Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature. (C) 2014 Elsevier Ltd. All rights reserved.

Length scales in glass-forming liquids and related systems: a review

The central problem in the study of glass-forming liquids and other glassy systems is the understanding of the complex structural relaxation and rapid growth of relaxation times seen on approaching the glass transition. A central conceptual question is whether one can identify one or more growing length scale(s) associated with this behavior. Given the diversity of molecular glass-formers and a vast body of experimental, computational and theoretical work addressing glassy behavior, a number of ideas and observations pertaining to growing length scales have been presented over the past few decades, but there is as yet no consensus view on this question. In this review, we will summarize the salient results and the state of our understanding of length scales associated with dynamical slow down. After a review of slow dynamics and the glass transition, pertinent theories of the glass transition will be summarized and a survey of ideas relating to length scales in glassy systems will be presented. A number of studies have focused on the emergence of preferred packing arrangements and discussed their role in glassy dynamics. More recently, a central object of attention has been the study of spatially correlated, heterogeneous dynamics and the associated length scale, studied in computer simulations and theoretical analysis such as inhomogeneous mode coupling theory. A number of static length scales have been proposed and studied recently, such as the mosaic length scale discussed in the random first-order transition theory and the related point-to-set correlation length. We will discuss these, elaborating on key results, along with a critical appraisal of the state of the art. Finally we will discuss length scales in driven soft matter, granular fluids and amorphous solids, and give a brief description of length scales in aging systems. Possible relations of these length scales with those in glass-forming liquids will be discussed.

A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. By incorporating a shear correction factor, the formulation also accommodates analysis of shells that have higher thickness. In order to attain this, a consistent second order approximation to the complementary energy density is considered and incorporated in peridynamics via constitutive correspondence. Unlike the uncoupled constitution for thin shells, a consequence of a first order approximation, constitutive relations for thick shells are fully coupled in that surface wryness influences the in-plane stress resultants and surface strain the moments. Our proposal on the peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells, that of flat plates and quasi-static fracture propagation in a cylindrical shell. (C) 2016 Elsevier Ltd. All rights reserved.

Object attributes combine additively in visual search

We perceive objects as containing a variety of attributes: local features, relations between features, internal details, and global properties. But we know little about how they combine. Here, we report a remarkably simple additive rule that governs how these diverse object attributes combine in vision. The perceived dissimilarity between two objects was accurately explained as a sum of (a) spatially tuned local contour-matching processes modulated by part decomposition; (b) differences in internal details, such as texture; (c) differences in emergent attributes, such as symmetry; and (d) differences in global properties, such as orientation or overall configuration of parts. Our results elucidate an enduring question in object vision by showing that the whole object is not a sum of its parts but a sum of its many attributes.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

A micromechanical damage theory for brittle materials with small cracks

For brittle solids containing numerous small cracks, a micromechanical damage theory is presented which accounts for the interactions between different small cracks and the effect of the boundary of a finite solid, and includes growth of the pre-existing small cracks. The analysis is based on a superposition scheme and series expansions of the complex potentials. The small crack evolution process is simulated through the use of fracture mechanics incorporating appropriate failure criteria. The stress-strain relations are obtained from the micromechanics analysis. Typical examples are given to illustrate the potential capability of the proposed theory. These results show that the present method provides a direct and efficient approach to deal with brittle finite solids containing multiple small cracks. The stress-strain relation curves are evaluated for a rectangular plate containing small cracks.

Influences of strain rate and temperature variation on material intrinsic length of plasticity strain gradient theory

Cowper-Symonds and Johnson-Cook dynamic constitutive relations are used to study the influence of both strain rate effect and temperature variation on the material intrinsic length scale in strain gradient plasticity. The material intrinsic length scale decreases with increasing strain rates, and this length scale increases with temperature.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

The Object Agreement Restriction

[EN]This paper deals with the so-called Person Case Constraint (Bonet, 1991), a universal constraint blocking accusative clitics and object agreement morphemes other than third person when a dative is inserted in the same clitic/agreement cluster. The aim of this paper is twofold. First, we argue that the scope of the PCC is considerably broader than assumed in previous work, and that neither its formulation in terms of person (1st/2nd vs. 3rd)-case (accusative vs. dative) restrictions nor its morphological nature are part of the right descriptive generalization.We present evidence (i) that the PCC is triggered by the presence of an animacy feature in the object’s agreement set; (ii) that it is not case dependent, also showing up in languages that lack dative case; and (iii) that it is not morphologically bound. Second, we argue that the PCC, even if it is modified accordingly, still puts together two different properties of the agreement system that should be set apart: (i) a cross linguistic sensitivity of object agreement to animacy and (ii) a similarly widespread restriction on multiple object agreement observed crosslinguistically. These properties lead us to propose a new generalization, the Object Agreement Constraint (OAC): if the verbal complex encodes object agreement, no other argument can be licensed through verbal agreement.

