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The deformation of disordered solids relies on swift and localisedrearrangements of particles. The inspection of soft vibrational modes can helppredict the locations of these rearrangements, while the strain that theyactually redistribute mediates collective effects. Here, we study soft modesand strain redistribution in a two-dimensional continuous mesoscopic modelbased on a Ginzburg-Landau free energy for perfect solids, supplemented with aplastic disorder potential that accounts for shear softening andrearrangements. Regardless of the disorder strength, our numerical simulationsshow soft modes that are always sharply peaked at the softest point of thematerial (unlike what happens for the depinning of an elastic interface).Contrary to widespread views, the deformation halo around this peak does notalways have a quadrupolar (Eshelby-like) shape. Instead, for finite andnarrowly-distributed disorder, it looks like a fracture, with a strain fieldthat concentrates along some easy directions. These findings are rationalisedwith analytical calculations in the case where the plastic disorder is confinedto a point-like `impurity'. In this case, we unveil a continuous family ofelastic propagators, which are identical for the soft modes and for theequilibrium configurations. This family interpolates between the standardquadrupolar propagator and the fracture-like one as the anisotropy of theelastic medium is increased. Therefore, we expect to see a fracture-likepropagator when extended regions on the brink of failure have already softenedalong the shear direction and thus rendered the material anisotropic, but notfailed yet. We speculate that this might be the case in carefully aged glassesjust before macroscopic failure.

Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?