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roelectricity and supersets

zoelectricity, a link between electrical and mechanical response, is exhibited by a large number of ceramic materials,uding the quartz used to measure time in watches and other electronics. Such devices use both properties ofzoelectrics, using electricity to produce a mechanical motion (powering the device) and then using this mechanicaltion to produce electricity (generating a signal). The unit of time measured is the natural interval required for electricitybe converted into mechanical energy and back again.

e piezoelectric effect is generally stronger in materials that also exhibit pyroelectricity, and all pyroelectric materials areo piezoelectric. These materials can be used to inter convert between thermal, mechanical, or electrical energy; forance, after synthesis in a furnace, a pyroelectric crystal allowed to cool under no applied stress generally builds up aic charge of thousands of volts. Such materials are used in motion sensors, where the tiny rise in temperature from am body entering the room is enough to produce a measurable voltage in the crystal.

urn, pyroelectricity is seen most strongly in materials which also display the ferroelectric effect, in which a stable electricole can be oriented or reversed by applying an electrostatic field. Pyroelectricity is also a necessary consequence ofoelectricity. This can be used to store information in ferroelectric capacitors, elements of ferroelectric RAM. 

e most common such materials are lead zirconate titanate and barium titanate. Aside from the uses mentioned above,r strong piezoelectric response is exploited in the design of high-frequency loudspeakers, transducers for sonar, and

uators for atomic forceand scanning tunneling microscopes. 

roelectricity is a property of certain materials which possess a spontaneous electric polarization that can be reversed

he application of an external electric field.[1][2] The term is used in analogy to ferromagnetism, in which a material

ibits a permanentmagnetic moment. Ferromagnetism was already known when ferroelectricity was discovered in 1920

Rochelle salt by Valasek.[3]Thus, the prefix ferro , meaning iron, was used to describe the property despite the fact that

st ferroelectric materials do not contain iron.

art materials or designed materials are materials that have one or more properties that can be significantly changedcontrolled fashion by external stimuli, such as stress, temperature, moisture, pH, electric or magnetic fields.

ere are a number of types of smart material, some of which are already common. Some examples are as following:

Piezoelectric materials are materials that produce a voltage when stress is applied. Since this effect also applies in thereverse manner, a voltage across the sample will produce stress within the sample. Suitably designed structures maderom these materials can therefore be made that bend, expand or contract when a voltage is applied.

Shape memory alloys and shape memory polymers are materials in which large deformation can be induced andrecovered through temperature changes or stress changes (pseudoelasticity). The large deformation results due tomartensitic phase change.

Magnetostrictive materials exhibit change in shape under the influence of magnetic field and also exhibit change in their

magnetization under the influence of mechanical stress.Magnetic shape memory alloys are materials that change their shape in response to a significant change in themagnetic field.

pH-sensitive polymers are materials that change in volume when the pH of the surrounding medium changes.

Temperature-responsive polymers are materials which undergo changes upon temperature.

Halochromic materials are commonly used materials that change their colour as a result of changing acidity. Onesuggested application is for paints that can change colour to indicate corrosion in the metal underneath them.

Chromogenic systems change colour in response to electrical, optical or thermal changes. These

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Basically, there is no standard definition for smart materials, and the term smart

material is generally defined as a material that can change one or more of its

properties in response to an external stimulus (Harrison JS & Oun aies Z, 2001). For

example, the shape of th e material will change in response to different temperature or

application of electrical charge or presenting of magnetic field. In gener al, it can be

catalogued to three main groups, which are thermo-to-mechanical,

electrical-to-mechanical and magnetic-to-mechanical. In the other hand, there are

some materials which termed as “smart material” do not have the properties stated  

above, like the material with self-healing property is also termed as “smart material”. 

Therefore, smart material can also be expressed as a material that can perform a

special action in response to some specific condition such as very high/low

temperature, high stress, very high/low pH value, even material failure, etc.

1.2 Background 

Materials have a strong relationship with aerospace industry, as it always determines

the weight, strength, efficiency, cost and difficu lty of maintenan ce of an aircraft.

Therefore, the discovery of new material usually mak es a breakthrough in

performance of an aircraft. Especially the findings of smart materials, it makes an

innovation in aircraft because it can provide a special function or property.

Accordingly, the smart materials receive a great attention in order to improve the

performance o f aircraft.

