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This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

This article describes a mathematical model and numerical simulation of gas-solid flow in a bubbling fluidized bed (BFB), where the the two-fluid Eulerian-Eulerian model was used and the solid phase stress tensor was modeled considering both the friction between particles and the kinetic theory of granular flows. The code MFIX (Multiphase Flow with Interphase eXchanges) developed by NETL (National Energy Technology Laboratory, U. S. Department of Energy) was used for numerical simulations, and the results were obtained through computing the granular temperature by using a partial differential equation (PDE) or an algebraic expression. More realistic results were obtained when a PDE with boundary conditions of the partial slip was used. However, for computing the granular temperature in the case of fine grids, it is recommended to use the algebraic equation because it will save computational effort in simulations. Variation in the diameter of the particles (Group B and Group A=B) was also analyzed, and, consequently, it was observed that in future analysis a term for capturing the influence of cohesive forces should be added for particles of Group A=B. This study has revealed that a smooth transition between the viscous regime and the plastic regime is necessary for simulating a hydrodynamic bubbling fluidized bed.