Dissipativity theory for discontinuous dynamical systems: Basic input, state, and output properties, and finite-time stability of feedback interconnections

In this paper, we develop dissipativity theory for discontinuous dynamical systems. Specifically, using set-valued supply rate maps and set-valued connective supply rate maps consisting of locally Lebesgue integrable supply rates and connective supply rates, respectively, and set-valued storage maps consisting of piecewise continuous storage functions, dissipativity properties for discontinuous dynamical systems are presented. Furthermore, extended Kalman–Yakubovich–Popov set-valued conditions, in terms of the discontinuous system dynamics, characterizing dissipativity via generalized Clarke gradients and locally Lipschitz continuous storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for discontinuous dynamical systems by appropriately combining the set-valued storage maps for the forward and feedback systems.     

Generalized Topological Essentiality and Coincidence Points of Multivalued Maps

A concept of generalized topological essentiality for a large class of multivalued maps in topological vector Klee admissible spaces is presented. Some direct applications to differential equations are discussed. Using the inverse systems approach the coincidence point sets of limit maps are examined. The main motivation as well as main aim of this note is a study of fixed points of multivalued maps in Fréchet spaces. The approach presented in the paper allows to check not only the nonemptiness of the fixed point set but also its topological structure.      

On strain and damage interactions during tearing: 3D in situ measurements and simulations for a ductile alloy (AA2139-T3)

Strain and damage interactions during tearing of a ductile Al-alloy with high work hardening are assessed in situ and in 3D combining two recently developed experimental techniques, namely, synchrotron laminography and digital volume correlation. Digital volume correlation consists of registering 3D laminography images. Via simultaneous assessments of 3D strain and damage at a distance of 1-mm ahead of a notch root of a thin Compact Tension-like specimen, it is found that parallel crossing slant strained bands are active from the beginning of loading in a region where the crack will be slanted. These bands have an intermittent activity but are stable in space. Even at late stages of deformation strained bands can stop their activity highlighting the importance of plasticity on the failure process rather than damage softening. One void is followed over the loading history and seen to grow and orient along the slant strained band at very late stages of deformation. Void growth and strain are quantified. Gurson–Tvergaard–Needleman-type simulations using damage nucleation for shear, which is based on the Lode parameter, are performed and capture slant fracture but not the initial strain fields and in particular the experimentally found slant bands. The band formation and strain distribution inside and outside the bands are discussed further using plane strain simulations accounting for plastic material heterogeneity in soft zones.     

Mean Green operators and Eshelby tensors for hemispherical inclusions and hemisphere interactions in spheres. Application to bi-material spherical inclusions in isotropic spaces

This paper mainly presents an exact expression for the mean shape function of a hemispherical inclusion, from which are obtained analytical forms for the mean Green operator (GO) and Eshelby tensor of this hemi-sphere as well as for the related mean pair interaction Green operator (IGO) between the two hemi-spheres of a sphere, in media with isotropic (elastic or dielectric) properties. We secondly address the problem of bi-material inclusions, in the sense of a two-phase compact set of two or a few elementary domains, a particular inclusion pattern case for which we give an estimate of the mean stress and strain in each phase accounting for interactions. This estimate results from knowing the mean GO (or Eshelby tensor) for each pattern element plus the mean IGO between element pairs, what is rarely fulfilled analytically. The here solved case for bi-material spherical inclusions made of two different hemispherical elements adds to the recently made available solution for bi-material cylindrical inclusions made of piled coaxial finite cylinders. The obtained mean stress estimates are exemplified able to satisfactorily match with FEM calculations up to highly contrasted bi-material inclusions. Other types of bi-material spherical inclusions are mentioned for which the mean GOs for the sub-domains and their pair IGO can be obtained without calculation, owing to particular symmetries of the phase arrangement. Mean GOs and IGOs are also useful in certain homogenization frameworks yielding overall property estimates for inclusion-reinforced matrices. Further discussions and specific applications will be presented in forthcoming papers.     

Influences of imperfect interfaces on effective properties of multiferroic composites with coated inclusion

In order to predict the effective properties of multiferroic composite materials, the effective material constants of multiferroic composites with the coated inclusion and imperfect interface are investigated. Based on the generalized self-consistent theory, the closed-form solutions of the effective material constants are derived. For the composites with piezomagnetic inclusion, piezoelectric coating and polymer matrix, numerical calculations are performed to present the influences of the imperfect interface cooperating with the coating on the effective material constants. From the results, it can be observed that the effective constants can be enhanced by the coating but reduced by the imperfect interface. Moreover, the coating has the shielding effects on the imperfect interface for the composite structures with its higher filling ratio.     

