The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique.
Strengthening reinforced concrete (RC) columns with external confining devices such as FRP wraps or steel tube is widely used in construction. By using external confining devices, both the strength and ductility of RC columns are significantly improved. However, numerical modeling to predict the capacity of strengthened RC columns is limited and often oversimplified. One of the biggest challenges in numerical modeling is to deal with unequal dilation between the concrete inner core (enclosed by both transverse steel and FRP wraps) and the concrete outer core (between the transverse steel and FRP wraps). Inaccurate modeling on the concrete dilatant behavior can lead to incorrect strength prediction. Sophisticated constitutive models which are able to model concrete dilation and robust modeling techniques are required. In this paper, three-dimensional non-linear finite element analysis (3D-NLFEA) of circular RC columns confined with conventional steel stirrups and FRP wraps is presented. In the FEA, the initial stiffness method with Process Modification (acceleration technique) is used to solve the equilibrium forces in the global solution. The constitutive model is based on the plasticity formulation proposed by the authors, which can capture the effective lateral modulus (EL) of the confining devices. This lateral modulus is obtained by observing the principal incremental stresses and strains at each element gauss point. It was found that, the lateral modulus is greatly affected by the boundary condition, dilatant behavior of the constitutive model and the Poisson's ratio of the external confining device. To validate the performance of the proposed model, several comparisons of the proposed model, using 3D-NLFEA, with experimental results is presented. The comparisons show that the predicted response using 3D-NLFEA and the experimental results of RC columns confined with FRP are in a good agreement.