Finite elements for materials with strain gradient effects

A finite element implementation is reported of the Fleck-Hutchinson phenome nological strain gradient theory. This theory fits within the Toupin-Mindli n framework and deals with first-order strain gradients and the associated work-conjugate higher-order stresses. In conventional displacement-based ap proaches, the interpolation of displacement requires C-1-continuity in orde r to ensure convergence of the finite element procedure for higher-order th eories. Mixed-type finite elements are developed herein for the Fleck-Hutch inson theory; these elements use standard C-0-continuous shape functions an d can achieve the same convergence as C-1 elements. These C-0 elements use displacements and displacement gradients as nodal degrees of freedom. Kinem atic constraints between displacement gradients are enforced via the Lagran ge multiplier method. The elements developed all pass a patch test. The res ulting finite element scheme is used to solve some representative linear el astic boundary value problems and the comparative accuracy of various types of element is evaluated. Copyright (C) 1999 John Wiley & Sons, Ltd.