Shape deformation from metric 's transport. (March 2020)

• Record Type: Journal Article
• Authors: Teresi, L.; Milicchio, F.; Gabriele, S.; Piras, P.; Varano, V.
• Is Part Of: International journal of non-linear mechanics. Volume 119(2020)
• Publication Date: 2020-03
• Subjects: Elastic metric -- Distortions -- Non linear elasticity -- Metric tensor; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.103326
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We exploit the possibility of deforming a solid volume, or a surface as well, by assigning a target metric. As well known, an elastic solid may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, aka, the pre-strains. Actually, a distortion prescribes the target metric sought by the solid, and the metric effectively realized is the one that minimize the distance, measured through an elastic energy, between the target metric and the actual one. The challenge of our work is to use the metric information taken from a pair of configurations X ¯, X of a given body B x, to deform a different body B y, so that its deformation be as similar as possible to the one suffered by B x . In particular, we assess the metric change between the two configurations X ¯, X of the template B x ; then, we use this information to build a target metric for B y, exploiting the notion of distortions: given a source configuration Y ¯, we find a target configuration Y by minimizing an appropriate elastic energy. The proposed method is very effective in deforming solids as well as surfaces, and in reproducing similar deformations even when applied to different bodies.