Performance of Enhanced Low-Order Elements for Plastic Continua

Abstract

Because of reasons of economy and easy mesh generation and post-processing, a huge effort has been invested in developing high-performance finite elements with interpolation functions of low order. Unfortunately, there are a number of cases where low-order, displacement-based elements perform poorly. A well-known example is the finite element modelling of incompressible material behaviour, where elements with low-order interpolations of displacements tend to ‘lock’ completely, thus yielding an overstiff solution (Nagtegaal et al. 1974). Many solutions have been put forward since, including special arrangements of elements (Nagtegaal et al. 1974), reduced or selective integration (Zienkiewicz and Taylor 1989), which is closely related to the B approach (Hughes 1980), the use of higher-order displacement models (Sloan and Randolph 1982, de Borst and Vermeer 1984), mixed approaches with an independent interpolation of displacements and pressures (Sussman and Bathe 1987, Van den Bogert et al. 1991), and most recently, the Enhanced Assumed Strain concept (Simo and Rifai 1990).