3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement e-ue-u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials. The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements. Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats. The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.Peer ReviewedPostprint (author's final draft

Stress-accurate Mixed FEM for soil failure under shallow foundations involving strain localization in plasticity

The development of slip lines, due to strain localization, is a common cause for failure of soil in many circumstances investigated in geotechnical engineering. Through the use of numerical methods - like finite elements - many practitioners are able to take into account complex geometrical and physical conditions in their analyses. However, when dealing with shear bands, standard finite elements display lack of precision, mesh dependency and locking. This paper introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. Von Mises and Drucker-Prager local plasticity models with strain softening are considered as constitutive law. This innovative formulation succeeds in overcoming the limitations of the standard formulation and provides accurate results within the vicinity of the shear bands, specifically without suffering from mesh dependency. Finally, 2D and 3D numerical examples demonstrate the accuracy and robustness in the computation of localization bands, without the introduction of additional tracking techniques as usually required by other methods. (C) 2014 Elsevier Ltd. All rights reserved.Peer ReviewedPostprint (author’s final draft

High-fidelity prediction of crack formation in 2D and 3D pullout tests

This paper presents the 2D and 3D numerical analysis of pullout tests on steel anchorages in concrete blocks using standard and mixed finite elements. A novel (stabilized) mixed formulation in the variables of total strain 8 and displacements u is introduced to overcome the intrinsic deficiencies of the standard displacement-based one in the context of localization of strains, such as mesh dependency. The quasi brittle behavior of concrete is described through an elastoplastic constitutive law with a local Rankine yielding criterion. The proposed formulation is shown to be a reliable and accurate tool, sensitive to the physical parameters of the pullout tests, but objective with respect to the adopted FE mesh. Furthermore, the mixed epsilon/u finite element is able to capture the correct failure mechanism with relatively coarse discretizations. At the same time, the spurious behavior of the standard formulation is not alleviated by mesh-refinement.Peer ReviewedPostprint (author's final draft

Fluid Pressurization and Entrapment Effects on the SIFs of Cracks produced under lubricated Rolling-Sliding Contact Fatigue

Abstract Pitting is one of the causes of failure for mechanical components subjected to rolling contact fatigue. In the present article, a FE model is described in which a 2D half-space with an edge crack is affected by a travelling contact load produced by a cylindrical body. The contact load is not approximated as usual by an analytical pressure distribution but the actual mating body is modelled. The presence of lubricant between the mating bodies and inside the crack is taken into account and its effect on the crack is modelled via hydrostatic elements. The lubricant is assumed to be entrapped into the crack by the external body when the latter covers the crack mouth, that is, the crack is sealed by the contact area and not by the contact between the crack faces (fluid entrapment mechanism). The pressure of the fluid is calculated via an iterative procedure by assuming that its volume stays constant inside the crack. Comparisons between this model and the alternative fluid pressurization mechanism have been made. The outcomes suggest that the fluid pressures inside the crack produced by the fluid entrapment mechanism tend to those of the fluid pressurization mechanisms as the crack becomes short

Hecke cycles on moduli of vector bundles and orbital degeneracy loci

Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank three semi-stable vector bundles on $C$ with trivial determinant is a double cover in $\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual is the famous Coble cubic, the unique cubic hypersurface that is singular along the Jacobian of $C$. In this paper we continue our exploration of the connections of such moduli spaces with the representation theory of $GL_9$, initiated in \cite{GSW} and pursued in \cite{GS, sam-rains1, sam-rains2, bmt}. Starting from a general trivector $v$ in $\wedge^3\mathbb{C}^9$, we construct a Fano manifold $D_{Z_{10}}(v)$ in $G(3,9)$ as a so-called orbital degeneracy locus, and we prove that it defines a family of Hecke lines in SU$_C(3)$. We deduce that $D_{Z_{10}}(v)$ is isomorphic to the odd moduli space SU$_C(3, \mathcal{O}_C(c))$ of rank three stable vector bundles on $C$ with fixed effective determinant of degree one. We deduce that the intersection of $D_{Z_{10}}(v)$ with a general translate of $G(3,7)$ in $G(3,9)$ is a K3 surface of genus $19$

Thermochromic Narrow Band Gap Phosphors for Multimodal Optical Thermometry: The Case of Y³⁺-Stabilized beta-Bi₂O₃:Nd³⁺

The design and development of effective luminescent thermal sensors have been driving technological progress in many different fields ranging from catalysis to biology and microelectronics, to name a few. The ratiometric concept of using the ratio between two luminescent emissions of lanthanide-doped phosphors allows overcoming some limitations resulting from the single emission-based thermometers. A fundamental requirement for the development of effective luminescent thermometers relies on efficient luminescence output, which is not always accessible. Therefore, alternative methods to probe the temperature in a reliable and simple way are still a challenge. Despite the conventional limits of using narrow band gap materials as hosts for lanthanoid ions, a smart design allows for the development of unusual phosphors with appealing properties. By taking advantage of the narrow band gap of Bi₂O₃ polymorphs, here we demonstrate the potential of the tetragonal Y-stabilized β-Bi₂O₃:Y³⁺, Nd³⁺ system as a multimodal thermometer combining the conventional Boltzmann thermometry based on Nd³⁺ together with the thermochromism of the host. With the aim of testing this new concept, the temperature dependence of the reflectance spectra was investigated. Moreover, from the application point of view, the chromaticity variations of the material described by means of simple thermometric parameters such as the ratio a*/b* and the hue angle hab are demonstrated to be particularly promising and already implemented in software commonly used worldwide. The results suggest the potential of the strategy of combining narrow band gap semiconductors with lanthanoid ions to design reliable and multimodal thermal sensors, paving the way to a new family of thermochromic and luminescent thermal sensors