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Shearing, shrinking, and stiffening in elastic networks
How do elastic networks stretch, shear, shrink, and expand ? Numerous materials ranging from biopolymers to solid foams to engineering frameworks have a network architecture : they consist of nodes connected by long-lived bonds that mediate local interactions. Even particulate systems such as emulsions and aqueous foams, which do not conform with this definition, are intimately related to networks within the harmonic approximation. Motivated both by their fundamental significance and application potential, in recent years there has been an enormous effort to understand elastic networks nonlinear mechanics. We have now reached the point where it is possible not only to describe their response, but also to tune it and/or design the network structure for a specific function.
I will provide an overview of recent work in the field, with emphasis on networks composed of fibers or simple harmonic springs. I will focus on three inter-related phenomena. (i) STRAIN STIFFENING, or the tendency to become stiffer under increasing deformation. (ii) NEGATIVE NORMAL STRESSES, the phenomenon where networks want to shrink when they are sheared, and so build up tension. (iii) PRE-STRESSES, or the coupling between a network’s instantaneous stress state and its response to further deformation. In each of these cases I will highlight the results of computer simulations of minimal models, and compare the results of scaling arguments for the mechanical response.