Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

Application of strain rate potentials with multiple linear transformations to the description of polycrystal plasticity

This paper reviews a class of anisotropic plastic strain-rate potentials, based on linear transformations of the plastic strain-rate tensor. A new formulation is proposed, which includes former models as particular cases and allows for an arbitrary number of linear transformations, involving an increasing number of anisotropy parameters. The formulation is convex and fully three-dimensional, thus being suitable for computer implementation in finite element codes. The parameter identification procedure uses a micromechanical model to generate evenly distributed reference points in the full space of possible loading modes. Material parameters are determined for several anisotropic, fcc and bcc sheet metals, and the gain in accuracy of the new models is demonstrated. For the considered materials, increasing the number of linear transformations leads to a systematic improvement of the accuracy, up to a number of five linear transformations. The proposed model fits very closely the predictions of the micromechanical model in the whole space of plastic strain-rate directions. The r-values, which are not directly used in the identification procedure, served for the validation of the models and to demonstrate their improved accuracy.     

Induction for weak symplectic Banach manifolds

The symplectic induction procedure is extended to the case of weak symplectic Banach manifolds. Using this procedure, one constructs hierarchies of integrable Hamiltonian systems related to the Banach Lie–Poisson spaces of k$k$-diagonal trace class operators.     

Quantifying nonclassicality of one-mode Gaussian states of the radiation field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.     

A cellular dynamical mean field theory approach to Mottness

We investigate the properties of a strongly correlated electron system in the proximity of a Mott insulating phase within the Hubbard model, using a cluster generalization of the dynamical mean field theory. We find that Mottness is intimately connected with the existence in momentum space of a surface of zeros of the single particle Green’s function. The opening of a Mott-Hubbard gap at half filling and the opening of a pseudogap at finite doping are necessary elements for the existence of this surface. At the same time, the Fermi surface may change topology or even disappear. Within this framework, we provide a simple picture for the appearance of Fermi arcs. We identify the strong short-range correlations as the source of these phenomena and we identify the cumulant as the natural irreducible quantity capable of describing this short-range physics. We develop a new version of the cellular dynamical mean field theory based on cumulants that provides the tools for a unified treatment of general lattice Hamiltonians.     

Total Curvature and Spiralling Shortest Paths

This paper gives a partial confirmation of a conjecture of Agarwal, Har-Peled, Sharir, and Varadarajan that the total curvature of a shortest path on the boundary of a convex polyhedron in R ³ cannot be arbitrarily large. It is shown here that the conjecture holds for a class of polytopes for which the ratio of the radii of the circumscribed and inscribed ball is bounded. On the other hand, an example is constructed to show that the total curvature of a shortest path on the boundary of a convex polyhedron in R ³ can exceed 2. Another example shows that the spiralling number of a shortest path on the boundary of a convex polyhedron can be arbitrarily large.