低温拉曼光谱分析流体包裹体盐度的条件约束

流体包裹体盐度及类型是分析地质流体作用的重要地球化学参数。NaCl-H₂O体系是地质体中最常见的流体体系之一,其盐度通常由显微测温法获得,而盐水合物的低温拉曼光谱不仅可以用来计算流体包裹体盐度,还可以区分盐水类型。理论上讲,低温冷冻条件下的流体包裹体并非均匀体系,单一测点的拉曼光谱具有较强的局限性,由其计算的盐度并不能代表整个流体包裹体的盐度。为了更好地了解低温条件下流体包裹体的相变特征及其拉曼光谱对盐度的响应,本文通过配置五种不同浓度的NaCl溶液,研究了其在低温下的结晶过程及拉曼光谱特征。结果显示,在反复冷冻与升温过程中,冰晶首先形成,而水石盐的形成依赖于盐溶液的浓缩,多形成于冰晶间的缝隙中。水石盐的四个拉曼特征峰中,p₁[(3 402±1) cm-1]和p₂[(3 419±1) cm-1]相对强度稳定,p₃[(3 432±2) cm-1]和p₄[(3 535±4) cm-1]相对强度随盐度增加发生大幅度变化,从而导致相同盐度样品不同测点的拉曼特征比值随盐度增加而愈发离散。因此,传统的流体包裹体单一测点低温拉曼测盐误差较大,数据分析显示多点测试统计平均值才能更好的反映流体的真实盐度。相对于强度和半高宽,总峰面积与盐度相关性最好,是计算盐度的首选参数。该研究阐述了低温拉曼测盐的实验操作和数据处理方法,并阐明了其在流体包裹体分析中的应用条件。尽管操作过程较复杂,但其抗干扰强,应用盐度范围广,计算结果可靠,是重要的测盐方法。     

NaCl-MgCl_2-H_2O体系低温拉曼光谱研究

通过在低温下进行大量的最优生成条件的实验探索,得到了NaCl-H2O体系和MgCl2-H2O体系水合物生成的最优实验条件——迅速降温至-180℃然后缓慢升温至观察到水合物生成过程结束(即视野突然变暗),最后快速降温至-180℃。对NaCl-MgCl2-H2O体系进行了定性和半定量尝试,并得到结论:3 537cm-1可以指示NaCl的存在,3 514 cm-1可以指示MgCl2的存在;3 537和3 514 cm-1峰的相对高低可以大致判断出NaCl和MgCl2的相对多少。这一发现为天然包裹体液相成分拉曼光谱原位定性、定量分析奠定了良好的基础。对于历史上亚稳低共熔混合物形成过程的模式的争议,实验结果初步赞同了Samson等的观点,即冰在最初的冷却中形成,在冰之间的空隙中剩余过饱和的盐溶液,再次升温时,盐的水合物从这个液体中结晶出来。     

Analytic plastic potential for porous aggregates with matrix exhibiting tension-compression asymmetry

This paper is devoted to modeling the effects of the tension-compression asymmetry of the matrix on yielding of the void-matrix aggregate. The matrix plastic behavior is described by the Cazacu et al. [2006. Orthotropic yield criterion for hexagonal closed packed metals. Int. J. Plasticity 22, 1171-1194] isotropic yield criterion, which captures strength differential effects. Using an upper-bound approach, a new analytic isotropic plastic potential for a random distribution of spherical voids is obtained. The derived analytic potential is sensitive to the third invariant of the stress deviator and displays tension-compression asymmetry. In the case when the matrix material has the same yield in tension and compression, it reduces to Gurson's [1977. Continuum theory of ductile rupture by void nucleation and growth: Part I: Yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. Trans. ASME Ser. H 99, 2-15.] criterion. Furthermore, the proposed criterion predicts the exact solution of a hollow sphere loaded in hydrostatic tension or compression. The accuracy of the proposed analytical criterion is assessed through comparisons with finite-element cell calculations.     

A generalized Nielsen number and multiplicity results for differential inclusions

The Nielsen number is defined for a rather general class of multivalued maps on compact connected ANRs, including, e.g., admissible maps (in the sense of Górniewicz (1976); compare also Górniewicz (1995)) on tori. Since the Poincaré maps generated by the Marchaud vector fields are of this type (see (Andres, 1997)), we can obtain in such a way multiplicity results for differential inclusions. More precisely, the nontrivial Nielsen number gives a lower estimate of coincidence points (in particular, fixed points) corresponding to the desired solutions.     

Extremality,Controllability, and Abundant Subsets of Generalized Control Systems

The generalized control system that we consider in this paper is a collection of vector fields, which are measurable in the time variable and Lipschitzian in the state variable. For such system, we define the concept of an abundant subset. Our definition follows the definition of an abundant set of control functions introduced by Warga. We prove a controllability–extremality theorem for generalized control systems, which says, in essence, that either a given trajectory satisfies a type of maximum principle or a neighborhood of the endpoint of the trajectory can be covered by trajectories of an abundant subset. We apply the theorem to a control system in the classical formulation and obtain a controllability–extremality result, which is stronger, in some respects, than all previous results of this type. Finally, we apply the theorem to differential inclusions and obtain, as an easy corollary, a Pontryagin-type maximum principle for nonconvex inclusions.