Dynamic explicit solution for higher-order crystal plasticity theories

• New higher-order crystal plasticity algorithm is proposed.
• Explicit method is proposed in order to avoid inversion of stiffness matrices.
• Algorithm is simple and robust.
• Good correlation is obtained with analytical solutions and discrete dislocation solutions.
• Size effect in nanoindentation is qualitatively captured.

Dynamic terms are included in the balance equations that govern a higher-order crystal plasticity formulation. The resulting equations are integrated in time by the central-difference explicit method. The methodology avoids solution methods based on the inversion of the associated stiffness matrices. This is a great advantage of the proposed methodology, considering that these matrices tend to be highly ill-conditioned. As the solution becomes dependent on the time-step size used in the integration, a stability study is presented. Only a rate independent constitutive law is taken into account. As examples, a crystal layer and a composite material under simple shear and the wedge indentation of a single crystal are considered. Comparisons with an implicit quasi-static solution method show the robustness of the proposed methodology, but reveal an elevated computational cost related to it.