Hardening and softening in an active elastic solid model of interacting myosin motors

Myosin motors and actin filaments are important for, among other phenomena, the cell cytoskeleton dynamics. Inspired by the above system, we study the mechanical properties of a one-dimensional discrete spring-mass system nonlinearly interacting and with internal active contracting forces (as those generated by myosins). This system is also coarse-grained, thus leading to continuum elastic equations for its displacement field, which are analytically solved and compared with numerical simulations of the discrete system. Interestingly, this simple active elastic solid presents both hardening and softening regions when compared with its passive counterpart. Specifically, this active material hardens under compression and under small stretching forces, but softens under larger ones. This peculiar behavior is exactly described by analytical expressions.