The Derivation of Dative Alternations

Maia Duguine, Susana Huidobro and Nerea Madariaga (eds.)

Feeding of Gammarus lacustris Sars under different conditions of habitation [Translation from: [Trophic relations of freshwater invertebrates.] (ed. G. G. Vinberg) pp.94-98. Leningrad, Zool.Inst.AN SSSR, 1980]

The amphipod Gammarus lacustris, a regular representative of lacustrine communities, often plays a significant role in the transformation of matter and energy. The object of the present work was to clarify the quantitative side of the feeding of the amphipod under different conditions of habitation. Experimental works on determination of the rate of consumption of food and its dependence on body-weight were carried out in the summer periods 1975-1978 on three water-bodies of the Krasnoyarsk region, of different conditions of habitation for the amphipods.

Plasma inverse scattering theory

The object of this report is to calculate the electron density profile of plane stratified inhomogeneous plasmas. The electron density profile is obtained through a numerical solution of the inverse scattering algorithm.

The inverse scattering algorithm connects the time dependent reflected field resulting from a δ-function field incident normally on the plasma to the inhomogeneous plasma density.

Examples show that the method produces uniquely the electron density on or behind maxima of the plasma frequency.

It is shown that the δ-function incident field used in the inverse scattering algorithm can be replaced by a thin square pulse.

Ditos populares em músicas do cancioneiro popular: uma abordagem cognitiva

Nesta dissertação, analisam-se alguns ditos populares retomados em músicas do cancioneiro popular, com base na teoria da metáfora conceptual (Lakoff e Jonhson, 1980; Kövecses, 2002), e na teoria da integração conceptual (Fauconnier e Turner, 2002). Busca se investigar se a projeção metafórica presente no dito empregado em situações cotidianas se sustenta, quando o mesmo é retomado em uma letra de música. Este estudo encontra sua justificativa em uma das assunções basilares da linguística cognitiva de que as metáforas conceptuais estão presentes tanto nas conversas cotidianas quanto nas manifestações literárias e artísticas. Pretende se, assim, observar a multidirecionalidade dos processos de significação desse tipo de construção linguística, a fim de postular seu poder projetivo e metafórico na mente dos falantes. Dentro do repertório de construções proverbiais em português, é perceptível a construção proverbial condicional com a configuração sintático semântica [x P Q], entre as quais foi escolhida como objeto de estudo a configuração [Quem P Q]. A escolha das músicas foi aleatória, já que não se buscou um gênero ou estilo específico, mas canções que possuíssem ditos populares em suas letras. Na análise, de cunho interpretativo, procedeu-se a identificação do papel da metáfora conceptual presente no dito empregado em situações cotidianas e nas 10 músicas selecionadas para este estudo. Em seguida, postularam-se redes de integração conceptual subjacente ao sentido dos ditos nas interações em geral e nas músicas, de modo a explicar que as diferenças de sentido observadas ou não nos ditos transpostos para letras de músicas estão relacionadas ao tipo de rede de integração conceptual ativado durante o processo de mesclagem. As redes de integração postuladas para explicar a construção de sentido dos ditos e destes nas músicas analisadas, revelam compressões das relações de CAUSA EFEITO, MUDANÇA, IDENTIDADE, ANALOGIA DESANALOGIA e TEMPO, devido, sobretudo, ao papel que os ditos desempenham ao ilustrar cenas da vida das pessoas. Entre as metáforas que estruturam os ditos, nas interações e nas músicas, encontram-se A VIDA É UMA VIAGEM / A VIDA É UM TRAJETO QUE DEVE SER PERCORRIDO COM CAUTELA / VIDA É UM JOGO DE AZAR; TEMPO É LOCAL PARA ONDE ALGO SE DESLOCA; DIFICULDADES SÃO IMPEDIMENTOS (IN) TRANSPONÍVEIS; RELIGIÃO É UMA TRANSAÇÃO COMERCIAL; MORAL É UM OBJETO PRECIOSO (MAS FRÁGIL COMO O VIDRO); EXAGEROS SÃO GOLPES INCERTOS. Espera-se que a hipótese aventada com este estudo motive outras pesquisas sob o escopo teórico da Linguística Cognitiva; em especial, as teorias da metáfora e da mesclagem conceptual, as quais revelaram um potencial descritivo promissor para análise de fenômenos semântico-pragmáticos da língua portuguesa, como os ditos populares, construções situadas no topo da escala de idiomaticidade