Nonlinear elasticity of amorphous solids

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Abstract
Structural phase transitions in amorphous solids associated with vanishing bulk modulus K or shear modulus μ are considered. We find that the transition (realized in gels) at K=0, though of second order, does not exhibit true scaling behavior of density fluctuations. An isotropic state with vanishing μ is unstable to the formation of an anisotropic glassy phase that has a phonon spectrum exhibiting soft directions in momentum space similar to those in liquid crystals. The effects of internal random stresses are studied.