SUMMARYWe propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piecewise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.

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The insight gained from the analysis conducted in Part I ͑see the preceding article͒ is used in the development of a general transport model for water and protons in perfluorosulfonic acid membranes based on the binary friction model. As a tool for investigating the unknown parameters in the general membrane transport model, a simplified conductivity model is derived to represent conditions found in alternating current ͑ac͒ impedance conductivity measurements. This binary friction conductivity model ͑BFCM͒ is applied to 1100 equivalent weight ͑EW͒ Nafion, and compared to other established membrane models. It is shown to provide a more consistent fit to the data over the entire range of water contents and at different temperatures. The subset of transport coefficients in the BFCM is the same as in the general binary friction membrane model ͑BFM2͒, and thus with additional data on water transport, the BFM2 model and all its required parameters can be fully specified. The paper discusses possible experimental investigations and fundamental simulations to determine the model parameters required to apply the general BFM2 to predict coupled proton and water transport in PEM fuel cells.

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