A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.     

High-pressure torsion applied to nickel single crystals

Nickel single crystals with different crystallographic orientations were deformed by high-pressure torsion. Special attention is devoted to examining the evolution of the micro-texture and microstructure. The initial crystal orientation was found to have a significant effect on the mechanical hardening and evolution of micro-texture at low and medium equivalent strains, whereas at very high strains no effect of the initial orientation was observed and the behaviour was very similar to a polycrystal. The evolution of micro-texture is in good qualitative agreement with the full constrained Taylor model. At very high equivalent strains the initial crystal orientation has no influence on micro-texture. At such strains, the hardening, the refinement of the structure and the texture reaches a saturation. The final micro-texture is explained by the change from one preferred crystallographic orientation to another.     

The Elastic–Plastic Torsion Problem: A Posteriori Error Estimates for Approximate Solutions

We consider the variational inequality that describes the torsion problem for a long elasto-plastic bar. Using duality methods of the variational calculus, we derive a posteriori estimates of functional type that provide computable and guaranteed upper bounds of the energy norm of the difference between the exact solution and any function from the corresponding energy space that satisfies the Dirichlet boundary condition.     

Euler Characteristics on virtually free products

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These formulas are obtained from a general result which applies to the rank gradient and the first L²?Betti number of a finitely generated group.     

The Ziegler Spectrum of a Locally Coherent Grothendieck Category

The general theory of locally coherent Grothendieck categoriesis presented. To each locally coherent Grothendieck categoryC a topological space, the Ziegler spectrum of C, is associated.It is proved that the open subsets of the Ziegler spectrum ofC are in bijective correspondence with the Serre subcategoriesof coh C the subcategory of coherent objects of C. This is aNullstellensatz for locally coherent Grothendieck categories.If R is a ring, there is a canonical locally coherent Grothendieckcategory RC (respectively, CR) used for the study of left (respectively,right) R-modules. This category contains the category of R-modulesand its Ziegler spectrum is quasi-compact, a property used toconstruct large (not finitely generated) indecomposable modulesover an artin algebra. Two kinds of examples of locally coherentGrothendieck categories are given: the abstract category theoreticexamples arising from torsion and localization and the examplesthat arise from particular modules over the ring R. The dualitybetween coh-(RC) and coh-CR is shown to give an isomorphismbetween the topologies of the left and right Ziegler spectraof a ring R. The Nullstellensatz is used to give a proof ofthe result of Crawley-Boevey that every character : K₀(coh-C) Z is uniquely expressible as a Z-linear combination of irreduciblecharacters. 1991 Mathematics Subject Classification: 16D90,18E15.     

Thermodynamic calculations for molecules with asymmetric internal rotors. II. Application to the 1,2-dihaloethanes

The thermodynamic properties of three halocarbon molecules relevant in atmospheric and public health applications are presented from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all the vibrational modes to a large-amplitude torsion for 1,2-difluoroethane, 1,2-dichloroethane, and 1,2-dibromoethane, each of which possesses a heavy asymmetric rotor. Optimized ab initio energies and Hessians were calculated at the CCSD(T) and MP2 levels of theory, respectively. In addition, to investigate the contribution of electronically excited states to thermodynamic properties, several excited singlet and triplet states for each of the halocarbons were computed at the CASSCF/MRCI level. Using the resulting potentials and projected frequencies, the couplings of all the vibrational modes to the large-amplitude torsion are calculated using the new STAR-P 2.4.0 software platform that automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Utilizing the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties for each of the halocarbons, with temperatures ranging from 298.15 to 1000 K. We propose that the free energies, entropies, and heat capacities obtained from our methods be used to supplement theoretical and experimental values found in current thermodynamic tables.     

Force field parameters for rotation around chi torsion axis in nucleic acids

To raise the accuracy of the force field for nucleic acids, several parameters were elaborated, focusing on the rotation around chi torsion axis. The reliability of molecular dynamics (MD) simulation was significantly increased by improving the torsion parameters at C8--N9--C1'--X (X = H1', C2', O4') in A, G and those at C6--N1--C1'--X in C, T, and U. In this work, we constructed small models representing the chemical structure of A, G, C, T, and U, and estimated energy profile for chi-axis rotation by executing numerous quantum mechanical (QM) calculations. The parameters were derived by discrete Fourier transformation of the calculated QM data. A comparison in energy profile between molecular mechanical (MM) calculation and QM one shows that our presently derived parameters well reproduce the energy surface of QM calculation for all the above torsion terms. Furthermore, our parameters show a good performance in MD simulations of some nucleic acids. Hence, the present refinement of parameters will enable us to perform more accurate simulations for various types of nucleic acids.