Storage modulus is related to elasticity. This property is hard to maintain/increase usually.

Storage modulus is the feature of visco-elastic material to store energy. You could use such materials where damping or piezo (like piezoelectric) characteristics are  required. 

Viscoelasticity is one of important parameters for char-acterization of processing and use properties of poly-meric materials. For polymer blends or inorganic parti-cle-filled polymer composites, the relationship between structure and properties tends towards more complexity owing to the formation of an interface between compo-nents, as well as between the fillers and matrix. The vis-coelastic parameter of polymer materials may be meas-ured using a dynamic mechanical analysis instrument, such as storage modulus, loss modulus and mechanical damping, etc. In addition, dynamic mechanical meas-urements over a range of temperatures provide valuable insight into the structure, morphology and properties of polymeric blends and composites. A lot of dynamic me-chanical analyses on polymeric blends and composites have been done

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As quoted by victor, the storage modulus is related to the elasticity. Is a traduction of how the material stored energy that can be integrally reused in form of elastic deformation of the material. In DMTA analysis the material is of good elasticity in a given temperature domain when the evolution of the storage modulus is kept constant. A frequence sweep is of great interest in appreciating the elasticity of the material.

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