bifurcation

The attached tutorial paper is yet unpublished but I am posting a pre-print since several students I know have found it to be a useful pedagogical resource. You may also access the document on arXiv.

Here is the abstract.

Transverse wrinkles usually occur in a uniaxially tensile elastic membrane and will be smoothed upon excess stretching. This instability-restabilization response (isola-center bifurcation) can originate from the nonlinear competition between stretching energy and bending energy. Here, we find a crucial factor, the curvature, which can control effectively and precisely the wrinkling and smoothing regimes. When the sheet is bent, the regime of wrinkling amplitude versus membrane elongation is narrowed, with local wrinkling instability coupled with global bending.

Tensional wrinkles are widely observed in elastic thin films, with mono-orientation of wrinkles being usually perpendicular to the stretching direction. Here, by changing material orthotropic direction, we present orientable wrinkles in uniaxially stretched orthotropic membranes. To quantitatively explore orthotropy-related wrinkles and their morphological evolution, we develop a mathematical model by introducing orthotropic, elastic constitution into the extended F\"oppl-von K\'arm\'an nonlinear plate theory that can describe large in-plane anisotropic deformations.

Wrinkles commonly occur in uniaxially stretched rectangular hyperelastic membranes with clamped-clamped boundaries, and can vanish upon excess stretching. Here we develop a modeling and resolution framework to solve this complex instability problem with highly geometric and material nonlinearities. We extend the nonlinear Foppl-von Karman thin plate model to finite membrane strain regime for various compressible and incompressible hyperelastic materials.

We would like to invite you to participate in the Mini-Symposium on "Mechanics and Physics of Solids and Structures" within "ESMC2018 - 10th European Solid Mechanics Conference" in Bologna (Italy), July 2-6, 2018.

The EXTENDED deadline for abstract submission is December 10, 2017.

Mini-symposium Organizers
Sebastien Neukirch (CNRS/UPMC),
Benoit Roman (CNRS/UPMC),
Keith Seffen (University of Cambridge),
Francesco Dal Corso (University of Trento)

Photo-chromic liquid crystalline polymer (LCP) is a type of smart materials which are sensitive to light. Here we harness its photo-mechanical response to flexibly control surface patterning, through modeling a film involving homeotropic nematic liquid crystals with director perpendicular to the polymer film attached on a compliant substrate. Theoretical and numerical analyses were conducted to explore the surface instability of such film/substrate systems under both uniform and non-uniform illuminations by ultraviolet (UV) light, respectively.

We would like to invite you to participate in the Mini-Symposium on "Mechanics and Physics of Solids and Structures" within "ESMC2018 - 10th European Solid Mechanics Conference" in Bologna (Italy), July 2-6, 2018.

The deadline for abstract submission is November 15th, 2017.

Mini-symposium Organizers
Sebastien Neukirch (CNRS/UPMC),
Benoit Roman (CNRS/UPMC),
Keith Seffen (University of Cambridge),
Francesco Dal Corso (University of Trento)

There has been a strong and recent research activity to obtain tunable wrinkling patterns in film/substrate systems, which proposes to use geometric curvature as a control parameter. This paper studies core-shell cylindrical systems under thermal loads, with the aim to describe possible wrinkling modes, bifurcation diagrams and dimensionless parameters influencing the response of the system.