Discrete micromechanics of elastoplastic crystals in the finite deformation range

We present a rate-independent crystal plasticity theory in the finite deformation range. The formulation revolves around theory of distribution and strong discontinuity concepts applied to the slip systems. Uniform and conforming deformation fields are introduced, from which deformation gradients for the crystal lattice and the crystal itself are derived. For a crystal deforming in single slip, we show that the crystal rotates the active slip system the same way as the lattice does, leading to an elegant and exact stress-point integration algorithm for the overall crystal stresses. For a crystal deforming in multiple slips the crystal no longer rotates the slip systems exactly as the lattice does. For this case, we present a stress-point integration algorithm accounting for the exact push-forward operation induced by the lattice on the active systems. We also consider a simplified stress-point integration algorithm for multislip systems that remains highly accurate for a wide range of stress paths considered. The framework for system activation and the selection of linearly independent slip systems follows a well-established ‘ultimate algorithm’ for rate-independent crystal plasticity developed for infinitesimal deformation.