TL;DR
This paper reviews mathematical and physical insights into the shape formation of soft constrained films, highlighting their relevance in biological and macroscopic systems like capillary films and adherent cells.
Contribution
It synthesizes recent developments in understanding how soft constraints influence the shape and mechanics of films and biological tissues.
Findings
Understanding of shape formation in softly constrained systems
Application to mechanics of adherent cells
Mathematical models for soft constraint effects
Abstract
The shape of materials is often subject to a number of geometric constraints that limit the size of the system or fix the structure of its boundary. In soft and biological materials, however, these constraints are not always hard, but are due to other physical mechanisms that affect the overall force balance. A capillary film spanning a flexible piece of wire or a cell anchored to a compliant substrate by mean of adhesive contacts are examples of these softly constrained systems in the macroscopic and microscopic world. In this article I review some of the important mathematical and physical developments that contributed to our understanding of shape formation in softly constrained films and their recent application to the mechanics of adherent cells.
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