An extension of the tearing instability theory to multiple loading parameters

The stability of a cracked, nonlinear component connected to an elastic structure and subjected to an arbitrary number of controlled loads or displacements, is discussed. First this is done with a general instability criterion expressed in terms of loads and displacements of the cracked part. Then general expressions for the tearing modulus are given for different loading situations. Finally the given equations are applied to SEN specimens under bending and tension.

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Résumé On discute de la stabilité d'un composant fissuré et non linéaire assemblé à une structure élastique et soumis à un monbre quelconque de charges ou de déplacements, appliqués dans des conditions connues. Ceci est réalisé en faisant appel, en premier lieu, à un critère général d'instabilité exprimé en termes the sollicitation et de déplacement de la portion fissurée. Ensuite, on fournit des expressions générales pour le module d'arrachement, correspondant à diverses situations de mise en charge. Enfin, les équations obtenues sont appliquées à des éprouvettes à entaille latérale simple soumises à flexion et traction.

     

The δ-Al2O3 (Saffil) fibre degradation during infiltration with MgLi alloy

The chemical and phase transformations of -Al₂O₃ (Saffil) fibres during their infiltration with Mg-8 wt% Li were studied by scanning and transmission electron microscopy, Auger electron spectroscopy, secondary ion mass spectrometry and X-ray diffraction methods. The infiltration experiments were carried out in autoclave under argon pressure at temperatures of 883–908 K and contact times of 4–30 s as well as at 918 K/420 s. During the course of infiltration, lithium penetrates the Saffil fibres and this process is accompanied by the gradual transformation of the tetragonal -Al₂O₃ lattice towards the cubic spinel LiAl₅O₈ compound, where part of the Li⁺ ions is probably substituted by Mg²⁺ No remarkable interfacial zone at the fibre/matrix interface was observed; however, the Saffil fibres became brittle which had been manifested by the occurrence of fragmentation on the metallographically treated fibre cross-sections. The tensile strength (maximum 220 MPa) of the corresponding metal matrix composite clearly decreased with increased infiltration time.     

The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.     

Adaptive isogeometric analysis by local h-refinement with T-splines

Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead. T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM. Obeying a few straightforward rules, rectangular patches in the parameter space of the T-splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry. Furthermore, it is shown how state-of-the-art a posteriori error estimation techniques can be combined with refinement by T-splines. Numerical examples underline the potential of isogeometric analysis with T-splines and give hints for further developments.     

Dissipative particle dynamics simulations for fibre suspensions in newtonian and viscoelastic fluids

A versatile model of fibre suspensions in Newtonian and viscoelastic fluids has been developed using dissipative particle dynamics method. The viscoelastic fluid is modelled by linear chains with linear connector spring force (the Oldroyd-B model), which is known to be a reasonable model for the so-called Boger fluid (a dilute suspension of polymer in a highly viscous solvent). The numerical results are in excellent agreement with the analytical results of the Oldroyd-B model in simple shear flow. An effective meso-scale model of fibre in DPD is proposed and then incorporated with simple Newtonian fluid and our Boger fluid to enable entirely study rheological properties of fibre suspensions in both Newtonian and viscoelastic solvents. The numerical results are well compared with available experimental data and other numerical models.     

A nonlinear Hu–Washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections

A nonlinear three-dimensional finite beam element based on a Hu–Washizu variational formulation is presented. In addition to the standard beam strains, based on kinematic assumptions, further deformation modes are introduced. These additional modes allow for (a) the consideration of a complete three-dimensional stress field, providing an interface for arbitrary three-dimensional material models, and (b) the consideration of cross-section warping, whose shape might shift during the elastic or inelastic deformation. Beside the fact that the resulting finite element formulation is locking free (full Gauss integration in length direction) and remarkable robustness (even for very large load steps), these additional degrees of freedom do not increase the total number of global unknowns of a beam structure. Each element node exhibits the common 3 translational and 3 rotational degrees of freedom. The additional degrees of freedom are eliminated on element level via static condensation. As a consequence, e.g. a bi-moment can not be applied at a free end. This restricts the applicability of the formulation to a class of problems where the influence of the bi-moment is negligible. It is shown that global acting polynomial ansatz functions are not suitable to describe warping of cross-sections with an arbitrary shape. For this reason a new concept based on local ansatz functions is presented. The general criteria to design the warping ansatz functions are discussed in detail. Several examples with moderate thick cross-sections are investigated.     

On the small crack fracture mechanics

The limit of validity of linear fracture mechanics is specified by the minimum allowable crack length through an ASTM convention. Extension into the non-linear region ought to imply an extension towards smaller allowable cracks. In order to elucidate the question “How short is the smallest crack that fits the methods of fracture mechanics, and how do shorter cracks than that behave?” a pilot investigation is carried out. The process region is modelled as a Barenblatt line region and plastic flow off-side the process region is neglected. Results show that instability occurs before the process region is fully developed (as at large cracks) if the crack is short. This implies large deviations from the large crack fracture mechanics if the crack is very small. Even cracks of infinitesimal length are included in the study.     

Bioelectrodynamics in living organisms

This article introduces an interdisciplinary subject of bioelectrodynamics in living organisms and its related research challenges and opportunities. Bioelectrodynamics in living organisms is aimed to reveal critical roles of electromagnetism and mechanics in biology, to correlate biophysical functions of living organisms with biochemical processes at the cellular level, and to introduce theoretical basis and methodology, such as modeling and simulations, for stimulating technical innovations and promoting technology development in biomedicine as well as for the study of human healthcare issues related to environments among others in our modern society. The article reviews some important issues in bioelectrodynamic modeling. This includes the modeling of living cells, blood, bones and soft tissues that may have unique properties, such as active control, regulation and remodeling capabilities that are completely different from those of conventionally man-made materials. Possible biological effects and potential biomedical usages of endogenous and exogenous electromagnetic fields and mechanical stresses in living organisms are also reviewed, which indicate promising future of biomedical imaging and therapeutic methods based on bioelectrodynamic techniques. The fact that living organisms may have well-organized structures, actively controlled actions and responses, extremely sensitivity in electromagnetic fields and mechanical actions, and amazing signal amplification functions may not only cause complexity and variety of the biological world, but also create opportunities for technical innovations in biomedicine to improve future quality of human life.