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In , elasticity (from
?λαστ?? "ductible") is the tendency of solid materials to return to their original shape after being deformed. Solid objects will
are applied on them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.
The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For
and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.
Perfect elasticity is an approximation of the real world, and few materials remain purely elastic even after very small deformations. In engineering, the amount of elasticity of a material is determined by two types of material parameter. The first type of material parameter is called a modulus, which measures the amount of force per unit area (stress) needed to achieve a given amount of deformation. The units of modulus are pascals (Pa) or pounds of force per square inch (psi, also lbf/in2). A higher modulus typically indicates that the material is harder to deform. The second type of parameter measures the elastic limit. The limit can be a stress beyond which the material no longer behaves elastic and deformation of the material will take place. If the stress is released, the material will elastically return to a permanent deformed shape instead of the original shape.
When describing the relative elasticities of two materials, both the modulus and the elastic limit have to be considered. Rubbers typically have a low modulus and tend to stretch a lot (that is, they have a high elastic limit) and so appear more elastic than metals (high modulus and low elastic limit) in everyday experience. Of two rubber materials with the same elastic limit, the one with a lower modulus will appear to be more elastic.
When an elastic material is deformed due to an external force, it experiences internal forces that oppose the deformation and restore it to its original state if the external force is no longer applied. There are various , such as , the , and the , all of which are measures of the inherent stiffness of a material as a resistance to deformation under an applied load. The various moduli apply to different kinds of deformation. For instance, Young's modulus applies to uniform extension, whereas the shear modulus applies to .
The elasticity of materials is described by a , which shows the relation between
(the average restorative internal
per unit ) and
(the relative deformation). For most metals or crystalline materials, the curve is linear for small deformations, and so the stress-strain relationship can adequately be described by , and higher-order terms can be ignored. However, for larger stresses beyond the , the relation is no longer linear. For even higher stresses, materials exhibit , that is, they deform irreversibly and do not return to their original shape after stress is no longer applied. For -like materials such as , the
of the stress-strain curve increases with stress, meaning that rubbers progressively become more difficult to stretch, while for most , the gradient decreases at very high stresses, meaning that they progressively become easier to stretch. Elasticity is not exhi , such as , will also exhibit elasticity in certain conditions. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a
Because the elasticity of a material is described in terms of a stress-strain relation, it is essential that the terms stress and strain be defined without ambiguity. Typically, two types of relation are considered. The first type deals with materials that are elastic only for small strains. The second deals with materials that are not limited to small strains. Clearly, the second type of relation is more general.
For small strains, the measure of stress that is used is the
while the measure of strain that is used is the . The stress and strain measures are related by a linear relation known as .
describes the behavior of such materials.
are models that extend Hooke's law to allow for the possibility of large rotations.
For more general situations, any of a number of
can be used provided they are
to an appropriate
measure, i.e., the product of the stress measure and the strain measure should be equal to the internal energy (which does not depend on how the stress or strain are measured).
is the preferred approach for dealing with finite strains and several material models analogous to Hooke's law are in use.
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As noted above, for small deformations, most elastic materials such as
exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as . A geometry-dependent version of the idea was first formulated by
in 1675 as a Latin , "ceiiinosssttuv". He published the answer in 1678: "Ut tensio, sic vis" meaning "As the extension, so the force", a linear relationship commonly referred to as . This law can be stated as a relationship between
where k is a constant known as the rate or spring constant. It can also be stated as a relationship between
where E Is known as the
Although the general proportionality constant between stress and strain in three dimensions is a 4th order , systems that exhibit , such as a one-dimensional rod, can often be reduced to applications of Hooke's law.
The elastic behavior of objects that undergo finite deformations have been described using a number of models, such as
models, and
models. The primary measure that is used to quantity finite strains is the
(F). More convenient strain measures can be derived from this primary quantity.
Main article:
A material is said to be Cauchy-elastic if the
σ is a function of the
() F alone:
Even though the stress in a Cauchy-elastic material depends only on the state of deformation, the work done by stresses may depend on the path of deformation. Therefore a Cauchy elastic material has a non-conservative structure, and the stress cannot be derived from a scalar "elastic potential" function.
Main article:
Hypoelastic materials are described by a relation of the form
This model is an extension of linear elasticity and suffers from the same form of non-conservative behaviour as Cauchy elastic materials.
Main article:
Hyperelastic materials (also called Green elastic materials) are conservative models that are derived from a
(W). The stress-strain relation for such materials takes the form
Linear elasticity is used widely in the design and analysis of structures such as , , and . This theory is also the basis of much of .
