fiber model respectively. When the aspectratio was small, beacause the mineral’s end was free in free-staggered model, the mineralcrystals were prone to have rigid body ration without bendign, while the protein had bothshear and tensile/compressive deformation. Note that the nanocomposite exhibited a typicallocal buckling mode with a periodic pattern along both horizontal and vertical direction;Because the constraint at the pinned joints of minerals was stronger than that of the freeends, the buckling strength of the pinned-staggered model was much higher than that of thefree-staggered model at small aspect ratio, and the local buckling was mostly localized atthe loading boundary. When the aspect ratio was increased, the mineral tended to bend butoverall rotate, what’s more, the buckling modes were consistently close in these twostaggered model and reached that of continuous model as shear buckling mode. Fortunately,the buckling strength we got kindly verified the analysis of mode is reasonable, and lageraspect ratio, higher the buckling strength. The second part was the theoretical analysis onbuckling of biological materials based on pinned-staggered model, and discussed two casesas aligned arrangement and staggered arrangement. The results showed that the bucklingstrength was lowest when the mineral crystals were arranged in a align manner, and highestat symmetrical staggered arrangement. What’s more, incrasing mineral’s aspect ratio or itsvolume fraction could improve the buckling strength, and tendsed to reach that ofcontinuous case. The staggered structure whether the free-staggered model orpinned-staggered model, staggered arrangement and increasing the mineral’s aspect ratio atthe same time can improve the buckling strength and approach to that of continuousstructure. We conclude that the staggered arrangement plays an active role on the stabilityof the nanostructure. Finally, we discussed the fracture behavior of staggered structure withone slit crack, and found that when the the minerals were parallel to the crack, there’s no effect on crack’s stress concentration phenomenon, but the stress intensity fractor (SIF) atthe crack tip was lowest if minerals were perpendicular to the crack. What’s more, closerthe symmetric staggered pattern, larger aspect ratio of mineral and highter mineral’s volumefraction, lower the SIF at the crack tip.