Many natural structures are made of soft tissue that undergoes complicated continuous shape transformations that accurately and reliably serve specific elaborate tasks. Such processes can be slow, as in growth of a tissue, leading from an initial, featureless, shape to the desired elaborate structure of the adult organ. In other cases continuous shape transformations of soft tissue are rapid and are used for the production of mechanical work, as in the case of the action of the hart. Our understanding of natural growth is limited and our ability to produce controlled motions of soft tissue is poor. A central problem in both cases is how to incorporate all local changes in the tissue in order to determine the mechanical state of the entire body. In addition, there are problems regarding how to measure a deforming body and how to characterize the deformation. Finally, there is a problem of how to control motion and growth in artificial and natural soft tissues. I propose a multi disciplinary study, based on an approach I have started developing. According to it there is an underlying common mathematical way to describe continuous large shape transformations of stretchable tissues. This approach clearly defines the way to determine the mechanical state of a deformed tissue and to measure its local growth/deformation. The project will involve a theoretical study within mechanics and differential geometry, an experimental-physics work, which will be focused on the construction of responsive deformable tissue elements and measurements of their shape evolution, and a biophysical work, in which the natural growth and motion of leaves will be measured and will be correlated with biological activities. Such an integrative study has the potential of advancing our understanding of the fascinating process of growth and to improve our ability to construct bio-inspired "soft machinery".
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