# Elasticity and rigidity

Is it possible for a tube (artery) to gain rigidity as well as lose elasticity at the same time? Isn't this situation paradoxical because increasing rigidity means increasing the elastic modulus? The reason why I am asking this is because in ageing or arteriosclerosis it is said that arteries become rigid as well as lose elasticity and become weak as well. Can someone please explain how this happens?

• Increasing the elastic modulus means that materials become stiffer not more easily deformed. Commented Apr 3, 2017 at 15:33
• Yeah so more elastic right ie means arteries become rigid and elastic then why every where on the net this process is described as loss of elasticity ie being more easily deformed Commented Apr 3, 2017 at 15:40
• The difficulty is the terminology. You need to define your terms. Modulus of elasticity is misleading : increasing modulus means increasing stiffness. As in my first comment, loss of elasticity means that elastic modulus increases and the material becomes stiffer, more rigid. Elastic vs plastic refers to ability to return to original shape. Commented Apr 3, 2017 at 15:53
• Elasticity means decreased strain for the same stress ie more resistance to deformation and a body which is more elastic is difficult to deform and can easily rebound to the original configuration as in steel which is more elastic than rubber Commented Apr 3, 2017 at 16:17
• I think the websites use the general term for elasticity which we use in daily lives as in more rubber band type than steel so that is the difference . Conventional and physical definitions Commented Apr 3, 2017 at 16:18

Elasticity refers to the ability of a material to return to its original shape after the load is removed. If the "elastic limit" of the material is exceeded, the material will retain some permanent deformation. The strain at the transition between elastic behavior and yield behavior of a material is called "the elastic limit."

Stiffness or rigidity is a different consideration. It is the stress that the material experiences divided by the strain that the material is subjected to (when the strain is below the elastic limit). The higher the stiffness, the more difficult is it to deform the material (at least in the region of elastic behavior)

• So as u said in the elastic limit a stiff material will be more elastic and vice versa because both have the same meaning in the elastic region right . And a material which is more elastic has to be more rigid because the cause of elasticity is internal forces and so is the cause of rigidity also internal forces Commented Apr 4, 2017 at 2:25
• Hu??? I don't even understand what this is saying, but it definitely is not what I said. Commented Apr 4, 2017 at 2:27
• Okay so can u tell me how a material can be inelastic and rigid at the same time Commented Apr 4, 2017 at 3:35
• @user141356, Nothing in the universe is truly rigid. An object is practically "rigid" if it never experiences significant strain. But the moment you say "inelastic", you are talking about significant strain. Better to say "stiff" instead of "rigid". Imagine a steel rod: It's stiff if you need a lot of strength to bend it, or flexible if you only need a little strength. It's elastic if you can bend it a long way and it snaps back to its original shape when you let go, or inelastic if you only have to bend it a little way before it stays bent when you let go. Commented Apr 4, 2017 at 5:03
• @user141356 "How can a material be inelastic and rigid at the same time.?" We have been talking about the meaning of the terms "elastic" and "rigid/stiff," as applied to real materials. The issue is, can I conceive of a material that is both inelastic and rigid? An extremely highly viscous Newtonian fluid would be stiff and hard to deform, yet it would be totally inelastic. If you deformed it, it would stay in the new shape and not return to its original shape. I can also conceive of an elastic material that has low rigidity. Rubber. Commented Apr 4, 2017 at 10:42

To begin with, the expression "loss of elasticity" is slightly inaccurate; one should say there is a "loss of strength" (either in stress or in strain).In fact, some published papers have found just that Hernández and Franke (2004), Greaney and Farquhar (2011).

The material of the artery in general would present a similar (visco)elastic behavior, but the effective Young's modulus under tensile forces will be greater, but the maximum achievable stress or strain will be lower. Therefore, the resilience does not change very much, a greater slope is partially compensated by a loss in the maximum values in which this slope operates.

• "Elasticity" is used especially inconsistently in the biophysics literature, with various authors using it to mean stiffness, compliance (the reciprocal of stiffness), and a number of other properties. Commented Jun 10, 2022 at 14:37