Fractals negative shear modulus

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. 

According to (314), a material with a negative Poisson s coefficient can be obtained either if it is very rigid (i.e. if its shear modulus fulfills the above condition) or by forming a structure with dimension less than 2 i/K (i.e., d < 2 i/K) or by combining the first and the second methods. Change of dimension of the system is impossible for continuum structures however, it is possible in fractal structures [163]. 

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