A geometrically nonlinear analysis of functionally graded shells is presented. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. A tensor-based finite element formulation with curvilinear coordinates and first-order shear deformation theory are used to develop the functionally graded shell finite element. The first-order shell theory consists of seven parameters and exact nonlinear deformations and under the framework of the Lagrangian description. High-order Lagrangian interpolation functions are used to approximate the field variables to avoid membrane, shear, and thickness locking. Numerical results obtained using the present shell element for typical benchmark problem geometries with functionally graded material compositions are presented.
We present a variational void coalescence model that includes all the essential ingredients of failure in ductile porous metals. The model is an extension of the variational void growth model by Weinberg et al. (Comput Mech 37:142-152, 2006). The extended model contains all the deformation phases in ductile porous materials, i.e. elastic deformation, plastic deformation including deviatoric and volumetric (void growth) plasticity followed by damage initiation and evolution due to void coalescence. Parametric studies have been performed to assess the model's dependence on the different input parameters. The model is then validated against uniaxial loading experiments for different materials. We finally show the model's ability to predict the damage mechanisms and fracture surface profile of a notched round bar under tension as observed in experiments
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