A Cosserat theory for elastoviscoplastic single crystals at finite deformation

Abstract

In this work, displacement and lattice rotation are regarded as independent degrees of freedom. They are connected only on the constitutive level and by the balance equations. The description of plastic deformation is based on the slip theory. Elastic lattice curvature and torsion are associated with couple-stresses. The continuum theory of dislocations has been revisited to derive the kinematics of plastic lattice torsion-curvature. Explicit constitutive equations and hardening rules are proposed to close the theory in the case of elastoviscoplasticity. The thermodynamical formulation of the model involves internal variables which are similar to the densities of statistically stored dislocations and the densities of geometrically necessary dislocations. Accordingly, the proposed Cosserat theory can be regarded, on the one hand, as the classical crystal plasticity theory complemented by lattice curvature and torsion variables and, on the other hand, as the continuum theory of dislocations closed by the missing hardening variables and constitutive equations within the appropriate micropolar framework. A generalization of Mandel's elastoviscoplastic decomposition of strain is used especially for the torsion-curvature measure at finite deformation.