This paper presents results of a numerical modelling of ductile fracture and failure of elements made of 5182H111 aluminium alloys subjected to dynamic traction. The analysis was performed using Johnson-Cook model based on ABAQUS software. The modelling difficulty related to prediction of ductile fracture mainly arises because there is a tremendous span of length scales from the structural problem to the micro-mechanics problem governing the material separation process. This study has been used the experimental results to calibrate a simple crack propagation criteria for shell elements of which one has often been used in practical analyses. The performance of the proposed model is in general good and it is believed that the presented results and experimental-numerical calibration procedure can be of use in practical finite-element simulations.

In order to investigate the role of TiO ₂ during plasma treatment, the degradation of the dye AO7 has been studied by gliding arc discharge in the presence of a TiO ₂ catalyst (CGAD). The results revealed that the adsorption of the dye on TiO ₂ is a physical adsorption in accordance with Langmuir isotherm, with a constant of adsorption K _L = 0.52 mg/L and a maximum adsorption capacity b = 18.1 mg/g. The temperature variation of the reaction medium made it possible to consider thermodynamic parameters. Indeed, the adsorption is exothermic (enthalpy: Δ H < 0), and spontaneous (free enthalpy: Δ G < 0). The negative entropy (Δ S < 0) confirms the affinity of the dye molecules for TiO ₂. 20 min of CGAD treatment in the presence of an optimal quantity of TiO ₂ (2 g/L enabled us to bleach the solution of AO7 (100 μM) completely. The discoloration rate with and without the addition of Ti...

The electronic and optical properties of M ₂S (M = Li, Na, K and Rb) compounds in the cubic antifluorite structure have been calculated, using a full relativistic version of the full-potential augmented plane-wave plus local orbitals method based on density functional theory, within both the local density approximation (LDA) and the generalized gradient approximation (GGA). Moreover, the Engel–Vosko GGA formalism (EV-GGA) is applied so as to optimize the corresponding potential for band structure calculations. The calculated equilibrium lattices and bulk moduli are in good agreement with the available data. Band structure, density of states, electron charge density and pressure coefficients of energy gaps are given. Results obtained for band structure using EV-GGA are larger than those with LDA and GGA. It is found that the spin–orbit coupling lifts the triple degeneracy at the Γ point and the double degeneracy at the X point. The analysis of the electron charge density...

Using the geometric engineering method of 4D quiver gauge theories and results on the classification of Kac–Moody (KM) algebras, we show by explicit examples that there exist three sectors of infrared CFT ₄s. Since the geometric engineering of these CFT ₄s involves type II strings on K3 fibred CY3 singularities, we conjecture the existence of three kinds of singular complex surfaces containing, in addition to the two standard classes, a third indefinite set. To illustrate this hypothesis, we give explicit examples of K3 surfaces with H ⁴ ₃ and E ₁₀ hyperbolic singularities. We also derive a hierarchy of indefinite complex algebraic geometries based on affine A _r and T _{( p, q, r)...}