Abstract
Abstract We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms. As well known, an elastic shell may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, also known as the pre-strains. Actually, the target fundamental forms prescribe a sought shape for the solid, and the metric effectively realized is the one that minimizes the distance, measured through an elastic energy, between the target and the actual fundamental forms. The proposed method is very effective in deforming shells.
Highlights
We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms
The effects of distortions are usually studied in small displacement regime, and few studies tackle the problem of large distortions that can yield large deformations; even more interesting are the cases where distortions induce large shape changes without stressing the structure
The morphing is obtained by assigning a distortion field, which in turns, induces a target metric: the actual configuration will minimize the elastic energy, measuring the distance between the target metric and the actual one
Summary
The problem of the shape reconstruction from local geometrical properties, such as the metric or the curvature, is common to different fields, among them are Shape Analysis, Computer Graphics [1, 2] and Solid Mechanics [3, 4]. A different case is when so-called inelastic deformations (thermal expansion, swelling, plasticity) are present, where the target metric (curvature) is no longer associated with the reference configuration or, more in general, with a global configuration, but is locally assigned in the body. If the target metric does not respect the compatibility equations or the compatibility with the boundary conditions, no target configuration exists and, in the absence of loads, the body will arrange itself in a configuration which will be as locally as possible similar to the elastic metric, in order to minimize the elastic energy. Within this configuration internally self-balanced stresses are present, named self-stresses. 3 2D Distortions and the elastic fundamental forms quadratic in ζ , which is neglected, plus a term which is constant, that is e3 ⊗ e3, and the term
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