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FROM:
Lorenzo Guiducci, John W.C. Dunlop and Peter Fratzl,
“An introduction into the physics of self-folding thin structures”, Publisher and date not given in the pdf file; most recent reference is dated 2016
INTRODUCTION: Spontaneous folding of matter has long been the subject of disparate branches of research, from the earlier vitalistic view of Leibniz1 to the mathematical description of morphogenetic processes of D’Arcy Thompson.2 Today, scientific advancements have shown how folding is a common strategy adopted in biological systems to build up more and more complex structures – in proteins, from a peptide chain to a functional enzyme; in plants, from bud petals to a developed flower; in organisms, from layers of cells to diversified embryos. One might think that such folding processes require exceptionally complex biological machineries to orchestrate them. On the contrary, with this contribution, we will show that folding can result from remarkably simple processes – and equally applies to both natural and artificial systems. In the following we will introduce the reader to the necessary theoretical concepts that are needed to understand these phenomena, providing examples from the common experience enabling a more systematic understanding.
When we talk about self-folding3 thin structures we refer to a broad class of spontaneous shape changes (that is not caused by an external load) that occur in thin bodies. The adjective thin here means that a three-dimensional body has at least one dimension much smaller than the other; that is, a rod can be considered one-dimensional since it has two small dimensions; a plate instead is two-dimensional since it has one small dimension. In particular we will refer to bodies that can be considered two-dimensional, that is plates (which are flat) and shells (which are curved). As will become clear in section 1, the fact that plates (and shells) are thin is at the base of the rich panorama of shape changes that are observed.
The goal of the present document is to provide an overview of some of the scientific literature dealing with shape changes in self-folding thin structures. Although these shape changes can be of a very different nature, size and origin – occurring in artificial as well as biological materials, and in systems that range from nanometer to centimeter sizes – all can be understood under some unifying concepts that will be introduced in the following. Thanks to our presentation, it becomes much easier to locate where research efforts have been focused until now and to identify new fields of interest that scientific research hasn’t addressed yet.
This document is organized as follows. In section 1 we introduce the reader to the basic concepts of the mechanics of a thin plate (the experienced reader can skip this part). In section 2 we will introduce many examples of self-folding systems, categorizing them on the base of how eigenstrains are distributed and orientated in the plate. In this section, we will discuss the folding (or more generally the morphing) of systems that: undergo confined expansion due to an attached elastic foundation (section 2.2); are subjected to the so-called edge growth (section 2.3); which change curvature (section 2.4). In section 3 we will give some concluding remarks on the present work.
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