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1.3 History of smart materials 

Actually, most of smart materials have been discovered around 50 years ago, but they

were not applied to aerospace industry yet. As the demand of smart structure of 

aircraft is increasing significantly, en gineers started to focus on the application of 

smart materials on aerospace industry. Accordingly, the attention of smart material has

been increasing continuously since the past decade (Monner HP 2005). By now, they

have been widely applied in aircrafts to improve their performance. For example, a

simply structured smart material actuator can r eplace the heavy, multi-components

structured actuator according to redu ce the weight and difficulty of maintenance.

Moreover, the fast r esponse in electro-to-mechanical effect of some smart material

achieves an excellent result of vibration/noise control.

1.4 Significance 

Studying of the smart materials is a key to make the innovation of aerospace industry.

The reason is the conventional automatic system has several limitations comparing to

the smart system. The limitations are multiple energ y conversions, large number of 

parts, high vulnerability (especially h ydraulic network) and narrower frequency

bandwidth (Yousefi-Koma A & Zimcik DG, 2003). Accordingly, the conventional

system has a larger weight, size and potential failure. In contr ast, smart actuators, e.g.

electrical-to-mechanical type, are much more efficient because the electricity is

directly converse to actuation and transmitting speed of electricity is much high er.

Moreover, the compact size and light weight of smart actuators will not give much

loading or r estriction to structure of aircraft, thus a higher freedom is given to the

aircraft design. Therefo re, studying smart material is necessary for improving

aircrafts’ performance. 

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2. Piezoelectric Materials 

2.1 Properties of piezoelectric materials 

Among different types of smart material, piezoelectric material is widely used

because of the fast electromechanical response, wide bandwidth, high generative

force and relatively lo w power r equirements (Harrison JS and Ounaies Z, 2001).

There are two main types of piezoelectric materials are applied as smart material,

which are piezoelectric ceramic and polymer. According to Harrison and Ounaies, the

classic definition of piezoelectricity is the gen eration of electricity polarization in a

material due to the mechanical stress. It is called as direct effect. Also, the

piezoelectric material has a converse effect that a mechanical deformation will happen

if an electrical charge or signal is applied. Accordingly, it can b e a sensor to detect the

mechanical stress b y direct effect. Altern atively, a significant increase of size due to

the electrical charge can be an actuator.

2.2 Theorem of Piezoelectric materials 

Basically, piezoelectric materials are a transducer between electricity and mechanical

stress. The piezoelectric material has this effect because of its crystallized structure.

For the crystal, each molecule has a polarization; it means one end is more negatively

charged while the other end is more positively charged, and it is called dipole.

Furthermore, it directly affects how the atoms make up the molecule and how the

molecules are shaped. Therefore, the basic concept of piezoelectricity is to change the

orientation of polarization of the molecules (RERC, 2007).

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To illustrate clearly, a p olar axis is imaginatively set in a molecule that run through

the center of two different charges. Regarding the orientation of polar axis, the crystal

can be divided into two types which ar e monocrystal and polycrystal (RERC, 2007).

The monocrystal means that all the molecules’ polar axes are oriented in the same 

direction (Figure 2.1), and the polycrystal means that the polar axis of the molecules

are randomly o riented (Figure 2.2).

Figure 2.1 Figure 2.2

For piezoelectric material, the crystal is in form of polycrystal initially and the crystal

is connected with the electrodes. By applying the electric ch arge to the polycrystal, it

almost become the monocrystal, accordingly the sharp will change which is shown as

the converse piezoelectric effect (Figure 2.3).

Figure 2.3

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In order to different direction of applied stress or charge, it will have different

outcome which is shown in figure 2.4 (RERC, 2007). In (a), it is the initial state of the

piezoelectric material. For (b), a compressive force is applied to the material, then the

polarity current will flow in the same direction with polar axis. Conversely, it will

have the opposite polarity current if it is in tension. In (c), it shown that the applied

opposite polarity current will result in elongation. Also, the same direction of polarity

voltage, (d), will result in compression. Finally, (e), a vibration will happen if the AC

signal is applied, furthermore, their frequency will be the same.

