Browsing > By author > Boudaoud Arezki

The elastic response of mechanical, chemical, and biological systems is often modeled using a
discrete arrangement of Hookean springs, either representing finite material elements or even the
molecular bonds of a system. However, to date, there is no direct derivation of the relation between
a general discrete spring network and it's corresponding elastic continuum. Furthermore,
understanding the network's mechanical response requires simulations that may be expensive computationally.
Here we report a method to derive the exact elastic continuum model of any discrete
network of springs, requiring network geometry and topology only. We identify and calculate the
so-called ”non-affine” displacements. Explicit comparison of our calculations to simulations of different
crystalline and disordered configurations, shows we successfully capture the mechanics even of
auxetic materials. Our method is valid for residually stressed systems with non-trivial geometries, is
easily generalizable to other discrete models, and opens the possibility of a rational design of elastic
systems.