Projects / Programmes
Crystallography of wrinkled elastic surfaces
| Code |
Science |
Field |
Subfield |
| 2.05.00 |
Engineering sciences and technologies |
Mechanics |
|
| Code |
Science |
Field |
| P250 |
Natural sciences and mathematics |
Condensed matter: structure, thermal and mechanical properties, crystallography, phase equilibria |
| Code |
Science |
Field |
| 2.03 |
Engineering and Technology |
Mechanical engineering |
Nonlinear Mechanics; Wrinkling; Crystallography; Deformation; Differential Geometry.
Researchers (17)
Organisations (2)
Abstract
Mechanical instabilities lead to many interesting phenomena involving bifurcation-buckling, snap-buckling, wrinkling, folding, etc. and can be found across many length-scales in Nature and engineering. Instabilities in structures have been traditionally associated with failure, catastrophic collapse and other strongly undesirable effects. Recently, an alternative view has been suggested as many state-of-the-art applications harvest the auspicious properties of their post-critical deformation field for advanced functionalities, especially those deriving from wrinkling. Inspired by the innovative use and the unique ability to form a wide range of complex self-arranged deformation patterns combined with a compact way to control them, convinced us to recognize wrinkling instabilities as an ideal system to test the proposed ideas and validate them theoretically and experimentally via precision model experiments.
The major goal of the proposed research project is to show that periodic self-arranged deformation patterns can be represented in the framework of solid crystals and smectic liquid crystals. The idea is based on the discovery (by the PI and collaborators) that such systems relax stresses both, by out-of-surface buckling through the formation of arrays of wrinkles and by simultaneously developing topological defects in their patterns. The key problem is finding a mapping from wrinkled topographies to the field of both well-established crystallographies. This will reveal some of the unknown properties of these deformable mechanical systems which cannot be described only from the perspective of structural mechanics. It will also enable us to port many ideas from crystallography back to deformations in the Continuum/Structural mechanics framework. The results of the proposed project will simplify the solution procedures in the Continuum/Structural framework and enable several original approaches to applications in mechanics of structures. As such, we see the crystallography of elastic self-arranged periodic deformation patterns as a new research direction which will illuminate the subject from a different perspective, and change the way we understand these deformations.
We will go beyond a systematic and accurate prediction of periodic elastic patterns, even though this task alone is far from trivial in most practical cases because these problems are highly nonlinear. Having a high number of close meta-stable states and the fact they grow exponentially with the system size, further drastically complicates calculations. Complex arrangements of experimentally observed defects in the crystal structure which do not occur in crystals in thermodynamic equilibrium will also be analyzed. Another focus of our research is on the study of several deformation modes (and transitions between them) which are otherwise observed in separate systems. A fascinating fact is that they may be detected in sequence, depending only on the level of the applied stress.
Rigorous analytical and numerical tools will be developed and validated via precision model macroscopic experiments on dimple, labyrinthine and hybrid phases. Several different shapes will be examined; planar and curved (spherical, cylindrical, toroidal, etc.) with an emphasis on the labyrinthine phase. A combined principle of objective-oriented and discovery driven research will be employed.
The work program is composed of three project phases, containing seven work packages, which are further broken down into separate main tasks. The research will be performed in the Laboratory for Nonlinear Mechanics at Faculty of Mechanical Engineering (UNI-LJ) under supervision of Assist. Prof. Dr. Miha Brojan (the head of the lab) and in collaboration with Prof. Dr. Primož Ziherl from Faculty of Mathematics and Physics (UNI-LJ).
Significance for science
The crystallography of elastic self-arranged periodic deformation patterns is a new research direction which will enable us to understand deformations from a different perspective. The idea to consider wrinkling patterns as crystals was first proposed by the PI and collaborators (see the paper by Brojan et al. in the References). It was shown for the first time in this study that the stresses are relaxed both, by out-of-surface buckling through the formation of arrays of dimples and by simultaneously developing topological defects in their patterns. Only the dimple pattern was analyzed, leaving the properties of the labyrinthine and the hybrid patterns (between dimple and labyrinthine) unknown.
We will show that elastic periodic self-arranged deformation patterns, such as wrinkles, 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 will enable us to port many ideas from crystallography back to deformations in the Continuum/Structural mechanics framework and reveal some of the unknown properties of deformable mechanical systems, which cannot be described from the perspective of mechanics alone. Planar and curved (spherical, cylindrical, toroidal, etc.) surface crystals will be examined theoretically and experimentally. A macroscopic experiment on toroids still represents an open challenge which we plan to solve.
The results of the proposed research will expectedly reveal more practical findings. Namely, simplified numerical solutions, finding precursors for buckling in numerical meshes, designing near optimal geodetic domes, understanding the effects of pre-patterning, etc. Note also that the impact of the proposed research reaches beyond engineering. One of the most obvious fields in which our findings will be relevant is biology, e.g. to study cortical convolutions, cell attachment, growth of bacteria in bio-films, etc.
Significance for the country
The crystallography of elastic self-arranged periodic deformation patterns is a new research direction which will enable us to understand deformations from a different perspective. The idea to consider wrinkling patterns as crystals was first proposed by the PI and collaborators (see the paper by Brojan et al. in the References). It was shown for the first time in this study that the stresses are relaxed both, by out-of-surface buckling through the formation of arrays of dimples and by simultaneously developing topological defects in their patterns. Only the dimple pattern was analyzed, leaving the properties of the labyrinthine and the hybrid patterns (between dimple and labyrinthine) unknown.
We will show that elastic periodic self-arranged deformation patterns, such as wrinkles, 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 will enable us to port many ideas from crystallography back to deformations in the Continuum/Structural mechanics framework and reveal some of the unknown properties of deformable mechanical systems, which cannot be described from the perspective of mechanics alone. Planar and curved (spherical, cylindrical, toroidal, etc.) surface crystals will be examined theoretically and experimentally. A macroscopic experiment on toroids still represents an open challenge which we plan to solve.
The results of the proposed research will expectedly reveal more practical findings. Namely, simplified numerical solutions, finding precursors for buckling in numerical meshes, designing near optimal geodetic domes, understanding the effects of pre-patterning, etc. Note also that the impact of the proposed research reaches beyond engineering. One of the most obvious fields in which our findings will be relevant is biology, e.g. to study cortical convolutions, cell attachment, growth of bacteria in bio-films, etc.
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Interim report
Most important socioeconomically and culturally relevant results
