  The rheology of F-actin networks has attracted a great attention during the
last years. In order to gain a complete understanding of the rheological
properties of these novel materials, it is necessary the study in a large
deformations regime to alter their internal structure. In this sense, Schmoller
et al. 2010 showed that the reconstituted networks of F-actin crosslinked with
$\alpha$-actinin unexpectedly harden when they are subjected to a cyclical
shear. This observation contradicts the expected Mullins effect observed in
most soft materials, such as rubber and living tissues, where a pronounced
softening is observed when they are cyclically deformed.
  We think that the key to understand this stunning effect is the gelation
process. To define it, the most relevant constituents are the chemical
crosslinks -$\alpha$-actinin-, the physical crosslinks -introduced by the
entanglement of the semiflexible network- and the interaction between them. As
a consequence of this interaction, a pre-stressed network emerges and
introduces a feedback effect, where the pre-stress also regulates the adhesion
energy of the $\alpha$-actinin, setting the structure in a metastable reference
configuration. Therefore, the external loads and the evolvement of the trapped
stress drive the microstructural changes during the cyclic loading protocol. In
this work, we propose a micromechanical model into the framework of nonlinear
continuum mechanics. The mechanics of the F-actin filaments is modeled using
the wormlike chain model for semiflexible filaments and the gelation process is
modeled as mesoscale dynamics for the $\alpha$-actinin and physical
crosslink.The model has been validated with reported experimental results.
