Shear modulus, fractal elastic properties

We have also studied the elastic properties of a nonuniform medium with chaotic structure in which one phase has a negative shear modulus. The analysis may be made using the fractal hierarchical structure model. 

The first models, describing elastic behavior of fractal structures, were used, as a rule, for simulation within the fimneworks of percolation theory [1-5], Nonhomogeneous statistical mixture of solid and liquid then only displays solid body properties (e g., not equal to zero shear modulus G), when solid component forms percolation cluster, like at gelation in pol5uner solutions. If liquid component there is replaced by vacuum, then bulk modulus. B will also be equal to zero below percolation threshold [1]. Such model gives the following relationship for elastic constants [1,3] ... 

The first models describing the elastic behaviour of fractal structures used, as a rule, simulation within the frameworks of percolation theory [21-25]. Anon-homogeneous statistical mixture of solid and liquid displays solid properties (for instance, shear modulus G not equal to zero) only, when the solid component forms a percolation cluster at gelation in polymer solutions. If the liquid component is replaced by a vacuum then the bulk modulus K. will also be equal to zero below the percolation threshold [21]. This model gives the following relationship for elastic constants [21] ... 

It was shown experimentally by Vreeker et al. [56] and by Rousseau and coworkers [38,58-64,76] that the elastic properties of fat crystal networks at low and high solid fat contents, respectively, are highly dependent on the fractal nature of the microstructure. For the shear elastic modulus G ... 

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