Asymptotic homogenisation in strength and fatigue durability analysis of composites

This is the post-print version of the Article. Copyright @ 2003 Kluwer Academic Publishers.Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength as the structure period tends to zero is proved and its limiting value is estimated.This work was supported under the research grant GR/M24592 from the Engineering and Physical Sciences Research Council, UK

Long Term Stabilization of Expanding Aortic Aneurysms by a Short Course of Cyclosporine A through Transforming Growth Factor-Beta Induction

Abdominal aortic aneurysms (AAAs) expand as a consequence of extracellular matrix destruction, and vascular smooth muscle cell (VSMC) depletion. Transforming growth factor (TGF)-beta 1 overexpression stabilizes expanding AAAs in rat. Cyclosporine A (CsA) promotes tissue accumulation and induces TGF -beta1 and, could thereby exert beneficial effects on AAA remodelling and expansion. In this study, we assessed whether a short administration of CsA could durably stabilize AAAs through TGF-beta induction. We showed that CsA induced TGF-beta1 and decreased MMP-9 expression dose-dependently in fragments of human AAAs in vitro, and in animal models of AAA in vivo. CsA prevented AAA formation at 14 days in the rat elastase (diameter increase: CsA: 131.9±44.2%; vehicle: 225.9±57.0%, P = 0.003) and calcium chloride mouse models (diameters: CsA: 0.72±0.14 mm; vehicle: 1.10±0.11 mm, P = .008), preserved elastic fiber network and VSMC content, and decreased inflammation. A seven day administration of CsA stabilized formed AAAs in rats seven weeks after drug withdrawal (diameter increase: CsA: 14.2±15.1%; vehicle: 45.2±13.7%, P = .017), down-regulated wall inflammation, and increased αSMA-positive cell content. Co-administration of a blocking anti-TGF-beta antibody abrogated CsA impact on inflammation, αSMA-positive cell accumulation and diameter control in expanding AAAs. Our study demonstrates that pharmacological induction of TGF-beta1 by a short course of CsA administration represents a new approach to induce aneurysm stabilization by shifting the degradation/repair balance towards healing

Homogenization of a model for the propagation of sound in the lungs

International audienceIn this paper, we are interested in the mathematical modeling of the propagation of sound waves in the lung parenchyma, which is a foam-like elastic material containing millions of air-filled alveoli. In this study, the parenchyma is governed by the linearized elasticity equations, and the air by the acoustic wave equations. The geometric arrangement of the alveoli is assumed to be periodic with a small period ε > 0. We consider the time-harmonic regime forced by vibrations induced by volumic forces. We use the two-scale convergence theory to study the asymptotic behavior as ε goes to zero and prove the convergence of the solutions of the coupled fluid-structure problem to the solution of a linear-elasticity boundary value problem

Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation

We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(x) \chi_{\{x_1>0\}}(x)+\Gamma_2(x) \chi_{\{x_1<0\}}(x)$ and with $V_1, V_2, \Gamma_1, \Gamma_2$ periodic in each coordinate direction. This problem describes the interface of two periodic media, e.g. photonic crystals. We study the existence of ground state $H^1$ solutions (surface gap soliton ground states) for $0<\min \sigma(-\Delta +V)$. Using a concentration compactness argument, we provide an abstract criterion for the existence based on ground state energies of each periodic problem (with $V\equiv V_1, \Gamma\equiv \Gamma_1$ and $V\equiv V_2, \Gamma\equiv \Gamma_2$) as well as a more practical criterion based on ground states themselves. Examples of interfaces satisfying these criteria are provided. In 1D it is shown that, surprisingly, the criteria can be reduced to conditions on the linear Bloch waves of the operators $-\tfrac{d^2}{dx^2} +V_1(x)$ and $-\tfrac{d^2}{dx^2} +V_2(x)$.Comment: definition of ground and bound states added, assumption (H2) weakened (sign changing nonlinearity is now allowed); 33 pages, 4 figure

Two Dimensional Flow Analysis of A Laboratory Centrifugal Pump,&quot;

ABSTRACT Two dimensional potential flow was used to determine the velocity field within a laboratory centrifugal pump. In particular, the finite element technique was used to model the impeller and volute simultaneously. The rotation of the impeller within the volute was simulated by using steady state solutions with the impeller in 10 different angular orientations. This allowed the interaction between the impeller and the volute to develop naturally as a result of the solution. The results for the complete pump model showed that there are circumferential asymmetries in the velocity field, even at the design flow rate. Differences in the relative velocity components were as large as 0.12 m/sec for the radial component and 0.38 m/sec for the tangential component, at the impeller exit. The magnitude of these variations was roughly 25% of the magnitude of the average radial and tangential velocities at the impeller exit. These asymmetries were even more pronounced at off design flow rates. The velocity field was also used to determine the location of the tongue stagnation point and to calculate the slip within the impeller. The stagnation point moved from the discharge side of the tongue to the impeller side of the tongue, as the flow rate increased from below design flow to above design flow. At design flow, values of slip ranged from 0.96 to 0.71, from impeller inlet to impeller exit. For all three types of data (velocity profiles, stagnation point location, and slip factor) comparison was made to laser velocimeter data, taken for the same pump. At the design flow, the computational and experimental results agreed to within 17% for the velocity magnitude, and 2° for the flow angle. The stagnation point locations coincided for the computational and experimental results, and the values for slip agreed to within 10%

