Wedge-shaped fracturing in the pull out of FRP stiffeners from quasi-brittle substrates

Fiber-Reinforced-Polymer (FRP) strips can be glued to the surface of concrete or masonry structures to improve their strength. Pull-out tests on FRP bonds have shown a progressive failure of the adhesive joint involving early-stage cracking parallel to the axis of the FRP stiffener, and an inclined crack initiating at the free end of the stiffener and extending into the quasi-brittle substrate in the latest stage. The subsurface crack produces a characteristic wedge-shaped spall. There is no consensus on the reasons for the transition from cracking along the bond to cracking within the substrate. Therefore a Linear Elastic Fracture Mechanics model problem is presented here that accounts for and provides improved understanding of the formation of the subsurface crack. The boundary value problem is solved analytically using the distributed dislocation technique. Competition between crack extension along the adhesive joint and into the substrate is quantified using a quantized crack propagation criterion, whereby the crack does not advance in infinitesimal continuous increments, but instead in finite steps of length comparable to the characteristic dimensions of the material microstructure. The model predicts results that are in good agreement with experimental evidence.     

Wave propagation and dispersion in elasto-plastic microstructured materials

A Mindlin continuum model that incorporates both a dependence upon the microstructure and inelastic (nonlinear) behavior is used to study dispersive effects in elasto-plastic microstructured materials. A one-dimensional equation of motion of such material systems is derived based on a combination of the Mindlin microcontinuum model and a hardening model both at the macroscopic and microscopic level. The dispersion relation of propagating waves is established and compared to the classical linear elastic and gradient-dependent solutions. It is shown that the observed wave dispersion is the result of introducing microstructural effects and material inelasticity. The introduction of an internal characteristic length scale regularizes the ill-posedness of the set of partial differential equations governing the wave propagation. The phase speed does not necessarily become imaginary at the onset of plastic softening, as it is the case in classical continuum models and the dispersive character of such models constrains strain softening regions to localize.     

Analytic Propagation for Nonlinear Weakly Hyperbolic Systems

The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax [14 Lax , P.D. ( 1953 ). Nonlinear hyperbolic equations . Comm. Pure Appl. Math. 6 : 231 – 258 . [Google Scholar]] and Alinhac and Métivier [2 Alinhac , S. , Métivier G. ( 1984 ). Propagation de l'analyticité des solutions de systèmes hyperboliques nonlinéaires [Propagation of analyticity for solutions of nonlinear hyperbolic systems]. Invent. Math. 75, 189–204 . [Google Scholar]]. Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m ? 1), m being the maximum multiplicity of the characteristics.     

Analytic Wave Front Set for Solutions to Schrödinger Equations II – Long Range Perturbations

This paper is a continuation of [9 Martinez , A. , Nakamura , S. , Sordoni , V. ( 2009 ). Analytic wave front set for solutions to Schrödinger equations . Adv. Math. 222 : 1277 – 1307 .[Crossref], [Web of Science ®] , [Google Scholar]], where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of [9 Martinez , A. , Nakamura , S. , Sordoni , V. ( 2009 ). Analytic wave front set for solutions to Schrödinger equations . Adv. Math. 222 : 1277 – 1307 .[Crossref], [Web of Science ®] , [Google Scholar]] to long-range perturbations (in particular, we can allow potentials growing like ?x?^2?? at infinity). More precisely, we construct a modified quantum free evolution G ₀(?s, hD _z ) acting on Sjöstrand's spaces, and we characterize the analytic wave front set of the solution e ^?itH u ₀ of the Schrödinger equation, in terms of the semiclassical exponential decay of G ₀(?th ^?1, hD _z )T u ₀, where T stands for the Bargmann-transform. The result is valid for t < 0 near the forward non trapping points, and for t > 0 near the backward non trapping points. It is an extension of [12 Nakamura , S. ( 2009 ). Semiclassical singularities propagation properties for the Schrödinger equations . J. Math. Soc. Japan 61 : 177 – 211 . [Google Scholar]] to the analytic framework.     

Economic production quantity model with repair failure and limited capacity

We develop an economic production quantity (EPQ) model with random defective items and failure in repair. The existence of only one machine results with limited production capacity and shortages. The aim of this research is to derive the optimal cycle length, the optimal production quantity and the optimal back ordered quantity for each product so as to minimize the total expected cost (holding, shortage, production, setup, defective items and repair costs). The convexity of the model is derived and the objective function is proved convex. Two numerical examples illustrate the practical usage of the proposed method.     

Problem of proper decomposition and initialization of acoustic and entropy modes in a gas affected by the mass force

The relations connecting perturbations specific for acoustic and entropy modes in an accelerated fluid or in a fluid affected by constant mass force, are derived. They allow to decompose the total vector of perturbations and the overall energy into acoustic and non-acoustic parts uniquely at any instant. In order to do this, three quantities are required, for example total perturbations in entropy, pressure and velocity. The evaluations are made in regard to the content of acoustic and non-acoustic parts of the total energy excluding its kinetic part. In some cases, exact relations may be derived.     

不同应变率下两种岩石的压缩破碎特征试验研究

为了研究不同岩石在不同应变率下压缩时裂纹的产生规律及破坏模式,将石灰岩和红砂岩制成试件,研究其在不同应变率和受力模式下裂纹的形成模式。开展了两种岩石的准静态压缩和动态压缩试验,采用高速摄影机记录了裂纹的产生和破坏模式。对两种岩石试件的裂纹形态进行对比,基于岩石的物理性质、受力状态、能量演化分析,得到了在不同应变率下压缩时产生差异性的原因。结果表明:准静态压缩下岩石试件受压的破坏模式也会因应变率的不同而存在差异,并且破坏模式的差异对岩石试件的抗压强度将产生显著的影响;从能量演化的角度分析,入射能量的大小将会决定岩石试样动态抗压强度曲线是否出现起伏;动态压缩时,裂纹的周向扩展速度与岩石抗压强度呈正相关。     

基于路径积分的声传播微观特性的研究

运用量子力学的Feynman路径积分理论,尝试研究空气中声传播的计算方法及其微观特性。选取一小团空气(小体元)为研究对象,将声传播过程中一列振动的空气小体元近似为一组谐振子集合,用路径积分方法给出系统的能量方程及波函数,研究并分析声传播的某些机制和它的微观特性。在量子分子状态下,用密度矩阵将系统概率波幅(跃迁幅)与配分函数相关联,给出了谐振子处于能量E_n的概率p(E_n)和能量的平均值(?)。