An overview of mixed finite elements for the analysis of inelastic bidimensional structures
For computational mechanics researchers, this paper offers a methodological review and comparison of mixed finite elements for inelastic structures, but it is incremental as it surveys existing methods without introducing new techniques.
This paper reviews mixed finite element methods for analyzing inelastic bidimensional structures, focusing on elastoplastic media. It provides a critical analysis of variational formulations, interpolation spaces, solution strategies, and stability, and compares several mixed formulations through numerical simulations.
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard displacement-based finite element formulations, attention is here focused on the use of mixed methods as approximation technique, within the small strain framework, for the mechanical problem of inelastic bidimensional structures. Despite a great flexibility characterizes mixed element formulations, several theoretical and numerical aspects have to be carefully taken into account in the design of a high-performance element. The present work aims at providing the basis for methodological analysis and comparison in such aspects, within the unified mathematical setting supplied by generalized standard material model and with special interest towards elastoplastic media. A critical review of the state-of-the-art computational methods is delivered in regard to variational formulations, selection of interpolation spaces, numerical solution strategies and numerical stability. Though those arguments are interrelated, a topic-oriented presentation is resorted to, for the very rich available literature to be properly examined. Finally, the performances of several significant mixed finite element formulations are investigated in numerical simulations.