Figure 2.4

2.3 Performance of piezoelectric material 

For different piezoelectric material, they have the differ ent performance and

application. In these piezoelectric materials, PZT, Lead Zironate Titanate, should be

the most popular. Because it can perform both the direct and conserve piezoelectric

effect, thus it can be used as a sensor and actuator. Besides that, it can apply the

longitudinal, transversal and shear deformation. Therefo re, it can be widely used in

different applications. Moreover, it is flex ible, light in weight and cost effective. In

general, it is used as actuator and vibration reducing device. The performance of PZT

is shown in next page:

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Material Young’s Max Density, Operating Blocking Volumetri Gravimetric

modulus, actuator g/cm3 frequency stress, work per work per

Gpa strain, at Max Mpa cycle, cycle, J/kg

m/m strain, Hz J/cm3

PZT 50-70 0.12-0.18 7.6 100000 72 0.0108 1.42

(Source from: http://rerc.icu.ac.kr/UploadFile/DOC/pzt_device_app_manual.pdf)

2.4 Application of piezoelectric material 

The material always influences the weight, service life, function and strength of the

aircraft. Hence discovery of new material is usually respecting an innovation in

aerospace industry. Regarding the application of piezoelectric material, there are two

main functions which are shape control and vibration control.

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2.4.1 Aerodynamic feature 

In term of shape changing, it means the changing of aerodynamic feature.

Conventionally, the aircrafts’ control surface is still controlled indirectly and lack of  

flexibility. However, the piezoelectric actuator can perform an innovative mechanism

of control system; it greatly increases the perfor mance and maneuverability due to

flexible, efficient and thin actuator.

2.4.2 Vibration control 

Regarding vibration, it is an unwanted effect in aircraft because it can contribute to

stress concentration, material fatigue, shortening service life, efficiency reduction and

noise. Obviously, these problems influence the safety and maintenance cost sharply.

Besides, the noise problem is always considered, especially the passen gers’ aircraft, as 

the noise is a great annoyance. Th erefore, the engineers always want to minimize the

vibration. Conventionally, it is difficult to provide a p recise active damping which

produces a vibration with anti-resonance frequency. By the piezoelectric material, it

can be used as sensor and actuator at the same time, so it has a fast enou gh response

to produce the anti-reson ance vibration (the mechanism of vibration is shown in fig.

2.4f). Furthermore, it is flexible, small and thin to be applied in many parts of aircr aft.

2.4.3 Adaptive smart wing 

Conventionally, the flap, rudder and elevator are adjusted by electronic motor or

mechanical control system like cable or hydraulic system. By applying piezoelectric

actuator, no discrete surfaces are required because the control surface can be change

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the sharp itself in order to change the aerodynamic feature (shown in Figure 2.5).

Therefore, it creates a continuous surface which will not cause early airflo w

separation hen ce to reduce the drag, but also the lift is increased due to the delay

airflow separation (Yousefi-Koma A & Zimcik DG 2003). Accordingly, it increases

the efficiency significantly.

Figure 2.5

Basically, the concept of smart wing is to construct a continuous control surface

embedded b y a series of piezoelectric actuator. Furthermore, it is required to have a

high strength-to-weight ratio; it means the actuator has to be placed strategically for

optimizing a light weight design. Finally, it should have an ability to change the shape

response to differ ent flight condition, hence the performance of cruise flight can be

improved that the conventional aircraft cannot achieve. In fact, this concept has

started to be investigated since 1990. However, the smart wing system is mainly focus

on military aircraft performance and maneuver improvement. Since 1994, this smart

wing project has been started by many industries and research centers such as US Air

Force, NASA, Northrop Grumman, Lockh eed Martin, UCLA and the Georgia

Institute of Technology (Yousefi-Koma A & Zimcik DG 2003). They constructed a

30% scale Unmanned Combat Air Vehicle (UCAV) at NASA Lan gley Research

Centre. By two wind tunnel testing, it showed that the system had a high rate, large

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deflection, conformal trailing edge control at realistic flight conditions.

2.4.4 Helicopter blade application 

For the improvement of helicopter, most of engineers focus on the eliminating

acoustic problem because it is the major problem and disadvantage. From the

theoretical and ex perimental work both in Europe and USA, it shows that the BVI

(Blade Vortex Interaction, shown in Figure 2.6) is the main source of noise,

fortunately it can be dramatically reduced, 8 to 10dB, by an app ropriate control of 

blades (Monner HP & Wierach P).

