Extended P-I diagram method

Abstract

The pressure-impulse (P-I) diagram method is used in practice (for civilian and military applications) for predicting the level of damage sustained by structures when subjected to blast loads and for assessing the imposed loading regime. Each P-I curve is associated with a certain structural configuration as well as a specific form of blast load and level of damage sustained. When assessing the effect of different parameters (associated with the form of the imposed load and the design of the structure considered) on structural performance, a series of new P-I curves need to be derived. This paper presents an extended P-I diagram method, which is based on derivation of complementary diagrams that can define the effect of two parameters (e.g., the level of axial loading imposed onto a column and the level of damage sustained) on the quasi-static and impulsive asymptotes, thus governing the positions of P-I curves in the diagram plane. The extended P-I diagram method is presented in dimensional and normalised forms. The dimensional form simplifies the derivation of new P-I curves, while the normalised form simplifies the procedure adopted for assessing the behaviour of a certain structure when subjected to a new set of loads.The application of the proposed method is demonstrated in both forms using a typical reinforced concrete (RC) column subjected to a blast load. The column is modelled using finite element analysis capable of accounting for the nonlinear behaviour of concrete and steel. A novel method is proposed for material modelling of concrete. The new material model is validated at both material and structural levels against relevant experimental data. P-I diagrams are initially derived for the axially unloaded column, while complementary diagrams are derived for the column loaded by different axial forces. The framework of the extended P-I diagram method employed for the derivation of new P-I curves and the assessment of

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

“…The proposed model seems to be a good compromise. It includes the effect of triaxiality of the stress state in contrast, e.g., to the model proposed in Reference [ 32 ] (because modules are related to octahedral shear strain and are prone to concrete crushing, as well). The model needs an appropriate number of load increments, since it is formulated in terms of hypoelasticity with unloading conditions.…”

“…Consequently, compression states with high values of hydrostatic stress, in which much more complex material models are needed, are quite rare in real structures. It is worth mentioning that even simpler material models are sometimes applied to some complex, in terms of computational effort, problems [ 32 ]. The function – is presented in Figure 2 , whereas the comparison of analytical and experimental test results [ 33 ] is presented in Figure 3 .…”

“…The UMAT procedure is called in every Gauss point and has to update: the stress vector, the internal variables and the material stiffness matrix. User procedures are common in scientific research [ 32 , 51 , 53 ], since they enable the user to focus on a specific phenomenon and the rest of the numerical model can be covered with algorithms available in the FEM code.…”

Blast energy absorption in topological interlocking elastic columns

“…It is necessary to note that the axial displacement loading method results in an insignificant loss of axial prestress due to the changes in the column length introduced by its lateral deformation and therefore does not represent accurately the supporting conditions of a column in a shear frame. However, this method is practiced widely(e.g., [26,27] as it stabilises the numerical algorithms applied in problem solution.…”

“…The blast load time history was modelled using a triangular shape with zero rise time. Note that similar simplifications were adopted in many previous research works, e.g., [3,30], [26,27].…”