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As inelastic structures are ubiquitous in many engineering fields, a centraltask in computational mechanics is to develop accurate, robust and efficienttools for their analysis. Motivated by the poor performances exhibited bystandard displacement-based finite element formulations, attention is herefocused on the use of mixed methods as approximation technique, within thesmall strain framework, for the mechanical problem of inelastic bidimensionalstructures. Despite a great flexibility characterizes mixed elementformulations, several theoretical and numerical aspects have to be carefullytaken into account in the design of a high-performance element. The presentwork aims at providing the basis for methodological analysis and comparison insuch aspects, within the unified mathematical setting supplied by generalizedstandard material model and with special interest towards elastoplastic media.A critical review of the state-of-the-art computational methods is delivered inregard to variational formulations, selection of interpolation spaces,numerical solution strategies and numerical stability. Though those argumentsare interrelated, a topic-oriented presentation is resorted to, for the veryrich available literature to be properly examined. Finally, the performances ofseveral significant mixed finite element formulations are investigated innumerical simulations.

An overview of mixed finite elements for the analysis of inelastic bidimensional structures