Figure 2.6

In order to solve this pro blem, there are two possible solutions. The first solution is to

construct the blade that can perform a continuous twisting. The second solution is the

servo-aerodynamic control surface like flap, tab, or blade-tip is installed on the blade

to generate aerodynamic force (Giurgiutiu, V 2000). Practically, it is difficult to install

any conventional actuator in the blades of helicopter. Howev er, the piezoelectric

actuator seems to be suitable for the blades, so it receives an extensive attention

(Giurgiutiu, V 2000).

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2.4.5 Twist blades concept 

The twist blades is a more difficult concept and it needs man y theoretical studies to

find out the twist angle to optimize the vibration elimination. However, this concept

receives many advantages such as smooth continuous deformed surface, high

aerodynamic sensitivity, excellent structural and dynamic compatibility, minor

influence of actuation forces on blade strength and no moving components involved

(Monner HP & Wierach P).

To perform the twist blades, the simple way is to embed the PZT in the blades skin. In

1997, Chen and Chopra constructed a 1:8 Froude scale composite blade with

diagonally oriented PZT wafers (shown in Figure 2.7). From the wind tunnel testing,

the twist angle at resonance frequency wer e 0.35 and 1.1

Giurgiutiu, V 2000).

Figure 2.7

According to German Aerospace Center, a BO105 model rotor blade was selected as a

demonstrator of twist blade system, the schematic graph is shown in Figure 2.8.

Comparing to the normal BO105 model rotor blade, there was a noise r eduction of 

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3dB for an active twist of 0.8 at blade tip. Furthermore, a power redu ction of 2.3% at

87m/s (Monner HP & Wierach P)

Figure 2.8

2.4.6 Rotor Blade flap 

In this concept, a discrete control surface is set on the blade. Although this concept

has less efficiency, it is a quicker-to-the-target method to perform a active control and

vibration reduction. Practically, a federally funded program at Boeing Mesa, Smart

Materials Actuation Rotor Technolo gy (SMART), is doing a full-scale demonstration

to proof the concept, and this concept can be applied to other model if it is successful

Giurgiutiu, V 2000).

In this demonstration, MD 900 bearingless rotor is used as demonstrator. “A prototype 

actuator with a two-stage amplification and bi-axial operation was constructed and

tested” (Straub  et al., 1999 in Giurgiutiu, V 2000). The schematic graph is shown in

figure 2.9.

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Figure 2.9

2.4.7 Cabin interior noise 

The noise of aircraft is a significant annoyance to the passen gers. Conventionally, the

passive damping device is used which is just capable of high frequency vibration.

However, the interior noise from vibration of fuselage and engine is low frequency

hence the passive damping device cannot perform a satisfied noise reduction.

Accordingly, an active damping device is needed and the piezoelectric material is a

suitable choice.

Basically, this noise reduction system is called Active Structural Acoustic Control

(ASAC). In this system, the piezoceramic patch actuators are used with passive

vibration insulations to optimize the capabilities (Monner HP & Wierach P). In

practice, there was a demonstration of ASAC to a full-scale aircraft. In this

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experiment, the Bombard ier Dash-8 turbo prop aircraft was used as the test model and

the result is satisfied ( Figure 2.10). There was a reduction more than 20dB at the

blade passage frequency of 61Hz (Yousefi-Koma A & Zimcik DG 2003).

Figure 2.10

2.4.8 Tail-buffet suppression 

Tail-buffet is an acute vibration caused by unsteady pressures associated with

separated flow, or vortices exciting the vibration modes of the v ertical-fin-structural

assemblies (Yousefi-Ko ma A & Zimcik DG 2003). This problem could contribute to a

high maintenance cost because frequent inspection is required, especially the high

performance aircraft. In real case, the fighters with twin-tail design, F/A-18 and F-15,

are exactly f acin g this problem. In order to keep the high standard of per formance and

safety, the piezoelectric actuator can be used to control the vibration.

To examine the effectiveness of applying piezoelectric material, the Technical

Cooperation Program (TTCP) with collaboration of Canada, USA and Australia have

done a demonstration of applying piezoelectric actuator on a full-scale F/A-18

(Yousefi-Koma A & Zimcik DG 2003). They installed the piezoelectric actuator on

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flight, and 10% at the worst case. In addition, the double durability of 

the

Applications

Main article:  Magnet#Common uses of magnets  

There are a great variety of applications of the hysteresis inferromagnets. Many of these make use of their ability to retain amemory, for example magnetic tape, hard disks, and credit cards. Inthese applications, hard magnets (high coercivity) like iron are desirableso the memory is not easily erased.

