newtonian mechanics - What is the difference between stress and pressure? - Physics Stack Exchange
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What is the difference between
and ? Are there any intuitive examples that explain the difference between the two?
How about an example of when pressure and stress are not equal?
67.3k1096263
Pressure is defined as force per unit area applied to an object in a direction perpendicular to the surface.
And naturally pressure can cause stress inside an object.
Whereas stress is the property of the body under load and is related to the internal forces. It is defined as a reaction produced by the molecules of the body under some action which may produce some deformation. The intensity of these additional forces produced per unit area is known as stress (pretty picture from wikipedia):
EDIT PER COMMENTS
Overburden Pressure or lithostatic pressure is a case where the gravity force of the object's own mass creates pressure and results in stress on the soil or rock column.
This stress increases as the mass (or depth) increases.
This type of stress is uniform because the gravity force is uniform.
Included in lithostatic pressure are the weight of the atmosphere and,
if beneath an ocean or lake, the weight of the column of water above
that point in the earth. However, compared to the pressure caused by
the weight of rocks above, the amount of pressure due to the weight of
water and air above a rock is negligible, except at the earth's
surface. The only way for lithostatic pressure on a rock to change is
for the rock's depth within the earth to change.
Since this is a uniform force applied throughout the substance due to mostly to the substance itself, the terms pressure and stress are somewhat interchangeable because pressure can be viewed as both an external and internal force.
For a case where they are not equal, just look that the image of the ruler.
If pressure is applied at the far end (top of image) it creates unequal stress inside the ruler, especially where the internal stress is high at the corners.
Given a stress tensor $\mathbf{\sigma}$, which has 9 components in general, the pressure (in continuum mechanics at least) is defined as $P = 1/3 tr(\mathbf{\sigma})$.
So the pressure at a point in the continuum is the average of the three normal stresses at the point. The off-diagonal terms manifest as shear stress.
It's hard to say "stress" without being more specific in your question because stress is not a scalar. Pressure is always different from stress, but the two are related.
10.8k13562
The difference between stress and pressure has to do with the difference between isotropic and anisotropic force. There's a Wikipedia
$\boldsymbol{\sigma}$ into "hydrostatic" and "deviatoric" components,
$$\boldsymbol{\sigma}=\mathbf{s}+p\mathbf{I}$$
where the pressure $p$ is
$$p=\frac{1}{3}\text{tr}(\boldsymbol{\sigma})$$
where $\mathbf{I}$ is the $3\times 3$ identity matrix, and where $\mathbf{s}$ is the traceless component of $\boldsymbol{\sigma}$.
The linked article actually gives a pretty good intuitive explanation of $p\mathbf{I}$:
(From article) A mean hydrostatic stress tensor $p\mathbf{I}$, which tends to change the volume of the stressed body.
This follows since the surface force experienced by a plane with normal vector $\mathbf{n}$ is given by
$$\mathbf{T}^{(\mathbf{n})}=\mathbf{n}\cdot\boldsymbol{\sigma}$$
which for a purely hydrostatic stress becomes
$$\mathbf{T}^{(\mathbf{n})}=\mathbf{n}\cdot p\mathbf{I}=p\mathbf{n}$$
which points in the same direction as the normal to the plane. This basically means that a cube of material will want to expand like a ballon if $p&0$, and contract if $p&0$.
Meanwhile, the deviatoric component means that there are forces at play which don't just tend to expand or contract things, such as shear forces.
How about an example of when pressure and stress are not equal?
In a solid, pure shear waves can exist. Unlike in acoustic pressure waves, shear waves ha the forces that propagate the wave are not due to pressure, but are due to shear strain.
8,57811726
Pressure is an external force, when applied on another body, the effect is easily seen on the outer part of body and it first affected the outer area of the body. In the case of stress, the molecular deformation is developed internal of the body and stress is generated slowly slowly in the internal part of any object due to load. And simply pressure affected the outer area of the body and stress affected the body internally.Stress is observed due to the load applied,whereas pressure is a sort of load on a body.
Pressure is perpendicular to the object, it is an external force only. Pressure causes stress inside of the object, so stress is an internal force.
