Elastic active matter — A composite mechanics approach via non-interaction approximation

An active composite material is assumed to be composed of a passive isotropic elastic matrix with spherical voids containing active rod-like elements, each of which being in diametrical contact with the void’s surface. A ball-bearing fixation between the rod and the contact pads is assumed, and thereby the normal contact becomes a primary mode through which the rod-like elements transfer active loading to the surrounding elastic matrix. Under the assumption that the radius of contact pads is small compared to the void radius, an asymptotic solution to the corresponding elasticity polarization matrix has been derived by the method of matched asymptotic expansions. The obtained explicit analytical results for the matrix/inclusion contact problem and a non-interaction approximation scheme are utilized for constructing an asymptotic model of the dilute elastic active microstructure.