What is elastic stiffness? What about 2nd and 3rd order elastic stiffness

In summary, the text discusses the force-displacement behavior of Graphene and its interpretation within a framework of nonlinear elastic stress-strain response. It yields second- and third-order elastic stiffnesses of 340 Newtons per meter (N m–1) and –690 Nm–1, respectively. These are considered as higher-order stiffnesses beyond the traditional Young's Modulus, indicating a more complicated relationship between stress and strain.
  • #1
dkell
1
0
I'm researching CNTs and am currently describing Graphene as I lead from carbon atoms to nano-tubes. I've come across this:

"The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 Newtons per meter (N m–1) and –690 Nm–1, respectively." http://www.sciencemag.org/content/321/5887/385.full

The text says that the the "Elastic Stiffness" = Young's Modulus, but what about second- and third-order elastic stiffnesses?

I know elasticity is a materials ability to return to its previous shape, and stiffness is resistance to deformation or strain.

Thank you for your help.
 
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  • #2
welcome to pf!

hi dkell! welcome to pf! :smile:
dkell said:
… nonlinear elastic stress-strain response …

linear elastic stress-strain response means that stress = constant times strain …

ie, hooke's law (and young's modulus) appplies​

non-linear elastic stress-strain response means that stress is a more complicated function of strain …

eg k1x + k2x2 + k3x3 + …

here, the constant k2 would be the second-order stiffness, the constant k3 would be the third-order stiffness, etc :wink:​
 

What is elastic stiffness?

Elastic stiffness is a measure of a material's resistance to deformation under an applied force. It describes how much a material will stretch or compress when a force is applied to it. It is often represented by the symbol "k" and is measured in units of force per unit of length, such as Newtons per meter (N/m).

What is 2nd order elastic stiffness?

2nd order elastic stiffness, also known as shear stiffness, is a measure of a material's resistance to shearing forces. It describes how much a material will deform or twist when a shear force is applied to it. It is often represented by the symbol "μ" and is measured in units of force per unit of area, such as Newtons per square meter (N/m^2).

What is 3rd order elastic stiffness?

3rd order elastic stiffness, also known as bulk stiffness, is a measure of a material's resistance to volumetric changes. It describes how much a material will change in volume when a force is applied to it. It is often represented by the symbol "β" and is measured in units of force per unit of volume, such as Newtons per cubic meter (N/m^3).

How do elastic stiffness, 2nd order elastic stiffness, and 3rd order elastic stiffness relate to each other?

Elastic stiffness, 2nd order elastic stiffness, and 3rd order elastic stiffness are all different measures of a material's resistance to deformation under an applied force. They are related to each other through the material's elastic modulus, which is a constant that describes the relationship between stress (force per unit area) and strain (deformation). The elastic modulus can be calculated from any of the three types of stiffness values.

How is elastic stiffness determined?

Elastic stiffness is determined through various experimental methods, such as tensile testing, compression testing, or shear testing. These tests involve applying a known force to a material and measuring the resulting deformation. The stiffness value can then be calculated by dividing the applied force by the amount of deformation. Additionally, elastic stiffness can also be calculated using theoretical models and equations based on a material's elastic properties and geometry.

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