19.2k103875
whenever external force is applied on the object automatically a restoring force is developed inside the object to restrict the deformation of the object.The ratio of restoring force perpendicular to the surface to the area is known as stress.The ratio of
external force perpendicular to the surface to the area is known as pressure.
for example if you press a ball u r applying pressure and what the ball apply to u you is stress and if both r not equal than one dominates over other
pressure is an external force and stress is an internal force
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Physics Stack Exchange works best with JavaScript enabledThe chair is between the twobeb.改错
那朵花87241
绝对是beds,复数啊
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介词：是一种用来表示词与词、词与句之间的关系的虚词，在句中不能单独作句子成分。介词后面一般有名词代词或相当于名词的其他词类，短语或从句作它的宾语。介词的分类：（1）表示时间，处所：从 自 自从 于 打 到 往 在 当 朝 向 顺着 沿着 随着（2）表示方式：按 照 按照 依 依照 本着 经过 通过 根据 以 凭（3）表示目的：为 为了 为着（4）表示原因：因 由于 因为（5）表示对象，范围：对 对于 把 向 跟 与 同 给 关于（6）表示排除：除 除了 除去 除非（7）表示被动：被 叫 让 给（8）表示比较：比 和 同上述介词中的“着，了，过”是语素，不是动态助词。介词at, in, on的区别:&1. 表示时间，注意以下用法：(1) 表示时间的某一点、某一时刻或年龄等用 at。如：I get up at six in the morning. 我早上六点钟起床。He got married at the age of 25. 他 25 岁结婚。(2) 泛指一般意义的上午、下午或晚上以及月或年等较长的时间，一般用 in。如：We watch TV in the evening. 我们晚上看电视。He went to Japan in 1946. 他于 1946 去了日本。(3) 若表示星期几或某一特定的日期，则用 on。如：He left here on the fifth of May. 他于 5 月 5 日离开这儿。2. 表示地点、场所、位置等，注意以下用法：(1) 表示某一点位置，用 at。如：We live at No 87 Beijing Road. 我们住在北京路 87 号。The hospital is at the end of the street. 医院在这条街的尽头。与名词所有格连用表示地点，也用 at。如：at my sister’s 在我姐姐家& at the doctor’s 在医务室(2) 表示空间或范围，用 in。如：What’s in the box? 这盒子里有什么?He lives in Paris with his wife. 他同他妻子住在巴黎。但有时两者可换用。如：The meeting was held at [in] the hotel. 会议在宾馆举行。(3) at 与 in 的另一个区别是：at 用于指较小的地方，而 in 用于指较大的地方。如：in Shanghai 在上海&&& at the station 在车站但是，大与小是相对的，有时随着说话者的着眼点不同，大地方也可能用 at(比如把一个大地方看作一个点时)。如：Our plane refuelled at London. 我们的飞机在伦敦加油。We stopped for an hour at Moscow on our way to Paris. 我们在去巴黎的途中在莫斯科停了 1 个小时。(4) 介词 on 用于地点，主要指在某物的表面。如：What’s on the table? 桌上有什么?There’s a wallet lying on the ground. 地上有个钱包。注：在少数搭配中，也用介词 on。如：He works on a farm. 他在农场工作。3. 在某些搭配中，三者的区别与英国英语和美国英语有关：in the street (英) / on the street (美) 在街上in the road (英) / on the road (美) 在路上in the team (英) / on the team (美) 在这个队at the weekend (英) / on the weekend (美) 在周末at weekends (英) / on weekends (美) 在周末4. 有时三者的差别与搭配习惯和用法有关：in bed / on the bed 在床上in the tree (多指树外之物) / on the tree (多指树本身之物) 在树上
