This paper, originally motivated by a question raised by Wood and Hanna [Soft Matter, 2019,
15, 2411], shows that pure measures of bending for soft plates can be defined by introducing …

In this paper we rediscover Grioli's important work on the optimality of the orthogonal factor
in the polar decomposition in an euclidean distance framework. We also draw attention to …

We propose bending energies for isotropic elastic plates and shells. For a plate, we define
and employ a surface tensor that symmetrically couples stretch and curvature such that any …

We derive stretching and bending energies for isotropic elastic plates and shells. Through
the dimensional reduction of a bulk elastic energy quadratic in Biot strains, we obtain two …

Recent developments in the theory of shells Advanced Structured Materials Holm Altenbach
Jacek Chróścielewski Victor A. Eremeyev Krzysztof Wiśniewski Editors Recent Developments in …

The problem of finding a deformation corresponding to a given Cauchy–Green strain is
approached with a procedure that employs the Gram decomposition of the deformation …

Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects
that bear a deformation content. By refining the resolution of the surface deformation …

Chien Wei-Zhang (1944) derived three equilibrium equations and three compatibility
conditions of the nonlinear theory of thin, isotropic elastic shells entirely in terms of the …

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 …

We introduce the tensor which maps the Cartesian plane into the tangent plane of the
surface. Then by analogy to the polar decomposition theorem widely used in the non‐linear …