Statistics informed boundary conditions for statistically equivalent representative volume elements of clustered composite microstructures

ABSTRACT

Homogenized effective constitutive response of arbitrarily dispersed multiphase composites systems are computed using property-based statistically equivalent representative volume elements or P-SERVEs. P-SERVEs are subjected to affine transformation-based displacement boundary conditions, uniform traction boundary conditions or periodic boundary conditions. Predicted P-SERVE sizes are larger as the above boundary conditions ignore the influence of the inclusions exterior to the P-SERVE. Exterior statistics-based boundary conditions (ESBCs) accounting for the presence of fibers and their interactions in the domain exterior to the P-SERVE have been derived in Ghosh and Kubair (2016, J. Mech. Phys. Solids, vol. 96, pp. 1–24). In the present study, ESBCs are derived for statistically inhomogeneous microstructures using the two-point correlation functions used in the statistically informed Greens functions. Comparisons are also made with the statistical volume element approach. It is concluded that the simulations with ESBCs prescribed on the P-SERVEs have a definite advantage over other methods in defining optimal sized P-SERVEs for clustered and matrix-rich microstructures.

KEYWORDS:

• Cluster
• composites
• exterior statistics-based boundary conditions
• SERVE
• two-point correlation functions