Hyperelasticity is primarily used to determine the response of -based objects such as
and of biological materials such as
For , the presence of
affects the
perpendicular to the planes of the cracks, which decrease (Young's modulus faster than the shear modulus) as the fracture
increases, indicating that the presence of cracks makes bodies brittler. , the stress-strain relationship of materials is in general governed by the , a .
settle in the configuration which minimizes the free energy, subject to constraints derived from their structure, and, depending on whether the
term dominates the free energy, materials can broadly be classified as energy-elastic and entropy-elastic. As such, microscopic factors affecting the free energy, such as the
distance between molecules, can affect the elasticity of materials: for instance, in
materials, as the equilibrium distance between molecules at
increases, the
decreases. The effect of
on elasticity is difficult to isolate, because there are numerous factors affecting it. For instance, the bulk modulus of a material is dependent on the form of its , its behavior under , as well as the
of the molecules, all of which are dependent on temperature.
Treloar, L. R. G. (1975). The Physics of Rubber Elasticity. Oxford: Clarendon Press. p. 2.  .
Sadd, Martin H. (2005). Elasticity: Theory, Applications, and Numerics. Oxford: Elsevier. p. 70.  .
de With, Gijsbertus (2006). Structure, Deformation, and Integrity of Materials, Volume I: Fundamentals and Elasticity. Weinheim: Wiley VCH. p. 32.  .
Descriptions of material behavior should be independent of the geometry and shape of the object made of the material under consideration. The original version of Hooke's law involves a stiffness constant that depends on the initial size and shape of the object. The stiffness constant is therefore not strictly a material property.
Atanackovic, Teodor M.; Guran, Ardéshir (2000). "Hooke's law". Theory of elasticity for scientists and engineers. Boston, Mass.: Birkh?user. p. 85.  .
. Centuries of Civil Engineering: A Rare Book Exhibition Celebrating the Heritage of Civil Engineering. Linda Hall Library of Science, Engineering & Technology.[]
Bigoni, D. Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability. Cambridge University Press, 2012 . .[]
Sadd, Martin H. (2005). Elasticity: Theory, Applications, and Numerics. Oxford: Elsevier. p. 387.  .
Sadd, Martin H. (2005). Elasticity: Theory, Applications, and Numerics. Oxford: Elsevier. p. 344.  .
Sadd, Martin H. (2005). Elasticity: Theory, Applications, and Numerics. Oxford: Elsevier. p. 365.  .
: Hidden categories:The Jewish Floridian ( April 16, 1954 )Take over the counter medication. Nonsteroidal anti-inflammatory drugs (NSAIDS) such as ibuprofen or naproxen are the first-line medicines for painful menstrual cramping. NSAIDs work by blocking the contractions that cause cramps. Ibuprofen is the most common of the two. You can take 400-600 mg of ibuprofen every 4-6 hours or 800 mg every 8 hours with a maximum dose of 2400 mg daily.
You should start taking them with the onset of symptoms and continue your dose for 2-3 days as needed, depending on your symptom pattern.
Try ibuprofen brands such as Advil and Motrin. You can also try naproxen brands such as Aleve.
Learn about hormonal birth control. If natural remedies, diet and nutrition, exercise, and NSAIDs do not work to relieve cramps in a satisfactory manner, hormonal birth control may be a good options for you. There are many different forms and kinds that can be effective in making menstruation lighter and less painful.
The method you chose depends on your general health, sexual practices, and personal and financial preferences. Discuss your options with your healthcare provider.
Take birth control pills. Birth control pills are an oral hormonal birth control that you take daily. Because you control when they are taken, they are easily stopped. They are widely used, readily available, and relatively inexpensive. However, they can be annoying because they must be taken daily at the same time.
They can also cause weight gain and are a constant monthly expense.
Wear the birth control patches. The patches work just like the pill, expect they are in a patch form. They must be applied monthly and, like the pills, can easily be stopped and cause weight gain.
They can also fall off accidentally, be easily seen when applied to certain areas, and are a constant monthly expense.
Try the vaginal ring. If you don’t want a pill or patch, you can try a vaginal ring. This form of hormonal birth control is only changed monthly and can easily be stopped when you don’t need them anymore. They are considered more private than the patch or pill because you don’t have to take a pill or put on a patch where anyone can see you.
The hormone acts locally inside you and has less systemic circulating hormone, which makes it less likely to cause weight gain. However, it can accidentally fall out during sexual activity and it is still a constant monthly expense.
Consider hormonal injections. If you don’t like any other options, you might consider taking a hormonal injection. They are more convenient because they are given only every 3 months, but they must be injected every time. However, they have worse side effects than the other options. You may stop having periods and can continue to be infertile for up to one year after stopping.
Like the pill and patch, the hormone circulates, so it may result in weight gain.
Get a hormonal birth control implant. Implants are more permanent options for menstrual cramp control. Once they are implanted, they last for 3-5 years. Despite their longevity, they are easily reversible once you remove the implant. Like many of the other options, it also may result in weight gain.
