What is finite elasticity talking about?

[fruitkiwi]

Hi, dear all,

recently study the solid mechanic continuity, keep reading about to solve large deformation of material, you will need so called "finite elasticity"

What is this finite elasticity refer to ?
"Finite elasticity is a theory of elastic materials capable of undergoing large deformations."

Erm, this sentence don't carry any meaning to me.
I thought elastic material should always be finite, as it has finite length, which allow us to have elasticity measurement. if i have large deformation, will it change anything about elasticity?or it refer to nonlinear elastic material?

mind to share?

 

[fruitkiwi]

anyone mind to share about this topic?
or my question is too general?

 

[K^2]

I think, "finite elasticity" in this context is simply used to distinguish from "rigid bodies", whose elastic coefficients are effectively infinite and deformations infinitesimal. Thus, a body exhibiting "finite elasticity" would be capable of "large deformations" that rigid body is not.

 

[fruitkiwi]

Hi, K^2.

thank you for your explanation.
It is solved

to support your statement, i find the following from wikipedia.
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected.

i never realize have such differences. thanks a lot

 

[PJC01]

Sure, let me explain. Finite elasticity is referring to a branch of mechanics that deals with the behavior of elastic materials, which are materials that can deform and then return to their original shape when the applied stress is removed. This theory specifically focuses on materials that can undergo large deformations, meaning that they can stretch or compress significantly without breaking or permanently deforming. This is in contrast to infinitesimal elasticity, which deals with small deformations.

You are correct in thinking that all elastic materials have finite elasticity, as they have a finite length and can be measured for their elasticity. However, the term "finite elasticity" is used to distinguish it from infinitesimal elasticity and to specifically refer to the study of large deformations.

In terms of nonlinear elastic materials, this theory does apply to them as well. Nonlinear elastic materials are those that do not have a linear relationship between the applied stress and resulting strain. This means that as the material deforms, the relationship between stress and strain changes. Finite elasticity takes into account this nonlinearity and can accurately predict the behavior of these materials under large deformations.

I hope this helps clarify the concept of finite elasticity for you. Let me know if you have any further questions.