nonlinear-moduli

This module provide a function to calculate effective linear and nonlinear elastic moduli of nanocomposites with spherical inclusions dispersed in a matrix. Linear moduli are present in the form of the bulk modulus K and the shear modulus μ. Nonlinear moduli are present in the form of the Murnaghan moduli l, m, n.

Linear effective elastic moduli of the composite with the volume fraction of inclusions c take the form:

Nonlinear effective elastic moduli of the composite take the form:

where 3x3 matrices P₀, P₁ and nonlinear moduli l_g, m_g, n_g depend on the linear moduli of the matrix K₀, μ₀ and those of inclusions K₁, μ₁. In general, P₀, P₁ and nonlinear moduli l_g, m_g, n_g depend also on the volume fraction of inclusions c.