We will show that periodic self-arranged deformation patterns such as found in wrinkled elastic surfaces can be represented in the framework of solid crystals and smectic liquid crystals. The key is to find a mapping from deformation topography to the field of both well established crystallographies. This mapping will enable us to port many ideas from crystallography back to deformations in the Continuum/Structural mechanics framework. The results of the proposed project will:

i) reveal some new properties of deformable mechanical systems which cannot be described only from the perspective of structural mechanics,

ii) simplify the solution procedures in the Continuum/Structural mechanics framework,

iii) enable several original approaches to applications in mechanics of structures.

The key parts of the project are:

a) development of analytical tools

b) development of numerical tools

c) simulations of given problems

d) experiments: polymer engineering and special devices, carrying out the experiments

e) dissemination, writing reports, scientific contributions

The key project phases are at the following stage (in %):

a) development of analytical tools (90 %) - almost done

b) development of numerical tools (100 %) + 40 % extra developed algorithms

c) simulations of given problems (100 %)

d) experiments: polymer engineering and special devices, carrying out the experiments (100 %) + 50 % additionally discovered properties of compounds and experimental procedures (very exciting!)

e) dissemination, writing reports, scientific contributions (80 %) - the last papers are soon to be submitted

Published papers:

7. E. Istenič, V. Šajn, M. Brojan. Influence of surface properties on the dynamics of fluid flow. Physics of fluids. Vol. 34(2), 1-17 (2022).

6. T. Veldin, B. Brank, M. Brojan. Discrete Kirchhoff-Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch, Thin-Walled Structures, Vol. 168, 108268 1-20 (2021)

5. J. Rozman, M. Krajnc, P. Ziherl. Morphologies of compressed active epithelial monolayers, The European Physical Journal E, Vol. 44, Article no.: 99 (2021)

4. T. Veldin, M. Lavrenčič, B. Brank, M. Brojan. A comparison of computational models for wrinkling of pressurized shell-core systems, International Journal of Non-Linear Mechanics, Vol. 127, pages: 103611 1-9 (2020)

3. M. Lavrenčič, B. Brank, M. Brojan. Multiple Wrinkling Mode Transitions in Axially Compressed Cylindrical Shell-Substrate in Dynamics, Thin-Walled Structures, Vol. 150, 106700 1-12 (2020).

2. J. Rozman, M. Krajnc, P. Ziherl. Collective cell mechanics of epithelial shells with organoid-like morphologies, Nature Communications, Vol. 11, Article no.: 3805 (2020)

1. T. Veldin, B. Brank, M. Brojan. Computational Finite Element Model for Surface Wrinkling of Shells on Soft Substrates, Communications in Nonlinear Science and Numerical Simulation, Vol. 79, 104863 1-17 (2019)

In submission:

Surface wrinkling of curved systems induced by shrinking (numerical models and experiments)

Stability of wrinkled plates

A new approach to the design of godesic domes