Analysis of sheet metal forming operations by a stress resultant constitutive law

Sheet metal forming is simulated by finite element methods using a stress resultant constitutive law in this paper. A Lagrangian description of axisymmetric and plane-strain shell deformation is first reviewed. Then a stress resultant constitutive law in rate form is presented, where the effect of thickness reduction due to large plastic deformation is considered. A finite element formulation in terms of stress resultants and their work-conjugate generalized strain rates is derived based on the virtual work principle. A hemispherical punch stretching operation and a plane-strain draw operation are simulated by a finite element program based on the finite element formulation. The results of these finite element simulations are in good-agreement with those using the through-the-thickness integration method. The results of the hemispherical punch stretching simulation suggest that the coupling term of moments and membrane forces of the modified Ilyushin yield function should be eliminated to avoid numerical instability under stretching-dominated conditions for this rate-independent plasticity formulation. Further, the results suggest that the hardening rule in a power-law form based on the small-strain approach must be modified to take account for finite deformation effects of combined stretching and bending. Under the plane-strain draw operation, the sheet experiences a large amount of bending before the final stretching. The simulation based on the stress resultant constitutive law can produce this essential aspect of deformation pattern as that of the through-the-thickness integration method, whereas a simulation based on a membrane theory cannot. In conclusion, the results of these simulations indicate that a finite element program based on the stress resultant constitutive law can simulate sheet-forming processes with much shorter computational time than that based on the through-the-thickness integration method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50100/1/1620370502_ftp.pd

Circular dichroism and bilayer splitting in the normal state of underdoped (Pb,Bi)2_2Sr2_2(Cax_xY1−x_{1-x})Cu2_2O8+δ_{8+\delta} and overdoped (Pb,Bi)2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

We report an ARPES investigation of the circular dichroism in the first Brillouin zone (BZ) of under- and overdoped Pb-Bi2212 samples. We show that the dichroism has opposite signs for bonding and antibonding components of the bilayer-split CuO-band and is antisymmetric with respect to reflections in both mirror planes parallel to the c-axis. Using this property of the energy and momentum intensity distributions we prove the existence of the bilayer splitting in the normal state of the underdoped compound and compare its value with the splitting in overdoped sample. In agreement with previous studies the magnitude of the interlayer coupling does not depend significantly on doping. We also discuss possible origins of the observed dichroism.Comment: 4 RevTex pages, 4 EPS figure

Direct k-space mapping of the electronic structure in an oxide-oxide interface

The interface between LaAlO3 and SrTiO3 hosts a two-dimensional electron system of itinerant carriers, although both oxides are band insulators. Interface ferromagnetism coexisting with superconductivity has been found and attributed to local moments. Experimentally, it has been established that Ti 3d electrons are confined to the interface. Using soft x-ray angle-resolved resonant photoelectron spectroscopy we have directly mapped the interface states in k-space. Our data demonstrate a charge dichotomy. A mobile fraction contributes to Fermi surface sheets, whereas a localized portion at higher binding energies is tentatively attributed to electrons trapped by O-vacancies in the SrTiO3. While photovoltage effects in the polar LaAlO3 layers cannot be excluded, the apparent absence of surface-related Fermi surface sheets could also be fully reconciled in a recently proposed electronic reconstruction picture where the built-in potential in the LaAlO3 is compensated by surface O-vacancies serving also as charge reservoir.Comment: 8 pages, 6 figures, incl. Supplemental Informatio

Pressure-induced metallization and structural phase transition of the Mott-Hubbard insulator TiOBr

We investigated the pressure-dependent optical response of the low-dimensional Mott-Hubbard insulator TiOBr by transmittance and reflectance measurements in the infrared and visible frequency range. A suppression of the transmittance above a critical pressure and a concomitant increase of the reflectance are observed, suggesting a pressure-induced metallization of TiOBr. The metallic phase of TiOBr at high pressure is confirmed by the presence of additional excitations extending down to the far-infrared range. The pressure-induced metallization coincides with a structural phase transition, according to the results of x-ray powder diffraction experiments under pressure.Comment: 4 pages, 3 figure

The use of measured genotype information in the analysis of quantitative phenotypes in man.

We have begun a measured genotype approach to the genetic analysis of lipid and lipoprotein variability. This approach enables one to simultaneously estimate the frequencies and effects of alleles at specific loci along with the residual polygenetic variance component. In this study we consider the contribution of three common alleles at the locus coding for apolipoprotein E to interindividual variation of total cholesterol, betalipoprotein, and triglyceride levels. A sample of 102 nuclear families consisting of 434 individuals was studied. The frequencies of the ε2, ε3, and ε4 alleles in this sample are 0·137,0·740, and 0·123, respectively. In separate analyses of cholesterol and betalipoprotein levels, a complete model that includes the effects of the six apo E genotypes, unmeasured polygenes, and individual specific environmental effects fits these data significantly better than a reduced model that does not include the effects of the apo E polymorphism or a reduced model that does not include the effects of polygenes. On the average the ε2 allele lowers total cholesterol and betalipoprotein levels by 0·425 mmol/l and 0·811 units, respectively. The ε4 allele is associated with an average increase of these phenotypes by 0·255 mmol/l and 0·628 units, respectively. Simultaneous estimates of the interindividual variability of total cholesterol levels attributable to the apo E polymorphism and to residual polygenic effects are 8% and 56%, respectively. For betalipoprotein levels, we simultaneously estimate these values to be 7% and 42%, respectively. A reduced model including the effects of polygenes but not the effects of the apo E polymorphism fitted the triglyceride data as well as the complete model. The estimate of the fraction of interindividual variability associated with polygenetic effects was 26.5%. We review our present understanding of the genetic architecture underlying variability of cholesterol levels in the population at large and infer that the majority of the genetic variability may be accounted for by polymorphic gene loci with moderate effects on cholesterol levels.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65212/1/j.1469-1809.1987.tb00874.x.pd

