A nonlinear active elastic solid made of contractile force dipoles: Mechanical properties

So far, active elastic solids have been mainly investigated in the linear interaction regime. This work introduces a nonlinear active elastic solid --a one-dimensional network of contracting force dipoles interacting by nonlinear hard springs-- and analyzes its mechanical properties. Interestingly, this system with respect to its passive counterpart, presents a stiffening effect during compression and extension, but as long as its active force becomes smaller than the applied stretching force, a transition to a softening behavior is observed. This behavior is expressed in the system's \textcolor{red}{force-strain diagram} as the appearance of a double $S$ curve, which is not common for a simple network made of hard springs, and hence considered it as anomalous. The latter properties are captured by employing both, a continuum (coarse-graining technique) and a discrete description which are solved both, analytically and numerically. It is then concluded that the combination of nonlinear elasticity, activity, and the appearance of an internal structure in the material (due to the active force dipoles) may also be another way of generating novel mechanical properties in active metamaterials.