A variational approach to nonlinear electro-magneto-elasticity: Convexity conditions and existence theorems

2017 ◽  
Vol 23 (6) ◽  
pp. 907-928 ◽  
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Smart Materials ◽  
Existence Theorems ◽  
Deformation Gradient ◽  
Minimum Energy ◽  
Electric Displacement ◽  
The Body ◽  
Simultaneous Occurrence ◽  
Dimension 2 ◽  
The Cross ◽  
Convexity Conditions

Electro- or magneto-sensitive elastomers are smart materials whose mechanical properties change instantly by the application of an electric or magnetic field. This paper analyses the convexity conditions (quasiconvexity, polyconvexity, ellipticity) of the free energy of such materials. These conditions are treated within the framework of the general A-quasiconvexity theory for the constraints [Formula: see text] where F is the deformation gradient, d is the electric displacement and b is the magnetic induction. If the energy depends separately only on F, or on d, or on b, the A-quasiconvexity reduces, respectively, to Morrey’s quasiconvexity, polyconvexity and ellipticity conditions or to convexity in d or in b. In the present case, the simultaneous occurrence of F, d and b leads to the cross-phenomena: mechanic–electric, mechanic–magnetic and electro–magnetic. The main results of the paper are as follows. In dimension 3 there are 32 linearly independent scalar A-affine functions (and 15 in dimension 2) corresponding to the constraints (*). Therefore, an energy function ψ ( F, d, b) is A-polyconvex if and only if it is of the form [Formula: see text] where Φ is a convex function (of 31 scalar variables). Apart from the expected terms F, cof F, det F, d and b, we have the cross-effect terms Fd, Fb (and in dimension 2 also d × b). An existence theorem is proved for a state of minimum energy for a system consisting of an A-polyconvex electro-magneto-elastic solid plus the vacuum electromagnetic field outside the body.

Isotropic polyconvex electromagnetoelastic bodies

2018 ◽  
Vol 24 (3) ◽  
pp. 738-747
Author(s):  
M Šilhavý
Keyword(s):  
Magnetic Field ◽  
Mechanical Properties ◽  
Electromagnetic Field ◽  
Smart Materials ◽  
Equilibrium Solution ◽  
Deformation Gradient ◽  
Electric Displacement ◽  
The Body ◽  
Sufficient Condition ◽  
Energy Functions

The recent renewal of interest in nonlinear electromagnetoelastic interactions comes from the technological importance of electro- or magnetosensitive elastomers, smart materials whose mechanical properties change instantly on the application of an electric or magnetic field. We consider materials with free energy functions of the form [Formula: see text], where F is the deformation gradient, d is the electric displacement, and b is the magnetic induction. It was recently shown by the author that such an energy function is polyconvex if and only if it is of the form [Formula: see text] where [Formula: see text] is a convex function (of 31 scalar variables). Moreover, an existence theorem was proved for the equilibrium solution for a system consisting of a polyconvex electromagnetoelastic solid plus the vacuum electromagnetic field outside the body. The condition (8), is not just the combination of Ball’s polyconvexity of elastomers [Formula: see text] with the convexity in the electromagnetic variables. The differential constraints div [Formula: see text], div [Formula: see text] allow for the cross mechanical–electric and mechanical–magnetic terms Fd and Fb which substantially enlarge the class of energies covered by the theory. The result (*), applies to a material of any symmetry; this paper analyzes the condition in the case of isotropic materials. A broad sufficient condition for the polyconvexity is given in that case. Further, it is shown that the commonly used isotropic electroelastic or magnetoelastic invariants are polyconvex except for the biquadratic ones; the paper explicitly determines their quasiconvex envelopes and shows that they are polyconvex.

scholarly journals Petiole-Lamina Transition Zone: A Functionally Crucial but Often Overlooked Leaf Trait

Plants ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 774
Author(s):  
Max Langer ◽  
Thomas Speck ◽  
Olga Speck
Keyword(s):  
Transition Zone ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Body Plan ◽  
The Body ◽  
Vascular Bundles ◽  
Cross Sectional ◽  
Thin Sections ◽  
Transition Zones ◽  
The Cross

Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans (monocotyledons vs. dicotyledons) and spatial arrangements of petiole and lamina (two-dimensional vs. three-dimensional configurations). Cross-sectional geometry and tissue arrangement of petioles and transition zones were investigated via serial thin-sections and µCT. The changes in the cross-sectional geometries from the petiole to the transition zone and the course of the vascular bundles in the transition zone apparently depend on the spatial arrangement, while the arrangement of the vascular bundles in the petioles depends on the body plan. We found an exponential acropetal increase in the cross-sectional area and axial and polar second moments of area to be the defining characteristic of all transition zones studied, regardless of body plan or spatial arrangement. In conclusion, a variety of terms is used in the literature for describing the region between petiole and lamina. We prefer the term “petiole–lamina transition zone” to underline its three-dimensional nature and the integration of multiple gradients of geometry, shape, and size.

Embodied interactions: Towards an exploration of the expressive and narrative potential of performance costume through wearable technologies

Scene ◽  
2014 ◽  
Vol 2 (1) ◽  
pp. 179-196 ◽  
Author(s):  
Sofia Pantouvaki
Keyword(s):  
Smart Materials ◽  
Costume Design ◽  
The Body ◽  
Wearable Electronics ◽  
Live Performance ◽  
Wearable Technologies ◽  
Opening Ceremony ◽  
Interactive Interfaces ◽  
Specific Fragment

The use of smart materials and wearable electronics has rapidly expanded in the field of fashion, introducing new interactive qualities of surfaces, materials and garments. In fashion garments, the performative environment functions as an abstract site for experimentation, expression and communication of the wearer through the intelligent garment. However, there is still limited use of embodied technologies in the field of performance costume for text-based and music-based performance, with the exception of integrated lighting technologies, currently broadly used in musical performance. This article provides a critical review of specific examples of technology-led garments in live performance, and uses a specific fragment from the Athens 2004 Olympic Games Opening Ceremony as a case study to highlight how technologies embedded in costume can create interactive interfaces between the body of the performer and the environment – the space, the other performers, the audience – becoming a transmitter and receiver of emotions, experiences and meanings in innovative ways. By analysing this case, as well as by posing questions, this article aims at generating a discourse on the expressive and narrative potential of the use of intelligent materials and embodied technologies within the creative practice of costume design.

The Easter Sepulchrum in its Relation to the Architecture of the High Altar

PMLA ◽  
1916 ◽  
Vol 31 (4) ◽  
pp. 664-712
Author(s):  
John K. Bonnell
Keyword(s):  
Middle Ages ◽  
Tenth Century ◽  
The Body ◽  
Good Friday ◽  
The Cross ◽  
The Middle Ages

By the term ‘sepulehrum’ is designated that device or structure employed in churches—especially in the middle ages—to symbolize, or in more complete manner to represent, the tomb of Christ. This sepulchrum, so named in the liturgy, first appears in connection with the ancient office of the Depositio Crucis, or burial of the cross, which after mass on Good Friday typified the burial of Christ. Complementing and completing the Depositio was another office, privately celebrated by the priest and clergy before matins on Easter Sunday, typifying the resurrection, and called the Elevatio Crucis. When, after the tenth century, troping of the Introit for Easter morning—the famous Quem Quaeritis—developed into a little liturgical play with the impersonation of the angel or angels, and of the three Maries coming to anoint the body of the Lord, there was naturally a development of the heretofore symbolic sepulchrum in the altar, into what resulted finally in a separate structure.

scholarly journals Stretching Out Life, Maintaining the Body: Part I - Vayas in Medical Literature

2017 ◽  
Vol 5 (2) ◽  
pp. 37-65
Author(s):  
Christèle Barois
Keyword(s):  
Old Age ◽  
Medical Literature ◽  
Human Life ◽  
Body Part ◽  
The Body ◽  
The Cross ◽  
Medieval India

The representation of the process of human life is at the heart of questions about longevity, rejuvenation practices and possibly those which aim at immortality. The key term for “age” in medieval India is vayas, which means “vigour”, “youth” or even  “any period of life”, that is to say  exactly the same meaning as ours (duration of life). As a criterion for the examination of the patient, vayas is invariably divided into three periods: childhood, intermediate age and old age, precisely defined in the ayurvedic saṃhitās. It seems that vayas might be a relevant gateway to the cross-disciplinary understandings of age in medieval India, and therefore to the conditions of its (relative) mastery.  

