Singular divergence instability thresholds of kinematically constrained circulatory systems

Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraints? coefficients. Particularly, the critical buckling load of the kinematically constrained Ziegler?s pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree n=2$n=2$. This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability.     

Some insights into structure instability and the second-order work criterion

This paper is an attempt to extend the approach of the second-order work criterion to the analysis of structural system instability. Elastic structural systems with a finite number of freedoms and subjected to a given loading are considered. It is shown that a general equation, relating the second-order time derivative of the kinetic energy to the second-order work, can be derived for kinetic perturbations. The case of constant, nonconservative loadings are then investigated, putting forward the role of the spectral properties of the symmetric part of the tangent stiffness matrix in the occurrence of instability. As an illustration, the case of the generalized Ziegler column is considered and the case of aircraft wings subjected to aeroelastic effects is investigated. In the both cases, the consequences of additional kinematic constraints are discussed.     

Metal‐Atom Impact on the Self‐Assembly of Cup‐and‐Ball Metalloporphyrin–Fullerene Conjugates

A fullerene ammonium derivative has been combined with different metalloporphyrin–crown ether receptors to generate very stable supramolecules. The combination of fullerene–porphyrin and ammonium–crown ether interactions leads to a strong chelate effect as evidenced by a high effective molarity (3.16 M ). The different parameters influencing the stability of the supramolecular ensembles, in particular the nature of the metal in the porphyrin moiety, have been rationalized with the help of theoretical calculations thus providing new insights into fullerene–porphyrin interactions.     

Inertia effects as a possible missing link between micro and macro second-order work in granular media

This paper is concerned with a theoretical question as to the definition of instabilities in a granular assembly and its proper formulation at the microscopic level. Recently, this question has taken up much prominence with the emergence of intriguing failure modes such as diffuse failure associated to unstable plasticity of granular materials and microstructural instabilities. An analysis of the second-order work as a general and necessary criterion to detect instabilities is conducted both at the macroscopic and microscopic levels including large deformations. On the basis of a micromechanical analysis of a body consisting of arbitrary interacting particles in a representative element volume (REV), a general formula is derived to quantify the microscopic second-order work involving local variables on the grain scale. The latter emerges as a sum of a configurational term that involves contact forces between neighboring grains, plus a kinetic part consisting of the mechanical unbalance of intergranular forces under dynamics at incipient failure. The present analysis is thought to serve as a clarification of the question of failure in geomaterials typified by a transition from static to a dynamic regime with release of kinetic energy originating from microstructural interactions.     

Enhanced CO<Subscript>2</Subscript> Storage and Sequestration in Deep Saline Aquifers by Nanoparticles: Commingled Disposal of Depleted Uranium and CO<Subscript>2</Subscript>

Geological storage of anthropogenic CO₂ emissions in deep saline aquifers has recently received tremendous attention in the scientific literature. Injected buoyant CO₂ accumulates at the top part of the aquifer under a sealing cap rock. Potential buoyant movement of CO₂ has caused some concern that the high-pressure CO₂ could breach the seal rock. However, CO₂ will diffuse into the brine underneath and generate a slightly denser fluid that may induce instability and convective mixing. Onset times of instability and convective mixing performance depend on the physical properties of the rock and fluids, such as permeability and density contrast. We present the novel idea of adding nanoparticles (NPs) to injected CO₂ to increase density contrast between the CO₂-rich brine and the underlying resident brine and, consequently, decrease onset time of instability and increase convective mixing. The analyses show that 0.001 volume fraction of NPs added to the CO₂ stream shortens onset time of mixing by approximately 80% and increases convective mixing by 50%. If it thus originally takes 5 years for the overlying CO₂ to start convective mixing, by adding NPs, onset time of mixing reduces to 1 year, and after initiation of convective mixing, mixing improves by 50%. A reduction of the CO₂ leakage risk ensues. In addition to other metallic NPs, use of processed depleted uranium oxide (DU) as the NPs is also proposed. DU-NPs are potentially stable and might be safely commingled with CO₂ to store in saline aquifers.     

Multiscale characterisation of diffuse granular failure

We study the evolution of structure inside a deforming, cohesionless granular material undergoing failure in the absence of strain localisation – so-called diffuse failure. The spatio-temporal evolution of the basic building blocks for self-organisation (i.e. force chains and minimal contact cycles) reveals direct insights into the structural origins of failure. Irrespective of failure mode, self-organisation is governed by the cooperative behaviour of truss-like 3-cycles providing lateral support to column-like force chains. The 3-cycles, which are initially in scarce supply, form a minority subset of the minimal contact cycle bases. At large length-scales (i.e. sample size), these structures are randomly dispersed, and remain as such while their population progressively falls as loading proceeds. Bereft of redundant constraints from the 3-cycles, the force chains are initially just above the isostatic state, a condition that progressively worsens as the sample dilates. This diminishing capacity for redistribution of forces without incurring physical rearrangements of member particles renders the force chains highly prone to buckling. A multiscale analysis of the spatial patterns of force chain buckling reveals no clustering or localisation with respect to the macroscopic scale. Temporal patterns of birth-and-death of 3-cycles and 3-force chains provide unambiguous evidence that significant structural reorganisations among these building blocks drive rheological behaviour at all stages of the loading history. The near-total collapse of all structural building blocks and the spatially random distribution of force chain buckling and 3-cycles hint at a possible signature of diffuse failure.