主要區別-彈性模量與剛性模量

彈性模量和剛度模量是材料工程師用來描述材料如何變形的兩個數字。彈性模量和剛度模量之間的主要區別在於，彈性模量描述了當力以直角施加於物體錶面時，材料是如何變形的，使材料拉長或縮短，而剛性模量描述了當平行於物體錶面施加力時，材料如何變形，從而導致其中一個錶面相對於同一物體的另一個錶面發生移動。

什麼是彈性模量(the modulus of elasticity)？

Modulus of elasticity (Young modulus) is a number that describes the ratio of stress to strain in an object that is being deformed by a force that is perpendicular to a surface of an object. The stress of a material is the deforming force per unit area. For instance, the figure below shows an object that becomes elongated as a result of a tensile force on it. In this case, the stress ( ) is given by:

由於變形力與物體錶面成直角，所以這種應力通常稱為法嚮應力。

Tensile stress from a force acting at right angles to a surface.

The strain is the fractional change in length of the object. Suppose the object had a length  before the deforming force acted on it, and if the object gets elongated by a length  under the deforming force, then the strain ( ) is given by:

The modulus of elasticity ( ) is then given by:

什麼是剛度模量(the modulus of rigidity)？

剛度模量（剪下模量）是一個給出單位面積作用在材料上的剪下應力的數字。在這裡，變形力平行於物體的一個面，導致一個面相對於另一個面發生位移。其描述如下：

Shear stress from a force parallel to the surface.

So, shear stress () is given as:

這個方程與法嚮應力方程的形式相同，不同之處在於力的作用方式。

The shear strain () is defined as the ratio of relative displacement between the surfaces to the separation between the surfaces. Here,

Once again the shear modulus () is the ratio between shear stress and shear strain:

彈性模量與剛度模量的關係

Modulus of elasticity ( ) and the modulus of rigidity ( ) are related by the following equation:

Here, represents a number called Poisson’s ratio given to the particular material. When the material is being stretched in one direction, it gets shortened in a perpendicular direction. In the direction that the material becomes elongated, the axial strain () is defined as the fractional increase in the length. In the direction that the material shortens, the transverse strain () gives the fractional reduction in length. The diagram below illustrates these changes in shape:

Defining Poisson’s ratio

在該圖中，軸嚮應變為：

橫嚮應變為：

Note that since the object shortens in the directiopn perpendicular to the force, . Poisson’s ratio ( ) is defined as:

The minus sign has been introduced to ensure that  takes a positive value.

彈性模量(modulus of elasticity)和剛度模數(modulus of rigidity)的區別

力的方向

彈性模量用於計算變形力與物體錶面成直角時物體的變形。

剛度模量用於計算變形力平行於物體錶面時的變形。

形狀變化

在計算彈性模量時，物體在變形力作用下要麼變長要麼變短。

在計算剛度模量時，物體的一個錶面相對於另一個錶面發生位移。

相對大小

對於大多數材料，彈性模量大於剛度模量。這一規則的例外是具有負泊松比的所謂“auxetic”材料，但這些材料不太常見。