Statistically augmented boundary conditions for statistically equivalent RVEs

Abstract eng:
Statistically equivalent representative volume elements (SERVEs) are used to obtain homogenized constitutive responses of composite microstructures with non-periodic (random) dispersion of heterogeneities. SERVEs are subjected to affine transformation based displacement, constant-traction or periodic boundary conditions ignoring the influence of the exterior microstructure, thus, leading to very large SERVE sizes. Novel statistically augmented boundary conditions (SABCs) derived in this paper accounts for the interaction between heterogeneities in the SERVE and exterior domain through the incorporation of microstructural statistics via the one-point and two-point correlation functions S1 and S2 , respectively. The converged size of the SERVE is significantly smaller with the SABCs in comparison with the conventional boundary conditions.

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