Bio-inspired Material And Structure Optimization

Natural materials such as bone, tooth, and nacre are nano-composites of proteins and minerals with superior stiffness and toughness. The components of mineral fibril have extremely different mechanical properties. The mineral is stiff and brittle while the (wet) protein is much softer but also much tougher than the mineral. Increasing the amount of mineral particles will always increase the stiffness but also the brittleness of the bone tissue at the same time. Experimental results show that the while the stiffness of bio-composites is close to that of its mineral constituent, its fracture strength and toughness are significantly higher than those of the mineral. This outstanding performance of bio-composites comes from their highly complex hierarchical structures at different length scales. How to make the bio-composite hard enough with high toughness? Nature solves this problem in an elegant way by the smart design of the size, shape and material distribution of the nano-structures of bio-composites.At the most elementary structure level, bio-composites exhibit a generic microstructure consisting of staggered mineral bricks wrapped by soft protein in nano-scale. Previous studies show that large aspect ratios and the pattern of a staggered alignment of mineral platelets are the key factors contributing to the large stiffness of biomaterials. On the other hand, proteins between staggered mineral platelets play the essential role of absorbing and dissipating a large amount of fracture energy. Furthermore, at the nano-scale, brittle mineral becomes insensitive to flaws, which makes it possible for it to sustain large stress without brittle fracture and in turn enhance the toughness of biomaterials. Why does the nature design building block of biological materials in this form? Can we reproduce this kind of structure from the structural optimization point of view? In order to obtain more insights for bio-inspired material design from nano-scale and up, in the present study, an optimization model is proposed to explain why nature designs building blocks of biological materials in the present form. An optimization problem is formulated to describe the bio-structures.Mathematically speaking, bio-mimicking or bio-inspired material design can be formulating as an inverse optimization problem. Here we have assumed implicitly that the building block of bio-composites is the "optimization result" of natural evolution, which is consistent with Neo-Darwin's theory of natural selection. In the present work, we postulate that biological materials are designed with simultaneous optimization of stiffness and toughness for maximum structural support and flaw tolerance. In the proposed optimization model, it requires that during the process of deformation, the effective strain of any material point in the unit cell should notexceed its critical value. And we tacitly assumed that the interfaces between different materials are strong enough. When the mineral size drops below this critical length scale, the theoretical strength of mineral platelet can be maintained in spite of defects. The results of this study show that an optimization model with appropriate material constitutive models, failure criteria as well as objective and constraint functions can reproduce the realistic material distribution in the nanostructure of bio-composites. It can be seen that with the use of the proposed optimization model, the staggered arrangement of the hard and soft materials, which is in reasonable agreement with that found in natural bio-composites, can be reproduced. A plausible explanation for the convergent evolution in biology can be given (at least partially) from the optimization point of view. The obtained results confirm the belief that a staggered arrangement of mineral particles in the fibrils is mechanically superior to a strictly parallel arrangement from optimization point of view.It is shown that the maximization of ductility may be an objective of nature to design the basic building blocks of bio-composites. Using optimization principl...