  In this paper, we are concerned with subwavelength resonant modes of two hard
inclusions embedding in soft elastic materials to realize negative materials in
elasticity. All the $12$ subwavelength resonant frequencies are derived
explicitly for general convex resonators. In addition, the resonant modes are
categorized into dipolar, quadrupolar, and hybrid groups, facilitating the
effective realization of negative mass density, negative shear modulus and
double-negative properties (both mass density and shear modulus) in elastic
metamaterials. Moreover, we analyze the stress distribution between two hard
inclusions when they are closely touching. We also precisely derive the sharp
blow-up rates of the gradient estimates of the resonant modes. Our findings
show that certain resonant modes have bounded stress estimates when the
curvature of the hard inclusions is appropriately designed. These results
provide valuable insights into the stability of the design and fabrication of
elastic metamaterials. Lastly, we express the scattering wave fields explicitly
in terms of resonant modes, offering a clear understanding of their impact on
the overall scattering behavior.
