# What is the relationship between Elasticity and Compliance?

Compliance is like elasticity of hollow tube. Elasticity is less for instance for arteries so they are less compliant. There seems to some sort of relationship between compliance and elasticity.

Based on Tyler's comments:

• Compliance is the derivative of strain with respect to stress (or derivative of displacement with respect to force).
• Elasticity is like opposite of stiffness.

about which I am not sure.

One figure about compliance for vein and artery: where I think the slope of the curve (gradient) is the compliance of each curve.

What is an approximate relationship between the elasticity and compliance?

• I think you need to define your terms more carefully. Compliance is the derivative of strain with respect to stress (or derivative of displacement with respect to force). "Elasticity" is usually called "stiffness", if I'm interpreting your meaning correctly. It is the derivative of stress wrt strain (force wrt displacement). For a hopefully helpful analogy, compliance is to stiffness as electrical resistance is to conductance. – Tyler Olsen May 1 '14 at 6:28
• You are right. I had mistake in the body. Inelastic object is like a stiff body. Elastic - the reverse. So there is no inverse relationship between the two. There must some polynomial relationship between the two. I think compliance is in 3D space while elasticity in 1D. Otherwise, similar thing. – Léo Léopold Hertz 준영 May 5 '14 at 8:58

## 3 Answers

But then more elastic the structure is more will be the difficulty in stretching it or trying to develop elastic energy in it having said that why cant we consider compliance to be the product of distentibility and the volume of the vessel and because of this even highly elastic vessels have higher compliance beacuse of the large volume of blood like the aorta which they can accomodate

$Elasticity$ describes the relation between the $force$ (or $stress$) on a body and the corresponding $distortion$ (or $strain$). $Force/distortion$ (or $stress/strain$) is called $stiffness$; the inverse, $distortion/strain$ (or $strain/stress$, is called $compliance$. Which is more useful depends on which of each pair you start with which of each pair you're trying to find.

Two misconceptions you have. Firstly, $inelastic$ doesn't mean stiff; it means the material doesn't return to its original shape when the force is removed. Sand is inelastic. Secondly, stiffness, compliance and elasticity can be modelled in any number of dimensions: a simple spring has them in 1-D, a rubber sheet has them in 2-D, a lump of metal has them in 3-D.

I think i got it elasticity will be inversely proprtional to the compliance only when we are talking about the number of elastic fibres or the elasticity imparted by them and no other fibres . However in the arteries as we go further into the arterial tree the sheer amount of elastic fibres decreases but there is an increase in the smooth muscle fibres which are now the weight bearing fibres and are devoid of elasticity hence this can be the reason as to why there is an increase in compliance although there is a decrease in elastic fibres but way more increase in non elastic smooth muscle fibres