On an implementation of the strain gradient plasticity with linear finite elements and reduced integration

The size effects exhibited in the structural behaviors of micro-sized loading components cannot be described with classical plasticity theory alone. Thus, strain gradient plasticity together with appropriate experiments has been used to account for this size effect. In previous implementations of strain gradient plasticity into finite element code, low order displacement elements with reduced integration, despite their versatility for solving various structural problems, have been excluded because of their inability to yield the strain gradient inside the element. In this work, a new method of evaluating the plastic strain gradient with linear displacement elements via an isoparametric interpolation of the averaged-at-nodal plastic strain is proposed. Rate-independent yield conditions are satisfied accurately by the Taylor dislocation hardening model with Abaqus UHARD subroutine. To verify the suggested approach, the structural behaviors of micro-sized specimens subjected to bending, twisting, and nano-indentation tests were modeled and analyzed. The predicted size effects are generally in good agreement with previously published experimental results. Computational efforts are minimized and user versatilities are maximized by the proposed implementation.

► Linear finite elements with reduced integration for strain gradient plasticity are developed.
► The constitutive relation is obtained using dislocation hardening with a single length parameter.
► A numerical scheme is devised to avoid any non-local integration, extra interpolation, and rate-type laws.
► Typical micro-structural problems are solved; the solutions are in agreement with the experimental results.