scholarly journals The analysis of localized effects in composites with periodic microstructure

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120373 ◽  
Author(s):  
Jacob Aboudi ◽  
Michael Ryvkin
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Single Cell ◽  
Order Theory ◽  
Higher Order ◽  
Thermomechanical Coupling ◽  
Transform Domain ◽  
Periodic Microstructure ◽  
Periodic Composite ◽  
Higher Order Theory

Several methods for the analysis of composite materials with periodic microstructure in which localized effects (such as concentrated loads, cracks and stationary/progressive damage) occur are resented. Owing to the loss of periodicity caused by these localized effects, it is no longer possible to identify and analyse a repeating unit cell that characterizes the periodic composite. For elastostatic problems, these methods are based on the combination of the representative cell method (RCM), the higher-order theory for functionally graded materials and often the high-fidelity generalized method of cells (HFGMC) micromechanical model. For elastodynamic problems, the combination of the dynamic RCM with a theory for wave propagation in heterogeneous media is used for the prediction of the time-dependent response of the periodic composite with localized effects. In the framework of the RCM, the problem for a periodic composite that is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher-order theory and the theory of wave propagation in composites, the resulting governing equations and interfacial conditions in the transform domain are solved by dividing the single cell into subcells and imposing the latter in an average (integral) sense. The HFGMC is often used for the prediction of the proper far-field boundary conditions based on the response of the unperturbed composite. The inverse of the Fourier transform provides the real elastic field at any point of a composite with localized effects. This research summarizes a series of investigations for the prediction of the behaviour of periodic composites with localized loading, fibre loss, damage and cracks subjected to static and dynamic loadings under isothermal and full thermomechanical coupling conditions.

Field distributions in piezoelectric composites with semi-infinite cracks

2016 ◽  
Vol 28 (4) ◽  
pp. 547-562 ◽  
Author(s):  
Jacob Aboudi
Keyword(s):  
Fourier Transform ◽  
Single Cell ◽  
Order Theory ◽  
Piezoelectric Composite ◽  
Piezoelectric Composites ◽  
Cell Method ◽  
Representative Cell ◽  
The Fourier Transform ◽  
Higher Order Theory ◽  
Electromechanical Field

A method is offered for the prediction of the electromechanical field in periodic piezoelectric composites with embedded semi-infinite cracks. It is based on the knowledge of the K-field in piezoelectric materials in which the material constants are replaced by the effective moduli of the piezoelectric composite. In addition to the existing semi-infinite crack, the proposed method can analyze localized inhomogeneities near the crack tip. The established effective K-field is applied at the boundaries of a rectangular domain that should be sufficiently far away from the crack tip and the other inhomogeneities. The proposed approach is based on the combined utilization of a micromechanical analysis, the representative cell method and the higher-order theory. The micromechanical analysis establishes the effective electromechanical constants of the piezoelectric composite, and the representative cell method reduces the periodic composite that is discretized into numerous identical cells to a single cell problem in the Fourier transform domain. The governing equations and constitutive relations that are formulated in this single cell are solved by employing the higher-order theory where discretization into subcells is employed. The inverse of the Fourier transform provides the electromechanical field at any point in the composite. The proposed approach is verified for crack fronts that are parallel and perpendicular to the poling direction (axis of symmetry). Applications are given for a cracked porous piezoelectric material, cracks that have been arrested by cavities and for a periodically bilayered composite with a semi-infinite crack.

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

2022 ◽  
pp. 1045389X2110721
Author(s):  
Mahmoud Askari ◽  
Eugenio Brusa ◽  
Cristiana Delprete
Keyword(s):  
Wave Propagation ◽  
Free Vibration ◽  
Analytical Solutions ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Fg Plates ◽  
Higher Order Theory

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

The behavior of cracked multiferroic composites: Fully coupled thermo-electro-magneto-elastic analysis

2018 ◽  
Vol 29 (15) ◽  
pp. 3037-3054 ◽  
Author(s):  
Jacob Aboudi
Keyword(s):  
Single Cell ◽  
Order Theory ◽  
Transform Domain ◽  
Scale Analysis ◽  
Thermal Coupling ◽  
Governing Equations ◽  
Cell Method ◽  
Representative Cell ◽  
Higher Order Theory ◽  
Fully Coupled

The response of cracked multiferroic composites that are subjected to thermo-electro-magneto-elastic loading is established by employing a two-scale analysis. To that end, the fully coupled constitutive and governing equations are utilized in the analysis. This form a generalization of a one-way thermal coupling analysis in which the electro-magneto-elastic field does not affect the thermal field. The micro-scale analysis is based on a micromechanical model which is capable of predicting the effective stiffness tensor of the undamaged multiferroic composite as well as the concentration tensors which enable the computation of the local field from the applied thermo-electro-magneto-elastic far-field. The macro-scale analysis provides the response of the cracked composite of periodic microstructure to the applied loading. It is based on the combined use of the representative cell method and the higher order theory. In the framework of the representative cell method, the problem for a periodic composite which is discretized into numerous identical cells is reduced to a problem of a single cell in the discrete Fourier transform domain. In the framework of the higher order theory, the governing equations and interfacial and periodic conditions formulated in the transform domain are solved by dividing the single cell into several subcells and imposing these conditions in an average (integral) sense. Results exhibit the responses caused by the application of mechanical, electric, magnetic, thermal, and heat flow loadings on two types of cracked periodically layered composites and provide comparisons between the predictions of the full and one-way thermal coupling analyses.

