Constitutive equation for concrete using strain-space plasticity model

Plasticity theory has been used to model the concrete constitutive relationship for about two decades. With the modifications and refinement based on experimental data, achievement has been made in these plasticity models for concrete. Almost all the existing models are developed in stress space. With a lot of experimental data and more understanding about stress states of concrete, the stress-space model shows many advantages. Because of this and also due to conventional engineering practice, the stress-space plasticity approach has been in the dominant position. However, the conventional stress-space plasticity method has one inherent drawback in which it cannot deal with the softening part of materials. To model effectively the descending part of the strain softening materials such as concrete on the basis of plasticity theory, strain space concept must be adopted. Some researcher used it as a supplemental means to the stress-space model for the post-peak stage. Inspired by this basic idea, attempt was made in this study, to set up a strain surface of concrete at critical stress, then an initial yield surface and subsequent yield surfaces were constructed in strain space according to the existing experimental results. A non-proportional hardening rule and a non-associated flow rule were adopted. Finally, a strain-space plasticity theory was presented in modeling the nonlinear multiaxial strain-hardening-softening behavior of concrete. It has been found that the model predictions of the ascending branch of stress-strain behavior are in good agreement with the experimental results involving a wide range of stress states and different types of concrete. The most important inelastic behavior of concrete, such as brittle failure in tension; ductile behavior in compression; hydrostatic sensitivities; and volumetric dilation under compressive loadings are included in these comparisons. It has also been found that the model can predict well the descending branch of strain-softening behavior of concrete

Generalized-Equiangular Geometry CT: Concept and Shift-Invariant FBP Algorithms

With advanced X-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs. GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered BackProjection (FBP) algorithms with a variety of weighting strategies has been conducted. The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. We further stretch the weighted FBP-type algorithms to GEGCT with dynamic NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.Comment: 31 pages, 13 figure

Electromechanical Impedance Response of a Cracked Timoshenko Beam

Typically, the Electromechanical Impedance (EMI) technique does not use an analytical model for basic damage identification. However, an accurate model is necessary for getting more information about any damage. In this paper, an EMI model is presented for predicting the electromechanical impedance of a cracked beam structure quantitatively. A coupled system of a cracked Timoshenko beam with a pair of PZT patches bonded on the top and bottom surfaces has been considered, where the bonding layers are assumed as a Kelvin-Voigt material. The shear lag model is introduced to describe the load transfer between the PZT patches and the beam structure. The beam crack is simulated as a massless torsional spring; the dynamic equations of the coupled system are derived, which include the crack information and the inertial forces of both PZT patches and adhesive layers. According to the boundary conditions and continuity conditions, the analytical expression of the admittance of PZT patch is obtained. In the case study, the influences of crack and the inertial forces of PZT patches are analyzed. The results show that: (1) the inertial forces affects significantly in high frequency band; and (2) the use of appropriate frequency range can improve the accuracy of damage identification