The Peierls--Nabarro FE model in two-phase microstructures -- a comparison with atomistics

This paper evaluates qualitatively as well as quantitatively the accuracy of a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for dislocations by a direct comparison with an equivalent molecular statics simulation. To this end, a two-dimensional microstructural specimen subjected to simple shear is considered, consisting of a central soft phase flanked by two hard-phase regions. A hexagonal atomic structure with equal lattice spacing is adopted, the interactions of which are described by the Lennard--Jones potential with phase specific depths of its energy well. During loading, edge dislocation dipoles centred in the soft phase are introduced, which progress towards the phase boundaries, where they pile up. Under a sufficiently high external shear load, the leading dislocation is eventually transmitted into the harder phase. The homogenized PN-FE model is calibrated to an atomistic model in terms of effective elasticity constants and glide plane properties as obtained from simple uniform deformations. To study the influence of different formulations of the glide plane potential, multiple approaches are employed, ranging from a simple sinusoidal function of the tangential disregistry to a complex model that couples the influence of the tangential and the normal disregistries. The obtained results show that, qualitatively, the dislocation structure, displacement, strain fields, and the dislocation evolution are captured adequately. The simplifications of the PN-FE model lead, however, to some discrepancies within the dislocation core. Such discrepancies play a dominant role in the dislocation transmission process, which thus cannot quantitatively be captured properly. Despite its simplicity, the PN-FE model proves to be an elegant tool for a qualitative study of edge dislocation behaviour in two-phase microstructures, although it may not be quantitatively predictive.Comment: 29 pages, 11 figures, 5 tables, abstract shortened to fulfill 1920 character limit, small changes after revie

Metric connections in projective differential geometry

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.Comment: 10 page

On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them

In the present article we study the principal bundles determined by the algebra of antiquaternions in the projective model. The projectivizations of the pseudoconformal models of fibrations determined by the subalgebra of complex numbers is considered as example

LOCALIZATION ANALYSIS OF DAMAGE FOR ONE-DIMENSIONAL PERIDYNAMIC MODEL

Peridynamics is a recently developed extension of continuum mechanics, which replaces the traditional concept of stress by force interactions between material points at a finite distance. The peridynamic continuum is thus intrinsically nonlocal. In this contribution, a bond-based peridynamic model with elastic-brittle interactions is considered and the critical strain is defined for each bond as a function of its length. Various forms of length functions are employed to achieve a variety of macroscopic responses. A detailed study of three different localization mechanisms is performed for a one-dimensional periodic unit cell. Furthermore, a convergence study of the adopted finite element discretization of the peridynamic model is provided and an effective event-driven numerical algorithm is described

Parental heights and maternal education as predictors of length/height of children at birth, age 3 and 19 years, independently on diet: the ELSPAC study

BACKGROUND/OBJECTIVES: Little is currently known about the relationship between the parental diet during pregnancy and the growth of the child from early childhood until early adulthood. This study was designed to examine whether the dietary patterns of the parents during a pregnancy and of the respective child at 3 years are associated with the length/height-for-age z-score of child at birth, 3 years of age and at 19 years of age. SUBJECTS/METHODS: Dietary patterns of pregnant women and their partners, and offspring at 3 years that were enroled in the 1990-1991 period in the Czech part of the European Longitudinal Study of Pregnancy and Childhood. Multivariable linear regression models were used to estimate the relationship between the dietary patterns of parents (835 child-mother-father trios) during pregnancy and the length/height-for-age z-score of their offspring at birth, 3 years and 19 years. RESULTS: The maternal health-conscious food pattern was found to predict lower child height at 3 years, but not at birth nor at 19 years of age. An increase in the health-conscious pattern score of the maternal diet was associated with significantly lower height-for-age z-score at 3 years; however, the observed effect lost its significance after the adjustment for diet of the child at 3 years. CONCLUSIONS: After full adjustment, the only significant predictors of the height-for-age z-score of the child at 3 years were the heights of both parents and maternal education. More research into the association of maternal diet in pregnancy and height of child is necessary.European Journal of Clinical Nutrition advance online publication, 8 February 2017; doi:10.1038/ejcn.2016.244

MOLECULAR STATICS SIMULATION OF NANOINDENTATION USING ADAPTIVE QUASICONTINUUM METHOD

In this work, molecular statics is used to model a nanoindentation test on a two-dimensional hexagonal lattice. To this end, the QuasiContinuum (QC) method with adaptive propagation of the fully resolved domain is used to reduce the computational cost required by the full atomistic model. Three different adaptive mesh refinement criteria are introduced and tested, based on: (i) the Zienkiewicz–Zhu criterion (used for the deformation gradient), (ii) local atoms’ site energy, and (iii) local lattice disregistry. Accuracy and efficiency of individual refinement schemes are compared against the full atomistic model and obtained results are discussed

On compact holomorphically pseudosymmetric K\"ahlerian manifolds

For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric K\"ahlerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric K\"ahlerian manifolds are discovered by W. Jelonek. In his examples, the structure functions change their signs on the manifold