A maximum-entropy length-orientation closure for short-fiber reinforced composites.

We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes which accounts for a coupling of the fiber-length and the fiber-orientation. For prescribed fiber-length distribution and fiber-orientation tensor of second order, a maximum-entropy estimate is used to produce a fiber-length-orientation distribution which mimics real injection molded specimens, where longer fibers show a stronger alignment than shorter fibers. We derive the length-orientation closure from scratch, discuss its integration into the sequential addition and migration algorithm for generating fiber-filled microstructures for industrial volume fractions and investigate the resulting effective elastic properties.

Imposing Dirichlet boundary conditions directly for FFT-based computational micromechanics.

We discuss how Dirichlet boundary conditions can be directly imposed for the Moulinec-Suquet discretization on the boundary of rectangular domains in iterative schemes based on the fast Fourier transform (FFT) and computational homogenization problems in mechanics. Classically, computational homogenization methods based on the fast Fourier transform work with periodic boundary conditions. There are applications, however, when Dirichlet (or Neumann) boundary conditions are required.