# Nonlinear bending theories for non Euclidean plates

Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is given by a nonlinear isometry-constrained bending energy functional which is a natural generalization of Kirchhoff's plate functional. We introduce and discuss a natural notion of (possibly non-minimising) stationarity points. We show that rotationally symmetric immersions of the unit disk are stationary, and we give examples of metrics $g$ leading to functionals with infinitely many stationary points.

## Similar Publications

**Affiliations:**

^{1}Syracuse University,

^{2}Syracuse University

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**Affiliations:**

^{1}IEMN,

^{2}IEMN,

^{3}IEMN,

^{4}IEMN,

^{5}IEMN

**Category:**Physics - Soft Condensed Matter

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**Authors:**S. Varagnolo

^{1}, F. Raccanello

^{2}, M. Pierno

^{3}, G. Mistura

^{4}, M. Moffa

^{5}, L. Persano

^{6}, D. Pisignano

^{7}

**Affiliations:**

^{1}CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova,

^{2}CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova,

^{3}CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova,

^{4}CNISM and Dipartimento di Fisica e Astronomia 'G. Galilei'- Università di Padova,

^{5}NEST, Istituto Nanoscienze-CNR Pisa,

^{6}NEST, Istituto Nanoscienze-CNR Pisa,

^{7}NEST, Istituto Nanoscienze-CNR Pisa

**Category:**Physics - Soft Condensed Matter

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