On Bulk Modulus Values in Dilatant Materials Varying with the Increase in Strain

The paper transforms non-linear tensor equations describing the relation of principal strains to the principal stress tensor into matrix form, leading to equations containing a sum of two terms representing linear and non-linear strain (dilatancy) that are required for derivation of a more general equation of volumetric strain. We present new statements for moduli and compliances in volumetric elasticity. We computed volumetric strain taking into account compliances of volumetric elasticity, since, being reciprocal to the "apparent" moduli, they are described by continuous smooth functions of principal stresses. We show that compliances as functions of principal stresses are almost linear, which does not reflect either the non-linearity of initial plots or the non-linearity of Poisson's ratios. We used our mathematical model to determine elastic properties, strain and anisotropy in composites and grey cast iron

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