The insertion process can also be quite painful, though you only have to do it once every few years.
Think about an intrauterine device (IUD). If an implant isn't quite right, you can try an even longer lasting option called an IUD. These devices are effective for 6-12 years and have very limited side-effects because it has a limited hormone absorbed within your system as well as limited likelihood of weight gain.
They can, however, make you susceptible to infection and are painful to be inserted. There have also been cases where menstrual pain is increased in some women. You may also stop having periods and can be infertile for up to one year after stopping.
See a doctor. If your cramps are more severe than usual, feel unusual for you, and if the timing or location of the cramps is different, you should contact your doctor. You should also consult your doctor if your cramps last more the 2-3 days. It is possible that you cramping may secondary dysmenorrhea, which is a more severe version of menstrual cramps that are usually caused by an underlying disease or disorder.
There are certain reproductive disorders that cause secondary dysmenorrhea. These disorders include endometriosis, pelvic inflammatory disease, stenosis of the cervix, and tumors on the wall of the uterus.
If your doctor suspects any of these disorders, she will perform a physical exam and run tests to see which is most likely. She will perform a pelvic exam and check for any abnormalities or infection in your reproductive organs. She may also give you an ultrasound, a CT scan, or an MRI. In some cases, your doctor may perform a laparoscopy, which is an outpatient procedure where a fiber optic tube is surgically inserted to examine your your abdominal cavity and reproductive organs.
Use heat. There are several natural therapies that have been studied and shown to help relieve pain from menstrual cramping. One of the most common and easiest methods to use is heat. Heat can be just as or more effective than over-the-counter pain medications, such as ibuprofen or acetaminophen. The heat aids in relaxing the contracting muscles that cause cramps. You should apply heat to your lower abdomen. You can also apply it to your lower back. Try a heating pad or a heat patch. Heat patches are adhesive, non-medicated pads that give off heat for up to 12 hours. You can apply them to skin or clothing, but make sure you read the directions.
Heat patches come in different shapes, sizes, and say they are for different uses, though you can use any patch for menstrual cramps. Some brands even have patches specifically for menstrual cramps, such as ThermaCare heat wraps.
Patches are more convenient than heating pads because they are portable, so you can apply it and go about your day.
If you don't have a heating pad and patch, you can try soaking in a hot bath or taking a hot shower to relax you and relieve cramps.
Try behavioral intervention. It may be helpful to develop certain kinds of behavioral intervention coping strategies, especially if you have persistently bad cramps. These strategies include relaxation training, which uses a repetitive activity, such as deep breathing, reciting a prayer, or repeating a word or sound, in combination with clearing your mind, ignoring distractions, and taking on a positive attitude. This is supposed to help you relax and let go of the pain.
You can also try imagery intervention, which uses positive thoughts and experiences to change your emotional state and distract you from and relieve the pain.
Hypnotherapy is another method that uses hypnosis to induce relaxation, decrease stress, and relieve pain.
Since cramps effect the same muscles as child birth, some women find it helpful to use Lamaze exercises to relieve menstrual cramps. Try the rhythmic breathing used in Lamaze exercises to help relieve or lessen the pain.
You can also attempt biofeedback, which is a method where you learn to control physiologic parameters such as heart rate, blood pressure, and temperature along with relaxation techniques to help train your body to control symptoms.
Distract yourself. Distraction is one of the most powerful and readily available painkillers. If you have intense cramps, do something that normally absorbs you completely, such as socializing with good friends, reading a book, playing a computer game, watching a movie or TV show, or spending time on Facebook.
Make sure you pick something that will keep your mind off of the pain and convince your body to focus on other things.
Give acupuncture a try. Acupuncture has been used as a pain relief method for over 2,000 years. In this method, hair-thin needles are placed into the skin on specific locations on your body. The needles do not cause pain for most people, and some women find that it reduces menstrual cramps.
Despite some word of mouth testimonies, studies of this are inconclusive.
Massage your abdomen. Sometimes, it helps to put gentle pressure on the affected areas. Lie down and prop your feet up. From your reclined position, gently massage your lower back and abdomen.
Make sure you don’t press too hard. You don’t want to cause more pain instead of relief. This can help relax the muscles and relieve the pain.
Take supplements. Research has shown that certain vitamin and nutritional supplements can help lessen menstrual cramps when taken daily. The mechanisms for this are not well understood, but the many dietary supplements have been shown to reduce cramping. Take 500U of Vitamin E, 100 mg of Vitamin B1, 200 mg of Vitamin B6, and a doctor approved level of Vitamin D3 daily.
A blood test can assess if you have enough of these vitamins in your diet, and a regimen of supplementation can be take accordingly.
