Consistency relations for linear viscoelastic functionally graded materials/inhomogeneous moduli and for separation of variable solutions

Abstract

The permissible forms and nature of linear viscoelastic functionally graded inhomogeneous material (VFGM) functions are formulated and examined in terms of consistency principles. It is shown that no separable temporal and spatial VFGM isotropic or anisotropic inhomogeneous modulus or compliance function is admissible nor can the VFGM solutions be cast into similarly separable constructions. However, finite or infinite sums of individual separable functions are admissible combinations provided each series term in its own form satisfies boundary and initial conditions, and provided one considers such an expressions as a mathematical model without necessarily any anity to generalized Kelvin or Maxwell models.