介词besides,but,except的用法区别：&1. 三者都可表示“除外”，但 besides 表示一种累加关系，意指“除了什么之外，还有……”；而 except 或 but 则表示一种排除关系，意指“除了什么之外，不再有……”。如：Besides his wife，his daughter also went to see him. 除他妻子外，他女儿也去看过他(即妻子女儿都去看过他)。Nobody went to see him except [but] his wife. 除他妻子外，没有一个人看过他(即只有他妻子去看过他)。注：在否定句中，besides 也表示“除……之外不再有…… ”，与but, except 同义。如：No one passed the exam besides [except] Jim. 除吉姆外，没一个人通过考试。2. 关于 but 与 except：(1) 两者都可表示“除……外不再有……”，但含义上略有差别：but侧重指意义的几乎完整性，而 except 则侧重指后面除去的部分。比较：All are here but one. 除一个人都到了。All are here except one. 还有一个人没到。(2) 在现代英语中，but 的介词用法十分有限，一般说来，它只能用在下列词语之后：① no, no one, nobody, nothing, nowhere 等② any, anyone, anybody, anything, anywhere 等③ every, everyone, everybody, everything, everywhere 等④ all, none 等⑤ who, what, where 等Everyone knows it but you. 除你之外大家都知道。I haven’t told anybody but you. 除你之外，我没告诉任何人。No one but he [him] showed much interest in it. 除他之外没有一个人对此有很大兴趣。一般说来，若没有出现上述词汇，就不宜使用介词 but，否则可能造成错句。但是 except 却没有以上限制。比较：正：The window is never opened except in summer. 除夏天外，这扇窗户从不打开。误：The window is never opened but in summer.(3) but 一定不能用于句首，except 通常不用于句首：除我之外每个人都累了。正：Everyone is tired but (except) me.正：Everyone but (except) me is tired.误：But (Except) me, everyone is tired.注：except for 可用于句首，表示 except 的意思：正：Except for me, everyone is tired.3. 关于 except 与 except for：except 主要用来谈论同类的东西，而 except for 则主要用来谈论不同类的东西，有时含有惋惜之意。如：All compositions are well written except yours. 除了你的作文外，其他的作文都写得很好。His composition is good except for a few spelling mistakes. 他的作文写得不错，只是有几处拼写错误。注：若用于句首，则 except for 与 except 同义(但 except 通常不用于句首)。4. 关于 except for 与 but for：except for 主要表示排除，but for 主要表示一种虚拟条件(与虚拟语气连用)。如：Except for me, everyone passed the exam. 除了我之外，大家都通过了考试。But for my help, she would not have passed the exam. 若不是我的帮助，她就不会通过考试。But for the atmosphere plants would die. 如果没有大气，植物就会死亡。5. besides 除用作介词外，还用作副词，其意为“此外”、“而且”，可用于分句句首(通常用逗号隔开)或句尾。如：I don’ besides, I’m too tired. 我不想去，而且我也太累了。This car belongs to Smith, and he has two others besides. 这部车是史密斯的，此外他还有两部。介词的用法口诀：
早、午、晚要用in，at黎明、午夜、点与分。
年、月、年月、季节、周，阳光、灯、影、衣、冒in。
将来时态in。。。以后，小处at大处in。
有形with无形by，语言、单位、材料in。
特征、方面与方式，心情成语惯用in。
介词at和to表方向，攻击、位置、恶、善分。
日子、日期、年月日，星期加上早、午、晚，
收音、农场、值日on，关于、基础、靠、着论。
着、罢、出售、偷、公、假，故意、支付、相反，准。
特定时日和“一……就”，on后常接动名词。
年、月、日加早、午、晚，of之前on代in。
步行、驴、马、玩笑on，cab，carriage则用in。
at山脚、门口、在当前，速、温、日落、价、核心。
工具、和、同随with，具有、独立、就、原因。
就……来说宾译主，对、有、方状、表细分。
海、陆、空、车、偶、被by，单数、人类knowtoman。
this、that、tomorrow，yesterday，next、last、one。
接年、月、季、星期、周，介词省略已习惯。
over、under正上下，above、below则不然，
若与数量词连用，混合使用亦无关。‘
beyond超出、无、不能，against靠着，对与反。
besides，except分内外，among之内along沿。
同类比较except，加for异类记心间。
原状becauseof，、owingto、dueto表语形容词
under后接修、建中，of、from物、化分。
before、after表一点，ago、later表一段。
before能接完成时，ago过去极有限。
since以来during间，since时态多变换。
与之相比beside，除了lastbutone。
复不定for、找、价、原，对、给、段、去、为、作、赞。
快到、对、向towards，工、学、军、城、北、上、南。
butfor否定用虚拟，复合介词待后言。
ing型由于鉴，除了除外与包合。
之后、关于、在。。。。。。方面，有关介词须记全。
in内to外表位置，山、水、国界to在前。
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