You can also take a supplement of fish oil or cod liver oil.&/ref&
Change your diet. One study showed that a diet low in fat and rich in vegetables helps decrease menstrual pain. You should eat green, leafy vegetables, which are rich in Vitamins A, C, E, B, K and folates. Much like with the supplements, these vitamins and minerals can help menstrual pain. These foods can also help prevent anemia from menstrual bleeding by providing nutrients necessary to create new red blood cells.
You should increase your iron as well while you are menstruating. You can eat lean red meat or take supplements to help prevent menstrual anemia.
Green vegetables and berries also contain antioxidants, which may play a role in fighting inflammation related to bloating.
Another study showed that women who ate 3-4 servings of dairy daily had lower rates of cramping. You should not eat this much dairy if you are prone to be gassy or bloated if you consume too much dairy.
Drink tea. Different varieties of teas may help to soothe cramps. Make sure when choosing a tea variety that you choose decaffeinated versions so you don't cancel out the soothing effects of the tea by increasing cramps with the caffeine. Raspberry, chamomile, and ginger tea may have anti-inflammatory capabilities to help relieve cramping..
You should avoid caffeinated teas because caffeine encourages anxiety and tension, which can make your cramps worse.
The amount of tea needed to provide relief is not documented, but as long as it is decaffeinated, you can enjoy as much as you’d like.
This can also help to keep you hydrated.
Avoid alcohol and tobacco. Alcohol can cause water retention and bloating. Nicotine in tobacco can cause increased tension and cause a narrowing of vessels called vasoconstriction. This issue leads to decreased blood flow to the uterus and a worsening of your cramps.
Exercise. Exercise can help relieve menstrual symptoms in general, include cramping. Exercise releases endorphins, which are natural pain relievers. Endorphins also help counteract the prostaglandins in your body that cause contractions and pain. Because of this, physical activity may help relieve cramps.
Try different kinds of aerobic exercise, such as walking, running, cycling, swimming, kayaking, hiking, or a class at the gym.
Do simple stretches. Stretching helps relax your muscles and alleviate cramps. Sit on the floor with your legs stretched far apart. Stretch forward to catch your toes or ankle. Breathe in while keeping your back straight. After a few breaths, lean forward towards the floor.
You can try other simple stretches as well to stretch out your back or abdomen, depending on which areas hurt the most.
Increase your sexual activity. Some women experience relief from menstrual cramping with orgasm. The reason behind this is not well understood, but may have something to do with endorphins released during sexual arousal. Much like with exercise, the endorphins released during orgasm can help relieve the menstrual cramps and inflammation.
Try yoga. Similar to aerobic exercise and stretching, yoga helps relax the body and reduce aches and pains in the lower back, legs, and abdomen. When you begin to feel menstrual cramps, you can try various yoga poses to help you with your pain. Before you start, get in some comfortable clothes and put on soothing music.
You can do the head-to-knee forward bend. Sit on the floor and extend your legs in front of you. Pull one of your legs in and bend it 90 degrees so that the sole of your foot rests against the inside of your thigh. Inhale and grab your shin, ankle, or foot. Stretch the torso over your leg towards the foot. Exhale and bend down from the groin. Lengthen and stretch your back instead of rounding it. Breathe as you hold the pose, extending through the heel and pressing your sitting bones towards the floor. Hold for 1-3 minutes, then switch sides.
You can also try the noose pose. Get into a full squat with your feet together. Lower down until your buttocks are towards your heels. Inhale, then move your knees to the left as you turn your torso to the right. As you exhale, wrap the left arm back behind you and around your knees and legs. Inhale and reach the right arm around to clasp your hands. Exhale as you gaze over the right shoulder. Hold for 30-60 seconds as you breathe. Switch sides.
You can also attempt camel pose. Get on your knees, hip-width apart. Make sure your shins and feet are pressed firmly into the floor. Rest your palms on the top of your buttocks with the fingers pointing down. Inhale. Lift your chest and move your shoulders down towards the ribs. Exhale, then push your hips forward as you arch back. To stabilize yourself, rest your hands on your heels. Lift the chest. Breathe steadily for 30-60 seconds.
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For example:Don't say: Eat more fats.Do say: Add fats with some nutritional value to the foods you already eat. Try olive oil, butter, avocado, and mayonnaise.
If you are you have uncommonly harsh cramps or feel like there may be a problem, see a healthcare provider to discuss your symptoms. The cramps may be a sign of an underlying disorder that requires treatment such as endometriosis, adenomyosis, uterine fibroids, pelvic inflammatory disease (PID), congenital anomalies, or cancer.
Other signs and symptoms that should prompt you to seek medical attention include fever, vomiting, heavy menstrual bleeding that soaks a pad or tampon more than every two hours, dizziness or fainting, sudden or severe pain, pain different from your normal menstrual pain, pain with urination, abnormal vaginal discharge, and pain with sexual activity.
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