“Beautiful on the Cross, Beautiful in His Torments”: The Place of the Body in the Thought of Paschasius Radbertus

Traditio ◽  
2005 ◽  
Vol 60 ◽  
pp. 1-46
Author(s):  
David Appleby
Keyword(s):  
Image Of God ◽  
The Body ◽  
The People ◽  
The Cross ◽  
Literary Portrait ◽  
The Image Of God ◽  
Mind's Eye

In his literary portrait of Abbot Adalhard, written soon after the abbot's death in 826, Paschasius Radbertus of Corbie compared his subject's moral and spiritual progress to the method of the ancient painter Zeuxis as this had been described in Cicero'sDe inventione.According to Cicero, the people of Cortona commissioned Zeuxis to decorate a temple with the image of Helen, who was reputed to be the most beautiful of mortal women. Because nature withheld overall perfection from any individual, Zeuxis studied several handsome models and combined the best features of each in an image that was more perfect than the form of any actual maiden. Adalhard too was an artist who sought to realize a work that somehow went beyond nature, but in his case the objective was a reformation of the image of God in himself. To achieve this, Adalhard too used models, in his case the lives and deeds of the saints, whose examples of virtue he discerned with the mind's eye and assimilated in an effort to resemble the transcendent archetype.

Paper 7. Unsteady Flow around a Slender Fish-Like Body

1972 ◽  
Vol 14 (7) ◽  
pp. 43-52 ◽  
Author(s):  
Th. Y. Wu ◽  
J. N. Newman
Keyword(s):  
Unsteady Flow ◽  
Theoretical Calculations ◽  
Cross Flow ◽  
Vortex Sheet ◽  
The Body ◽  
Dynamic Force ◽  
Cross Sectional ◽  
Vortex Sheets ◽  
Flat Fish ◽  
The Cross

This paper attempts to extend some recent theoretical calculations on the unsteady flow generated by body movements of a slender ‘flat’ fish by further including the effect of finite body thickness in the consideration for various configurations of side and caudal fins as major appendages. Based on the slender-body approximation, the cross-flow is determined for different longitudinal body sections which are characterized by a variety of cross-sectional shapes and flow conditions (such as having smooth or fin-edged body contours, with or without vortex sheets alongside the body section). The effect of body thickness is found to arise primarily from its interaction with the vortex sheet already existing in the cross-flow. New results for the transverse hydro-dynamic force acting on the body are obtained, and their physical significances are discussed.

scholarly journals Purification of the Body and the Reign of God in the Gospel of Mark

2020 ◽  
Vol 71 (1) ◽  
pp. 62-89
Author(s):  
Elizabeth E Shively
Keyword(s):  
Gospel Of Mark ◽  
The Body ◽  
Theology Of The Cross ◽  
Human Mortality ◽  
God's People ◽  
Bodily Resurrection ◽  
The Dead ◽  
The Cross ◽  
Reign Of God

Abstract The thesis of this study is that the Markan Jesus’ activities of healing and exorcisms are evocative of resurrection of the body. Through the accumulation of these stories Mark communicates that Jesus has come to address the problem of human mortality in the light of the nearness of God’s reign. These activities anticipate Jesus’ resurrection from the dead, which pioneers the purification of the body at the turn of the ages. I show that Mark’s presentation of Jesus’ healings and exorcisms crucially reflects ideas of (im)purity in Jewish scripture and tradition that are bound up with mortality. In the light of this background, I show that Mark presents Jesus’ healings and exorcisms as anticipations of his bodily resurrection. These resurrection-type stories depict the movement from the mortality incurred by defiling diseases or defiling spirits to the immortality of God’s reign. The repetition of resurrection-type healings that eventually culminate in Jesus’ own resurrection suggests that the announcement of God’s reign is not only about responding to the call for repentance from sin (1:14–15), but also about having one’s body raised. Thus, Mark presents not only a theology of the cross, but also a theology of the resurrection as the purification of God’s people.

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