Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson's ratio(PR)are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials' auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.     

Probabilistic approaches to compute uncertainty intervals and sensitivity factors of ultrasonic simulations of a weld inspection

For comprehension purpose, numerical computations are more and more used to simulate the propagation phenomena observed during experimental inspections. However, the good agreement between experimental and simulated data necessitates the use of accurate input data and thus a good characterization of the inspected material. Generally the input data are provided by experimental measurements and are consequently tainted with uncertainties. Thus, it becomes necessary to evaluate the impact of these uncertainties on the outputs of the numerical model. The aim of this study is to perform a probabilistic analysis of an ultrasonic inspection of an austenitic weld containing a manufactured defect based on advanced techniques such as polynomial chaos expansions and computation of sensitivity factors (Sobol, DGSM). The simulation of this configuration with the finite element code ATHENA2D was performed 6000 times with variations of the input parameters (the columnar grain orientation and the elastic constants of the material). The 6000 sets of input parameters were obtained from adapted statistical laws. The output parameters (the amplitude and the position of the defect echo) distributions were then analyzed and the 95% confidence intervals were determined.     

Automatic β-expansions of formal Laurent series over finite fields

We consider β-expansions of formal Laurent series over finite fields. If the base β is a Pisot or Salem series, we prove that the β-expansion of a Laurent series α is automatic if and only if α is algebraic.     

A Finite Volume Implicit Euler Scheme for the Linearized Shallow Water Equations: Stability and Convergence

The linearized shallow water equations are discretized in space by a finite volume method and in time by an implicit Euler scheme. Stability and convergence of the scheme are proved.     

Module Correspondences for Twisted Group Algebras

Abstract

Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K ^α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K ^α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K ^α G-modules and the set of irreducible K ^α C _G (A)-modules.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.     

A class of finite groups with complete character degree graphs

In this paper, we construct a new class of finite groups whose common divisor graphs are complete graphs, while there is no prime dividing all the nontrivial degrees.     

Thermomechanical formulation of ductile damage coupled to nonlinear isotropic hardening and multiplicative viscoplasticity

In this paper, we present a thermomechanical framework which makes use of the internal variable theory of thermodynamics for damage-coupled finite viscoplasticity with nonlinear isotropic hardening. Damage evolution, being an irreversible process, generates heat. In addition to its direct effect on material's strength and stiffness, it causes deterioration of the heat conduction. The formulation, following the footsteps of Simó and Miehe (1992), introduces inelastic entropy as an additional state variable. Given a temperature dependent damage dissipation potential, we show that the evolution of inelastic entropy assumes a split form relating to plastic and damage parts, respectively. The solution of the thermomechanical problem is based on the so-called isothermal split. This allows the use of the model in 2D and 3D example problems involving geometrical imperfection triggered necking in an axisymmetric bar and thermally triggered necking of a 3D rectangular bar.     

Growth limit of carbon onions – A continuum mechanical study

The growth of carbon onions is simulated using continuum mechanical shell models. With this models it is shown that, if a carbon onion has grown to a critical size, the formation of an additional layer leads to the occurrence of a structural instability. This instability inhibits further growth of carbon onions and, thus, can be a reason for the limited size of such particles. The loss of stability is mainly evoked by van der Waals interactions between misfitting neighboring layers leading to self-equilibrating stress states in the layers due to mutual accommodation. The influence of the curvature induced surface energy and its consequential stress state is investigated and found to be rather negligible. Furthermore, it is shown that the nonlinear character of the van der Waals interactions has to be considered to obtain maximum layer numbers comparable to experimental observations. The proposed model gives insight into mechanisms which are assumed to limit the size of carbon onions and can serve as basis for further investigations, e.g., of the formation of nanodiamonds in the center of carbon onions.