4-(Methyl­sulfon­yl)piperazin-1-ium chloride

In the title mol­ecular salt, C5H13N2O2S+·Cl−, the complete cation is generated by crystallographic mirror symmetry, with both N atoms, the S atom and one C atom lying on the reflecting plane. The chloride ion also lies on the mirror plane. The piperazinium ring adopts a chair conformation and the N—S bond adopts an equatorial orientation. In the crystal structure, the component ions are linked into a three-dimensional framework by inter­molecular N—H⋯Cl and C—H⋯Cl hydrogen bonds

Constitutive laws for thin plates of power-law materials

With the Kirchhoff assumption, a stress resultant constitutive law as a function of the kinematic variables for thin plates of power-law hardening materials is derived under proportional straining conditions. Also, in analogy to the Jz deformation plasticity and incremental plasticity theory, a flow rule, based on the constitutive law, to describe the elastic plastic behavior of the plate is proposed. The constitutive behavior of the plates subjected to uniaxial combined membrane force and bending moment is examined in detail and the results are compared with those for the corresponding clastic plastic materials using the through-the-thickness integration method. The yield surfaces for power-law materials are constructed and the formation of vertiees on the yield surfaces for perfectly plastic materials under such a loading condition is clearly demonstrated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29666/1/0000755.pd

A new method of extraction of amoxicillin using mixed reverse micelles

A completely new method of extraction of amoxicillin using solubilisation by mixed reverse micelles was proposed and the optimal conditions for the process were found. Mixed AOT-TWEEN 85 reverse micelles were used for the first time as a new approach for extraction of amoxicillin. The effects of different process variables such as AOT-TWEEN 85 molar fractions, total surfactant concentration, pH of aqueous feed solution and potassium chloride concentration during forward extraction; stripping aqueous phase pH, potassium chloride (KCl) concentration and extraction time during backward extraction were investigated and the optimal conditions were found for all mentioned parameters. With the aid of response surface methodology, the optimum conditions for forward extraction are identified as (i) 5.5:1 molar ratio of AOT/TWEEN 85, (ii) total surfactant concentration 102.57. g/L, (ii) pH 1.90, and (vi) KCl concentration 8.54. g/L. The percentage of amoxicillin solubilised in isooctane was 95.54% under these optimal conditions. On the other hand, the optimum conditions for backward extraction are identified as (i) stripping aqueous phase pH 6.58, (ii) KCl concentration 11.02. g/L, and (iii) extraction time 15. min. Under these optimal conditions, the percentage of amoxicillin recovered was 90.79%. AOT/TWEEN 85 mixed surfactant system shows a significant advantage of saving the amount of surfactant for forward extraction. The addition of non-ionic surfactant helps to preserve natural function/activity of antibiotics as compared with a pure AOT surfactant used. The optimum conditions were also found for a backward recovery of amoxicillin

Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials

A stress resultant constitutive law in rate form is constructed for power-law hardening materials. The change of plate thickness is considered in the constitutive law. The elastic-plastic behavior of a plate element based on the stress resultant constitutive law under uniaxial combined tension and bending is determined under a limited number of nonproportional and unloading paths. The results based on the stress resultant constitutive law and the through-the-thickness integration method are compared within the context of both the small-strain and finite deformation approaches. The results indicate that the selection of the normalized equivalent stress resultant and the corresponding work-conjugate normalized equivalent generalized strain is appropriate for describing the hardening behavior in the stress resultant space. However, the hardening rule in a power law form must be modified for low hardening materials at large plastic deformation when finite deformation effects are considered.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31919/1/0000872.pd

Coherent amplitudon generation in K_0.3MoO_3 through ultrafast inter-band quasi particle decay

The charge density wave system K_0.3MoO_3 has been studied using variable energy pump-probe spectroscopy, ellipsometry, and inelastic light scattering. The observed transient reflectivity response exhibits quite a complex behavior, containing contributions due to quasi particle excitations, coherent amplitudons and phonons, and heating effects. The generation of coherent amplitudons is discussed in terms of relaxation of photo-excited quasi particles, and is found to be resonant with the interband plasmon frequency. Two additional coherent excitations observed in the transients are assigned to zone-folding modes of the charge density wave state