楊氏模數---Young's modulus

(Source ：Wikipedia) (備存)


定義：

楊氏模量，也稱楊氏模數（英語：Young's modulus），是材料力學中的名詞。彈性材料承受正向應力時會產生正向應變，在形變量沒有超過對應材料的一定彈性限度時，定義正向應力與正向應變的比值為這種材料的楊氏模量。公式記為

${\displaystyle E={\frac {\sigma }{\epsilon }}}$

其中，${\displaystyle E}$ 表示楊氏模量，${\displaystyle \sigma }$ 表示正向應力，${\displaystyle \epsilon }$ 表示正向應變。

where

E is the Young's modulus (modulus of elasticity)

F is the force exerted on an object under tension;

A₀ is the actual cross-sectional area through which the force is applied;

ΔL is the amount by which the length of the object changes;

L₀ is the original length of the object.

楊氏模量以英國科學家托馬斯·楊命名。

Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a solid material. It is a mechanical property of linear elastic solid materials. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material. Young's modulus is named after the 19th-century British scientist Thomas Young. However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young's modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years.^[1] The term modulus is the diminutive of the Latin term modus which means measure.

A solid material will deform when a load is applied to it. If it returns to its original shape after the load is removed, this is called elastic deformation. In the range where the ratio between load and deformation remains constant, the stress-strain curve is linear. Not many materials are linear and elastic beyond a small amount of deformation. A stiff material needs more force to deform compared to a soft material, and an infinite force would be needed to deform a perfectly rigid material, implying that it would have an infinite Young's modulus. Although such a material cannot exist, a material with a very high Young's modulus can be approximated as rigid.^[2]

Material stiffness should not be confused with:

• Strength: the strength of material is the amount of force it can withstand and still recover its original shape;
• Geometric stiffness: the geometric stiffness depends on shape, e.g. the stiffness of an I beam is much higher than that of a round tube made of the same steel, thus having the same rigidity, and same mass of material per length;
• Hardness: the hardness of a material defines the relative resistance that its surface imposes against the penetration of a harder body;
• Toughness: toughness is the amount of energy that a material can absorb before fracturing.