Finite element formulations of strain gradient theory for microstructures and the C0-1 patch test

Abstract

Based on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C0-1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C0-1 patch test is proposed. The displacement functions of several plane triangular elements, which satisfy the C0 continuity and weak C1 continuity conditions are evaluated by the C0-1 patch test. The difference between the proposed C0-1 patch test and the C0 constant stress and C1 constant curvature patch tests is elucidated. An 18-DOF plane strain gradient triangular element (RCT9+RT9), which passes the C0-1 patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performance of the proposed element by carrying out the C0-1 patch test and eigenvalue test. The proposed element is found to be without spurious zero energy modes, and it possesses higher accuracy compared with other strain gradient elements. © 2004 John Wiley and Sons, Ltd.