A new hybrid homogenization theory for periodic composites with random fiber distributions

Abstract

A new homogenization theory is constructed for unidirectional composites with periodic domains containing random fiber distributions. Periodic domains are partitioned into subdomains comprised of single fibers embedded in matrix phase. The subdomain displacement field solutions combine finite-volume and locally-exact elasticity approaches. Inclusions are regarded as meshfree components whose displacement fields are represented by discrete Fourier transforms that satisfy exactly Navier’s equations. In contrast, the matrix is discretized into subvolumes and handled within the finite-volume micromechanics framework. Novel use of traction and displacement continuity conditions at the inclusion/matrix interface seamlessly connect inclusion and matrix phases. Subdomains’ assembly enforces traction, displacement continuity and periodicity conditions in a surface-average sense. Quadratic convergence of stress fields with decreasing matrix discretization relative to exact elasticity solution is obtained, yielding accurate homogenized moduli with relatively coarse matrix meshes. Fourfold and greater reductions in execution times relative to the finite-volume micromechanics justify the new theory’s construction. The proposed theory facilitates accurate and efficient studies of the rarely reported effect of random fiber distributions on homogenized moduli and local stress fields as a function of inclusion content and number of microstructural realizations. We illustrate this by computing probability distributions of homogenized moduli for up to 60,000 microstructural realizations of multi-inclusion periodic domains that may be used in machine-learning algorithms.