主要区别-弹性模量与刚性模量

弹性模量和刚度模量是材料工程师用来描述材料如何变形的两个数字。弹性模量和刚度模量之间的主要区别在于，弹性模量描述了当力以直角施加于物体表面时，材料是如何变形的，使材料拉长或缩短，而刚性模量描述了当平行于物体表面施加力时，材料如何变形，从而导致其中一个表面相对于同一物体的另一个表面发生移动。

什么是弹性模量(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:

由于变形力与物体表面成直角，所以这种应力通常称为法向应力。

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:

什么是刚度模量(the modulus of rigidity)？

刚度模量（剪切模量）是一个给出单位面积作用在材料上的剪切应力的数字。在这里，变形力平行于物体的一个面，导致一个面相对于另一个面发生位移。其描述如下：

Shear stress from a force parallel to the surface.

So, shear stress () is given as:

这个方程与法向应力方程的形式相同，不同之处在于力的作用方式。

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:

弹性模量与刚度模量的关系

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

在该图中，轴向应变为：

横向应变为：

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.

弹性模量(modulus of elasticity)和刚度模数(modulus of rigidity)的区别

力的方向

弹性模量用于计算变形力与物体表面成直角时物体的变形。

刚度模量用于计算变形力平行于物体表面时的变形。

形状变化

在计算弹性模量时，物体在变形力作用下要么变长要么变短。

在计算刚度模量时，物体的一个表面相对于另一个表面发生位移。

相对大小

对于大多数材料，弹性模量大于刚度模量。这一规则的例外是具有负泊松比的所谓“auxetic”材料，但这些材料不太常见。