Visco-elastic regularization and strain softening

In this paper it is intended to verify the capacity of regularization of the numerical solution of an elasto-plastic problem with linear strain softening. The finite element method with a displacement approach is used. Drucker-Prager yield criteria is considered. The radial return method is used for the integration of the elasto-plastic constitutive relations. An elastovisco- plastic scheme is used to regularize the numerical solution. Two constitutive laws have been developed and implemented in a FE-program, the first represent the radial return method applied to Drucker-Prager yield criteria and the second is a time integration procedure for the Maxwell visco-elastic model. Attention is paid to finite deformations. An associative plastic flow is considered in the Drucker-Prager elasto-plastic model. The algorithms are tested in two problems with softening. Figures showing the capability of the algorithms to regularize the solution are presented

Preliminary Results on the Empirical Applicability of the Tsallis Distribution in Elastic Hadron Scattering

We show that the proton-proton elastic differential cross section data at dip position and beyond can be quite well described by a parametrization based on the Tsallis distribution, with only five free fit parameters. Extrapolation of the results obtained at 7 TeV to large momentum transfer, suggests that hadrons may not behave as a black-disk at the asymptotic energy region.Comment: 3 pages, 1 figure, version matching proceedings style, XII Hadron Physics, 2012, AIP Proc. Con

Janus Scorpionates: Supramolecular Tectons for the Directed Assembly of Hard−Soft Alkali Metallopolymer Chains

A new scorpionate ligand [HB(mtda)3-] containing mercaptothiadiazolyl (mtda) heterocyclic rings with both hard nitrogen donors and soft sulfur donors has been prepared. This new ligand, the Janus scorpionate, is a hybrid of a tris(pyrazolyl)borate and a tris(mercaptoimidazolyl)borate. The differential hard/soft character of the dissimilar donor groups in this bridging ligand was exploited for the controlled solid-state organization of homometallic and heterometallic alkali metal coordination polymers. Remarkably, in the case of sodium, coordination polymers with both acentric (with NaS3N3H kernels) and centric (with alternating NaN6 and NaS6H2 kernels) chains are found in the same crystal (where the centricity is defined by the relative orientations of the B−H bonds of the ligands along the lattice). For the homometallic potassium congener, the larger cation size, compared to sodium, induced significant distortions and favored a polar arrangement of ligands in the resulting coordination polymer chain. An examination of the solid-state structure of the mixed alkali metal salt system revealed that synergistic binding of smaller sodium cations to the nitrogen portion and of the larger potassium cations to the sulfur portion of the ligand minimizes the ligand distortions relative to the homometallic coordination polymer counterparts, a design feature of the ligand that likely assists in thermodynamically driving the self-assembly of the heterometallic chains. The effect of alkali metal complexation on the solution properties of the ligand was studied by comparing NMR chemical shifts, B−H stretching frequencies, and electrochemical properties with those of the noncoordinating tetrabutylammonium salt of the scorpionate. The similarity of these data regardless of cation indicates that the salts are likely dissociated in solution rather than maintaining their solid-state polymeric structures. This data is augmented by the ESI(±) mass spectral data for a series of mixed alkali metal tris(mercaptothiadiazolyl)borates that also indicate that dissociation occurs in solution

Toward Charge-neutral ‘soft scorpionates’: Coordination Chemistry and Lewis Acid Promoted Isomerization of tris(1-organo-imidazol-2-ylthio)methanes

Two tris(1-organo-imidazol-2-ylthio)methanes, HC(S-timR)3 (R = organo = methyl, tert-butyl), have been prepared by a triphasic reaction between chloroform, the appropriate heterocycle, and saturated aqueous solutions of Na2CO3, in the presence of a phase transfer agent, (NBu4)(Br). These ligands have been characterized both spectroscopically and by single crystal X-ray diffraction. The reaction chemistry of these potentially N,N,N-tripodal ligands with AgBF4 was also explored where simple 1:1 coordination complexes could be isolated from reactions performed in THF solution at room temperature. The derivative {Ag[HC(S-timMe)3]}(BF4) was structurally characterized which showed that the ligand binds in a μ–κ2N,κ1N-mode to give a coordination polymer with an interesting layered supramolecular structure. Surprisingly, heating CH3CN solutions of the silver complexes at reflux resulted in decomposition of the complex and concomitant isomerization of the ligands to give metal-free tris(3-organo-1-imidazole-2-thione)methane, HC(N-imtR)3; the heretofore elusive charge-neutral analogues of the well-studied ‘soft scorpionate’ TmR− anions. The solution isomerization of HC(S-timR)3 to HC(N-imtR)3 was found to be general, occurring in a variety of solvents with any of a host of different Lewis acids [para-toluenesulfonic acid, KPF6, and M(CO)5Br (M = Mn, Re)] but did not occur by heating in the absence of Lewis acid. The compound HC(N-imtMe)3 exhibited unusually low solubility in common organic solvents. Single crystal X-ray diffraction of HC(N-imtMe)3 revealed a remarkable honeycomb supramolecular structure with ca. 5 Å channels filled with solvent. The robust nature of this solid is a result of strong dipolar stacking interactions of molecules into polymer chains bolstered by concerted π–π and CH–π interactions involving the heterocycles, holding the chains together in the remaining two dimensions