Generalized FVDAM Theory for Periodic Materials Undergoing Finite Deformations—Part II: Results

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Displacement Field ◽  
Computer Code ◽  
Biological Tissues ◽  
Order Theory ◽  
Substantial Improvement ◽  
Higher Order ◽  
Finite Deformations ◽  
Stress Distributions ◽  
Field Representation ◽  
Periodic Materials

In Part I, a generalized finite-volume direct averaging micromechanics (FVDAM) theory was constructed for periodic materials with complex microstructures undergoing finite deformations. The generalization involves the use of a higher-order displacement field representation within individual subvolumes of a discretized analysis domain whose coefficients were expressed in terms of surface-averaged kinematic variables required to be continuous across adjacent subvolume faces. In Part II of this contribution we demonstrate that the higher-order displacement representation leads to a substantial improvement in subvolume interfacial conformability and smoother stress distributions relative to the original theory based on a quadratic displacement field representation, herein called the 0th order theory. This improvement is particularly important in the finite-deformation domain wherein large differences in adjacent subvolume face rotations may lead to the loss of mesh integrity. The advantages of the generalized theory are illustrated through examples based on a known analytical solution and finite-element results generated with a computer code that mimics the generalized theory's framework. An application of the generalized FVDAM theory involving the response of wavy multilayers confirms previously generated results with the 0th order theory that revealed microstructural effects in this class of materials which are important in bio-inspired material architectures that mimic certain biological tissues.

Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part II: Results

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Element ◽  
Finite Volume ◽  
Displacement Field ◽  
Solid Mechanics ◽  
Order Theory ◽  
Substantial Improvement ◽  
Higher Order ◽  
Stress Distributions ◽  
Field Representation ◽  
First Order Theory

In Part I, a generalized finite-volume theory was constructed for two-dimensional elasticity problems on rectangular domains based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain. The higher-order displacement field was expressed in terms of elasticity-based surface-averaged kinematic variables that were subsequently related to corresponding static variables through a local stiffness matrix derived in closed form. The theory was constructed in a manner that enables systematic specialization through reductions to lower-order versions, including the original theory based on a quadratic displacement field representation, herein called the zeroth-order theory. Comparison of predictions generated by the generalized theory with its predecessor, analytical and finite-element results in Part II illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability. While in certain instances the first-order theory produces acceptably smooth stress distributions, concentrated loadings require the second-order (generalized) theory to reproduce stress and displacement fields with fidelity comparable to analytical and finite-element results.

Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part I: Framework

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Volume ◽  
Displacement Field ◽  
Stiffness Matrix ◽  
Solid Mechanics ◽  
Substantial Improvement ◽  
Higher Order ◽  
Standard Theory ◽  
Equilibrium Equations ◽  
Field Representation ◽  
Local Stiffness

A generalized finite-volume theory is proposed for two-dimensional elasticity problems on rectangular domains. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in our standard theory. The higher-order displacement field is expressed in terms of elasticity-based surface-averaged kinematic variables, which are subsequently related to corresponding static variables through a local stiffness matrix derived in closed form. The novel manner of defining the surface-averaged kinematic and static variables is a key feature of the generalized finite-volume theory, which provides opportunities for further exploration. Satisfaction of subvolume equilibrium equations in an integral sense, a defining feature of finite-volume theories, provides the required additional equations for the local stiffness matrix construction. The theory is constructed in a manner which enables systematic specialization through reductions to lower-order versions. Part I presents the theoretical framework. Comparison of predictions by the generalized theory with its predecessor, analytical and finite-element results in Part II illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 697-707 ◽  
Author(s):  
J. Aboudi ◽  
M.-J. Pindera ◽  
S. M. Arnold
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Local Stress ◽  
Computer Code ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Infinite Matrix ◽  
Homogenization Technique ◽  
Higher Order Theory

A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material’s periodic microstructure. The model’s analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model’s predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

Generalized FVDAM Theory for Periodic Materials Undergoing Finite Deformations—Part I: Framework

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Marcio A. A. Cavalcante ◽  
Marek-Jerzy Pindera
Keyword(s):  
Finite Volume ◽  
Finite Deformation ◽  
Large Deformations ◽  
Finite Deformations ◽  
Stress Concentrations ◽  
Field Representation ◽  
Deformation Features ◽  
Elasticity Problems ◽  
Periodic Materials ◽  
Artificial Stress

The recently constructed generalized finite-volume theory for two-dimensional linear elasticity problems on rectangular domains is further extended to make possible simulation of periodic materials with complex microstructures undergoing finite deformations. This is accomplished by embedding the generalized finite-volume theory with newly incorporated finite-deformation features into the 0th order homogenization framework, and introducing parametric mapping to enable efficient mimicking of complex microstructural details without artificial stress concentrations by stepwise approximation of curved surfaces separating adjacent phases. The higher-order displacement field representation within subvolumes of the discretized unit cell microstructure, expressed in terms of elasticity-based surface-averaged kinematic variables, substantially improves interfacial conformability and pointwise traction and nontraction stress continuity between adjacent subvolumes. These features enable application of much larger deformations in comparison with the standard finite-volume direct averaging micromechanics (FVDAM) theory developed for finite-deformation applications by minimizing interfacial interpenetrations through additional kinematic constraints. The theory is constructed in a manner which facilitates systematic specialization through reductions to lower-order versions with the 0th order corresponding to the standard FVDAM theory. Part I presents the theoretical framework. Comparison of predictions by the generalized FVDAM theory with its predecessor, analytical and finite-element results in Part II illustrates the proposed theory's superiority in applications involving very large deformations.

scholarly journals Thermal Buckling of Angle-Ply Laminated Plates Using New Displacement Function

2019 ◽  
Vol 25 (12) ◽  
pp. 96-113
Author(s):  
Ibtehal Abbas Sadiq ◽  
Widad Majeed
Keyword(s):  
Displacement Field ◽  
Equations Of Motion ◽  
Order Theory ◽  
Higher Order ◽  
Displacement Function ◽  
Thermal Buckling ◽  
Laminated Plates ◽  
Three Dimensions ◽  
Thin Plates ◽  
Aspect Ratios

ABSTRACT Critical buckling temperature of angle-ply laminated plate is developed using a higher-order displacement field. This displacement field used by Mantari et al based on a constant ‘‘m’’, which is determined to give results closest to the three dimensions elasticity (3-D) theory. Equations of motion based on higher-order theory angle ply plates are derived through Hamilton, s principle, and solved using Navier-type solution to obtain critical buckling temperature for simply supported laminated plates. Changing (α2/ α1) ratios, number of layers, aspect ratios, E1/E2 ratios for thick and thin plates and their effect on thermal buckling of angle-ply laminates are studied in detail. It is concluded that, this displacement field produces numerical results close to 3-D elasticity theory with maximum discrepancy (7.4 %).

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.

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