Tension at the borders: perceptions of role overload, conflict, strain and facilitation in work, family and health roles among employed individuals with arthritis

Objective. To examine inter-relationships among arthritis (A), work (W) and personal life (P) roles and their reciprocal influences, especially experiences of role balance/imbalance among individuals with inflammatory arthritis (IA) and OA

Homogenization of Biomechanical Models for Plant Tissues

In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and Stokes equations for fluid flow inside the cells. The chemical process in cells and the elastic properties of cell walls and middle lamella are coupled because elastic moduli depend on densities involved in chemical reactions, whereas chemical reactions depend on mechanical stresses. Using homogenization techniques we derive rigorously a macroscopic model for plant biomechanics. To pass to the limit in the nonlinear reaction terms, which depend on elastic strain, we prove the strong two-scale convergence of the displacement gradient and velocity field

The associations between QCT-based vertebral bone measurements and prevalent vertebral fractures depend on the spinal locations of both bone measurement and fracture

Summary We examined how spinal location affects the relationships between quantitative computed tomography (QCT)-based bone measurements and prevalent vertebral fractures. Upper spine (T4–T10) fractures appear to be more strongly related to bone measures than lower spine (T11–L4) fractures, while lower spine measurements are at least as strongly related to fractures as upper spine measurements. Introduction Vertebral fracture (VF), a common injury in older adults, is most prevalent in the mid-thoracic (T7–T8) and thoracolumbar (T12–L1) areas of the spine. However, measurements of bone mineral density (BMD) are typically made in the lumbar spine. It is not clear how the associations between bone measurements and VFs are affected by the spinal locations of both bone measurements and VF. Methods A community-based case–control study includes 40 cases with moderate or severe prevalent VF and 80 age- and sex-matched controls. Measures of vertebral BMD, strength (estimated by finite element analysis), and factor of risk (load:strength ratio) were determined based on QCT scans at the L3 and T10 vertebrae. Associations were determined between bone measures and prevalent VF occurring at any location, in the upper spine (T4–T10), or in the lower spine (T11–L4). Results Prevalent VF at any location was significantly associated with bone measures, with odds ratios (ORs) generally higher for measurements made at L3 (ORs = 1.9–3.9) than at T10 (ORs = 1.5–2.4). Upper spine fracture was associated with these measures at both T10 and L3 (ORs = 1.9–8.2), while lower spine fracture was less strongly associated (ORs = 1.0–2.4) and only reached significance for volumetric BMD measures at L3. Conclusions Closer proximity between the locations of bone measures and prevalent VF does not strengthen associations between bone measures and fracture. Furthermore, VF etiology may vary by region, with VFs in the upper spine more strongly related to skeletal fragility.National Institutes of Health (U.S.) (Grants R01AR053986, R01AR/AG041398, T32AG023480, and F31AG041629)National Heart, Lung, and Blood Institute. Framingham Heart Study (NIH/NHLBI Contract N01-HC-25195

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200

SMN deficiency in severe models of spinal muscular atrophy causes widespread intron retention and DNA damage

Spinal muscular atrophy (SMA), an autosomal recessive neuromuscular disease, is the leading monogenic cause of infant mortality. Homozygous loss of the gene survival of motor neuron 1 (SMN1) causes the selective degeneration of lower motor neurons and subsequent atrophy of proximal skeletal muscles. The SMN1 protein product, survival of motor neuron (SMN), is ubiquitously expressed and is a key factor in the assembly of the core splicing machinery. The molecular mechanisms by which disruption of the broad functions of SMN leads to neurodegeneration remain unclear. We used an antisense oligonucleotide (ASO)-based inducible mouse model of SMA to investigate the SMN-specific transcriptome changes associated with neurodegeneration. We found evidence of widespread intron retention, particularly of minor U12 introns, in the spinal cord of mice 30 d after SMA induction, which was then rescued by a therapeutic ASO. Intron retention was concomitant with a strong induction of the p53 pathway and DNA damage response, manifesting as gamma-H2A.X positivity in neurons of the spinal cord and brain. Widespread intron retention and markers of the DNA damage response were also observed with SMN depletion in human SH-SY5Y neuroblastoma cells and human induced pluripotent stem cell-derived motor neurons. We also found that retained introns, high in GC content, served as substrates for the formation of transcriptional R-loops. We propose that defects in intron removal in SMA promote DNA damage in part through the formation of RNA:DNA hybrid structures, leading to motor neuron death