A generic Green operator based analytical solution form for all the effective generalized elastic-like moduli of n-phase laminates. (1st December 2021) - Franciosi, Patrick
Abstract: In linear elasticity, the exact first order analytical expressions for each of the effective moduli of n-phase laminate composites are accessible from solving the stress-strain relations under the conditions of uniform stresses and uniform strains normally and transversally to the layers respectively. Several authors have extended successfully this here called "consistency phase boundary conditions" (CBC) solution method to coupled properties of the generalized elastic types, as magnetic-electric-elastic (MEE) ones. This solution for laminates is also shown since long accessible from the Fourier-Green-Eshelby homogenization frameworks whose all (Hashin-Shtrikman, Mori-Tanaka, Self-Consistent, …) estimates coincide into the first order linear solution. It is here pointed that all the analytical expressions of the individual moduli from the CBC solution obey a same generic explicit simple form that results from a known essential property of the strain and stress dual Green operators (GOs) for infinite layers in infinite media. Using both these two GOs, this "generic GO-based" (gGO) solution for laminates retrieves the entire tensors of effective stiffness and compliance moduli whose terms are verified identical to those from the CBC - hence homogenization - solution.