Soft magnets (low coercivity) are used as cores in electromagnets. Thenonlinear response of the magnetic moment to a magnetic field booststhe response of the coil wrapped around it. The low coercivity reducesthat energy loss associated with hysteresis.

Physical origin

Main article:  Ferromagnetism  

The phenomenon of hysteresis in ferromagnetic materials is the result oftwo effects: rotation of magnetization and changes in size or numberof magnetic domains. In general, the magnetization varies (in directionbut not magnitude) across a magnet, but in sufficiently small magnets, itdoes not. In these single-domain magnets, and the magnetizationresponds to a magnetic field by rotating. Single-domain magnets are

used wherever a strong, stable magnetization is needed (forexample, magnetic recording).

Larger magnets are divided into regions called domains . Across eachdomain, the magnetization does not vary; but between domains arerelatively thin domain walls in which the direction of magnetizationrotates from the direction of one domain to another. If the magnetic fieldchanges, the walls move, changing the relative sizes of the domains.Because the domains are not magnetized in the same direction,the magnetic moment per unit volume is smaller than it would be in a

single-domain magnet; but domain walls involve rotation of only a smallpart of the magnetization, so it is much easier to change the magnetic

the both sides of fin over a wide area (shown in Figure 2.11). In the result, itshowed

the active control was effective to reduce the amplitude up to 60% at the

nominal

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moment. The magnetization can also change by addition or subtractionof domains (called nucleation and denucleation ).

Magnetic hysteresis

Fig. 2. A plot of magnetization m

against magnetic field h

calculatedusing atheoretical model. Starting at the origin, the upward curve isthe initial magnetization curve . The downward curve after saturation,along with the lower return curve, form the main loop . Theintercepts hc and mrs are the coercivity  andsaturation remanence . 

When an external magnetic field is applied to aferromagnet such as iron, the atomic dipoles align themselves with it. Even when the field isremoved, part of the alignment will be retained: the material hasbecomemagnetized . Once magnetized, the magnet will stay magnetized

indefinitely. To demagnetize it requires heat or a magnetic field in theopposite direction. This is the effect that provides the element of memoryin a hard disk drive. 

The relationship between field strength H and magnetization M is notlinear in such materials. If a magnet is demagnetized ( H=M=0) and therelationship between H and M is plotted for increasing levels of fieldstrength, M follows the initial magnetization curve . This curve increasesrapidly at first and then approaches anasymptote called magneticsaturation. If the magnetic field is now reduced monotonically, M followsa different curve. At zero field strength, the magnetization is offset from

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the origin by an amount called the remanence. If the H-M relationship isplotted for all strengths of applied magnetic field the result is a hysteresisloop called themain loop . The width of the middle section is twicethecoercivity of the material.[15] 

A closer look at a magnetization curve generally reveals a series ofsmall, random jumps in magnetization called Barkhausen jumps. Thiseffect is due to crystallographic defects such asdislocations.[16] 

Electrical hysteresis

Electrical hysteresis typically occurs in ferroelectric material, wheredomains of polarization contribute to the total polarization. Polarization isthe electrical dipole moment (either C·m−2 or C·m). The mechanism, anorganization of the polarization into domains, is similar to that of

magnetic hysteresis.Hysteresis

From Wikipedia, the free encyclopedia

Not to be confused with  Hysteria . 

Fig. 1. Electric displacement field D of aferroelectric material asthe electric field E  is first decreased, then increased. The curves form

ahysteresis loop .

Hysteresis is the dependence of a system not only on its current

environment but also on its past environment. This dependence arises

because the system can be in more than one internal state. To predict

its future development, either its internal state or its history must be

known.[1] If a given input alternately increases and decreases, the output

tends to form a loop as in Fig. 1. However, loops may also occur

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because of a dynamic lag between input and output. Often, this effect is

also referred to as hysteresis, or rate-dependent hysteresis . This effect

disappears as the input changes more slowly, so many experts do not

regard it as true hysteresis.

Hysteresis occurs in ferromagnetic materials and ferroelectric materials,

as well as in the deformation of some materials (such as rubber

bands and shape-memory alloys) in response to a varying force. In

natural systems hysteresis is often associated with irreversible

thermodynamic change. Many artificial systems are designed to have

hysteresis: for example, in thermostats and Schmitt triggers, hysteresis

is produced by positive feedback to avoid unwanted rapid switching.

