<p>Material failure at different scales and processes can be modeled as an emergent feature in terms of avalanche dynamics in micromechanical systems.&#160;<br>Event-event triggering -or aftershocks- is common in seismological catalogs and acoustic emission experiments <sup>[1]</sup> among other phenomena.<br>Stochastic branching and linear Hawkes processes are used to model the statistical properties of catalogs.&#160; In the micromechanical approach, viscoelastic stress transfer and after-slip are among the proposed mechanism of aftershocks. Here we ask this simple question: '<em>Do aftershock sequences in micromechanical models agree with such epidemic branching paradigm?</em>'</p><p><br>We introduce two fibrous models as prototypes of viscoelastic fracture <sup>[2]</sup> which <em>(i)</em> provides an analytical explanation to the acceleration of activity in absence of critical failure observed in acoustic emission experiments <sup>[3]</sup>; <em>(ii)</em> reproduce the typical spatio-temporal properties of triggering found in field catalogs, acoustic emission experiments; but <em>(iii)</em> display discrepancies with the branching topological properties predicted by stochastic models <sup>[4]</sup>, probably due to physical constrains. <br><br>[1] J. Bar&#243; et al.,<em> Phys. Rev. Lett.</em> <strong>110</strong> (8), 088702 (2013).<br>[2] J. Bar&#243;, J. Davidsen, <em>Phys. Rev. E</em>&#160; <strong>97</strong> (3), 033002 (2018).<br>[3] J. Bar&#243;, et al., <em>Phys. Rev. Lett.</em> <strong>120</strong> (24), 245501 (2018).<br>[4] S. Saichev, et al., <em>Pure and App. Geoph.</em> <strong>162</strong> (6), 1113-1134 (2005).</p>