Consciousness, Metacognition, & Perceptual Reality Monitoring

2019 ◽  
Author(s):  
Hakwan Lau
Keyword(s):  
Epistemic Justification ◽  
Order Theory ◽  
Higher Order ◽  
Belief Formation ◽  
Reality Monitoring ◽  
Conscious Perception ◽  
Brute Fact ◽  
Higher Order Theory ◽  
Subjective Level

I introduce an empirically-grounded version of a higher-order theory of conscious perception. Traditionally, theories of consciousness either focus on the global availability of conscious information, or take conscious phenomenology as a brute fact due to some biological or basic representational properties. Here I argue instead that the key to characterizing the consciousness lies in its connections to belief formation and epistemic justification on a subjective level.

Dual Aspect Theory

2018 ◽  
Author(s):  
J. Christopher Maloney
Keyword(s):  
Phenomenal Character ◽  
Order Theory ◽  
Higher Order ◽  
Normal Variation ◽  
Perceptual Representations ◽  
Order Representation ◽  
Management Conflicts ◽  
Higher Order Theory

Carruthers proposes a subtle dispositionalist rendition of higher order theory regarding phenomenal character. The theory would distinguish unconscious movement management from conscious attitude management as perceptual processes. Each process takes perceptual representations as inputs. A representation subject to attitude management is apt to induce a higher order representation of itself that secures a self-referential aspect of its content supposedly determinative of phenomenal character. Unfortunately, the account requires a problematic cognitive ambiguity while failing to explain why attitude, but not movement, management, determines character. Moreover, normal variation in attitudinal management conflicts with the constancy typical of phenomenal character. And although an agent denied perceptual access to a scene about which she is otherwise well informed would suffer no phenomenal character, dispositionalist theory entails otherwise. Such problems, together with the results of the previous chapters, suggest that, whether cloaked under intentionalism or higher order theory, representationalism mistakes content for character.

Higher Order Theory

2018 ◽  
Author(s):  
J. Christopher Maloney
Keyword(s):  
Phenomenal Character ◽  
Order Theory ◽  
Higher Order ◽  
Cognitive State ◽  
Unconscious Perception ◽  
Higher Order Theory ◽  
Order State

Rosenthal's rendition of representationalism denies intentionalism. His higher order theory instead asserts that a perceptual state's phenomenal character is set by that state's being related to, because represented by, another, but higher order, cognitive state. The theory arises from the doubtful supposition of unconscious perception and mistakenly construes intrinsic phenomenal character extrinsically, as one state's serving as the content of another. Yet it remains mysterious how and why a higher order state might be so potent as to determine phenomenal character at all. Better to resist higher order theory’s embrace of dubious unconscious perceptual states and account for states so-called simply in terms of humdrum mnemonic malfeasance. Moreover, since the suspect theory allows higher order misrepresentation, it implies sufferance of impossible phenomenal character. Equally problematic, representationalism pitched at the higher order entails the existence of bogus phenomenal character when upstairs states represent downstairs nonperceptual states.

Seeming to Seem

2018 ◽  
Author(s):  
David Rosenthal
Keyword(s):  
Mental States ◽  
Order Theory ◽  
Higher Order ◽  
Psychological State ◽  
Intentional Stance ◽  
First Person ◽  
Psychological States ◽  
Third Person ◽  
Higher Order Theory ◽  
The Third Person

Dennett’s account of consciousness starts from third-person considerations. I argue this is wise, since beginning with first-person access precludes accommodating the third-person access we have to others’ mental states. But Dennett’s first-person operationalism, which seeks to save the first person in third-person, operationalist terms, denies the occurrence of folk-psychological states that one doesn’t believe oneself to be in, and so the occurrence of folk-psychological states that aren’t conscious. This conflicts with Dennett’s intentional-stance approach to the mental, on which we discern others’ mental states independently of those states’ being conscious. We can avoid this conflict with a higher-order theory of consciousness, which saves the spirit of Dennett’s approach, but enables us to distinguish conscious folk-psychological states from nonconscious ones. The intentional stance by itself can’t do this, since it can’t discern a higher-order awareness of a psychological state. But we can supplement the intentional stance with the higher-order theoretical apparatus.

Sign in / Sign up

Export Citation Format

Share Document