Hysteresis has been identified in many other fields,

including economics andbiology. 

Applications

The nonlinear nature of ferroelectric materials can be used to makecapacitors with tunable capacitance. Typically, a ferroelectriccapacitor simply consists of a pair of electrodes sandwiching a layer offerroelectric material. The permittivity of ferroelectrics is not only tunablebut commonly also very high in absolute value, especially when close tothe phase transition temperature. Because of this, ferroelectric

capacitors are small in physical size compared to dielectric (non-tunable)capacitors of similar capacitance.

The spontaneous polarization of ferroelectric materials impliesa hysteresis effect which can be used as a memory function, andferroelectric capacitors are indeed used to make ferroelectric RAM[4] forcomputers and RFID cards. In these applications thin films offerroelectric materials are typically used, as this allows the field requiredto switch the polarization to be achieved with a moderate voltage.However, when using thin films a great deal of attention needs to bepaid to the interfaces, electrodes and sample quality for devices to workreliably.[5] 

Ferroelectric materials are required by symmetry considerations to bealso piezoelectric and pyroelectric. The combined properties ofmemory, piezoelectricity, and pyroelectricity make ferroelectriccapacitors very useful, e.g. for sensor applications. Ferroelectriccapacitors are used in medical ultrasound machines (the capacitorsgenerate and then listen for the ultrasound ping used to image theinternal organs of a body), high quality infrared cameras (the infraredimage is projected onto a two dimensional array of ferroelectric

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capacitors capable of detecting temperature differences as small asmillionths of a degree Celsius), fire sensors, sonar, vibration sensors,and even fuel injectors on diesel engines.

Another idea of recent interest is the ferroelectric tunnel junction (FTJ ) in

which a contact made up by nanometer-thick ferroelectric film placedbetween metal electrodes.[6] The thickness of the ferroelectric layer issmall enough to allow tunneling of electrons. The piezoelectric andinterface effects as well as the depolarization field may lead to a giantelectroresistance (GER) switching effect.

Yet another hot topic is multiferroics, where researchers are looking forways to couple magnetic and ferroelectric ordering within a material orheterostructure; there are several recent reviews on this topic.[7] 

[edit]MaterialsThe internal electric dipoles of a ferroelectric material are coupled to thematerial lattice so anything that changes the lattice will change thestrength of the dipoles (in other words, a change in the spontaneouspolarization). The change in the spontaneous polarization results in achange in the surface charge. This can cause current flow in the case ofa ferroelectric capacitor even without the presence of an external voltageacross the capacitor. Two stimuli that will change the lattice dimensionsof a material are force and temperature. The generation of a surface

charge in response to the application of an external stress to a materialis called piezoelectricity. A change in the spontaneous polarization of amaterial in response to a change in temperature is called pyroelectricity. 

Ferroelectric phase transitions are often characterized as eitherdisplacive (such as BaTiO3) or order-disorder (such as NaNO2), thoughoften phase transitions will demonstrate elements of both behaviors.In barium titanate, a typical ferroelectric of the displacive type, thetransition can be understood in terms of a polarization catastrophe, inwhich, if an ion is displaced from equilibrium slightly, the force from the

local electric fields due to the ions in the crystal increases faster than theelastic-restoring forces. This leads to an asymmetrical shift in theequilibrium ion positions and hence to a permanent dipole moment. Theionic displacement in barium titanate concerns the relative position of thetitanium ion within the oxygen octahedral cage. In lead titanate, anotherkey ferroelectric material, although the structure is rather similar tobarium titanate the driving force for ferroelectricity is more complex withinteractions between the lead and oxygen ions also playing an importantrole. In an order-disorder ferroelectric, there is a dipole moment in each

unit cell, but at high temperatures they are pointing in random directions.

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Upon lowering the temperature and going through the phase transition,the dipoles order, all pointing in the same direction within a domain.

An important ferroelectric material for applications is lead zirconatetitanate (PZT), which is part of the solid solution formed between

ferroelectric lead titanate and anti-ferroelectric lead zirconate. Differentcompositions are used for different applications; for memoryapplications, PZT closer in composition to lead titanate is preferred,whereas piezoelectric applications make use of the divergingpiezoelectric coefficients associated with the morphotropic phaseboundary that is found close to the 50/50 composition.

