Finite elements for materials with strain gradient effects

✍ Scribed by John Y. Shu; Wayne E. King; Norman A. Fleck

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 188 KB
• Volume: 44
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990130)44:3<373::aid-nme508>3.0.co;2-7

✦ Synopsis

A finite element implementation is reported of the Fleck-Hutchinson phenomenological strain gradient theory. This theory fits within the Toupin-Mindlin framework and deals with first-order strain gradients and the associated work-conjugate higher-order stresses. In conventional displacement-based approaches, the interpolation of displacement requires C-continuity in order to ensure convergence of the finite element procedure for higher-order theories. Mixed-type finite elements are developed herein for the Fleck-Hutchinson theory; these elements use standard C-continuous shape functions and can achieve the same convergence as C elements. These C elements use displacements and displacement gradients as nodal degrees of freedom. Kinematic constraints between displacement gradients are enforced via the Lagrange multiplier method. The elements developed all pass a patch test. The resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated.