The composite voxel technique for inelastic problems

The composite voxel technique was developed in the framework of linear elasticity and hyperelasticity for regular voxel grid discretizations which cannot resolve material interfaces exactly in general. In this work, we study the inelastic behavior of two-phase laminates. In particular, we derive an analytical nonlinear formula for the unknown rank one jump of the strain across the interface. This enables us to extend the composite voxel technique to account for inelastic material behavior at small strains. We demonstrate by numerical experiments on continuously and discontinuously reinforced thermoplastics with elastoplastic matrix behavior that FFT-based computational homogenization on downsampled microstructures equipped with composite voxels produces stressâstrain curves mimicking those obtained for the full resolution. For industrial sized microstructures it turns out that the computations can be accelerated by a factor of up to 40 compared to a direct paralleliza tion of the fully resolved problem.