Ferroelectric crystals often show several transitiontemperatures and domain structure hysteresis, much asdo ferromagnetic crystals. The nature of the phase transition in some

ferroelectric crystals is still not well understood.

In 1974 R.B. Meyer used symmetry arguments to predict ferroelectricliquid crystals[8], and the prediction could immediately be verified byseveral observations of behavior connected to ferroelectricity in smecticliquid-crystal phases that are chiral and tilted. The technology allows thebuilding of flat-screen monitors. Mass production began in 1994 byCanon. However, the costs were too high, and the production was shutdown 1999 (or before) after big losses.

In 2010 David Field found that prosaic films of chemicals such as nitrousoxide or propane exhibited ferroelectric properties. This new class offerroelectric materials may have wide ranging applications in device andnano-technology and also influence the electrical nature of dust in theinterstellar medium.

Continuum mechanics

From Wikipedia, the free encyclopedia

Continuum mechanics

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Classical mechanics

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History of classical mechanics ·Timeline of 

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mechanics · Celestial mechanics ·Continuum

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Continuum mechanics is a branch of mechanics that deals with theanalysis of thekinematics and the mechanical behavior of materials

modelled as a continuous mass rather than as discrete particles. The

French mathematician Augustin Louis Cauchy was the first to formulate

such models in the 19th century, but research in the area continues

today.

Modelling an object as a continuum assumes that the substance of the

object completely fills the space it occupies. Modelling objects in this

way ignores the fact that matter is made of atoms, and so is notcontinuous; however, on length scales much greater than that of inter-

atomic distances, such models are highly accurate. Fundamental

physical laws such as the conservation of mass, the conservation of

momentum, and the conservation of energy may be applied to such

models to derivedifferential equations describing the behavior of such

objects, and some information about the particular material studied is

added through a constitutive relation. 

Continuum mechanics deals with physical properties of solids and fluidswhich are independent of any particular coordinate system in which they

are observed. These physical properties are then represented

by tensors, which are mathematical objects that have the required

property of being independent of coordinate system. These tensors can

be expressed in coordinate systems for computational convenience.

Concept of a continuum

Materials, such as solids, liquids and gases, are composed

of molecules separated by empty space. On a macroscopic scale,materials have cracks and discontinuities. However, certain physicalphenomena can be modelled assuming the materials exist asa continuum, meaning the matter in the body is continuouslydistributed and fills the entire region of space it occupies. Acontinuum is a body that can be continually sub-dividedinto infinitesimal elements with properties being those of the bulkmaterial.

The validity of the continuum assumption may be verified by a

theoretical analysis, in which either some clear periodicity is identified

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orstatistical homogeneity and ergodicity of the microstructure exists.More specifically, the continuum hypothesis/assumption hinges on theconcepts of a representative volume element (RVE) (sometimes called"representative elementary volume") and separation of scales based on

the Hill –Mandel condition. This condition provides a link between anexperimentalist's and a theoretician's viewpoint on constitutive equations(linear and nonlinear elastic/inelastic or coupled fields) as well as a wayof spatial and statistical averaging of the microstructure.[1] 

When the separation of scales does not hold, or when one wants toestablish a continuum of a finer resolution than that of the RVE size, oneemploys a statistical volume element (SVE), which, in turn, leads torandom continuum fields. The latter then provide a micromechanicsbasis for stochastic finite elements (SFE). The levels of SVE and RVE

link continuum mechanics to statistical mechanics. The RVE may beassessed only in a limited way via experimental testing: when theconstitutive response becomes spatially homogeneous.

Specifically for fluids, the Knudsen number is used to assess to whatextent the approximation of continuity can be made.

[edit]Major areas of continuum mechanics

Continuummechanics The study of

the physics ofcontinuousmaterials

Solid mechanics The study of thephysics ofcontinuousmaterials with adefined restshape.

Elasticity 

Describes materials that return totheir rest shape after anapplied stress. 

Plasticity Describesmaterials thatpermanently

deform after asufficient appliedstress.

Rheology The study ofmaterials with bothsolid and fluidcharacteristics.

Fluid mechanics The study of thephysics ofcontinuousmaterials which

take the shape of

Non-Newtonianfluids

Newtonian fluids

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their container.