Super-convergent second derivative recovery for lower-order strain gradient plasticity

• A super-convergent second derivative recovery technique is developed.
• Element based patches are defined and patch least square fitting is introduced.
• Both the first and second strain derivatives of a lower-order strain gradient plasticity model are evaluated effectively.
• Different size meshes with mixed quadratic C0 elements are constructed and tested.

An element patch based super-convergent second derivative recovery technique is developed in this paper for evaluating the first and second strain derivatives for a lower-order strain gradient plasticity model. The element based patches are defined and the patch least square fitting process is introduced. A classical shear band simulation is then conducted to test the new technique with various unstructured meshes with mixed quadratic quadrilateral and triangular C0 elements. The result shows that a direct recovery from the patch least square fitting process is more reliable than that from the nodal averaging process usually necessary for the super-convergent second derivative recovery methods. The proposed technique is proven to be effective for recovering both first and second order strain derivatives and has the potential for even higher order derivative recovery.