  We show how strain stiffening affects the elastic response to internal
forces, caused either by material defects and inhomogeneities or by active
forces that molecular motors generate in living cells. For a spherical force
dipole in a material with a strongly nonlinear strain energy density, strains
change sign with distance, indicating that even around a contractile inclusion
or molecular motor there is radial compression; it is only at long distance
that one recovers the linear response in which the medium is radially
stretched. Scaling laws with irrational exponents relate the far-field
renormalized strain to the near-field strain applied by the inclusion or active
force.
