Is material stiffness can be related to inertia of the material???

Question

The material stiffness "k" that we model in any mechanical system, can we relate it the inertia of the system?
-The inertia is resistance to motion, but when we talk about stiffness its the measure of how much force is required to deform the material, now in classical spring element, deformation is considered as displacement, does that mean, we are talking about the same thing in different ways??

Answer 1

No. It is a property of material not related to inertia in any way.

Answer 2

Stiffness of a material is the ratio of the stress to strain of the material. ie., the ratio between the force for deforming the material and and the amount of deformation undergone by the material.

Inertia is nothing but stored energy, like in ur capacitor (or) battery. The the angular velovity of the fly wheel will tend to produce a centripetal force trying to tear away the fly wheel.

The greater the force the greater the distortion.

The relation ur trying to bring between inertia and stiffness is like comparing the force required to break a slack rubberband and a stretched rubberband. They will be same because of the extra force required to actually stretch the rubberband.

Stiffness of a material is a constant under identical conditions

Answer 3

I'm afraid you may have two different mechanical models confused. Inertia is a measure of energy that is a function of a body's speed. This has nothing to do with stiffness.

However "moment of inertia" and stiffness are both factors for bending strength. A beam's moment of inertia is a function of the depth of the beam and shape. Steel is a lot stiffer than wood or plastic. The factors of "moment of inertia" and stiffness generally determine the strength of a beam.

Answer 4

The concept of inertia whether for rectilinear or rotational motion is the property of the system looked from outside. For rectilinear motion mass is the measure of that quantity and for rotational motion the sum of mass times square of the distance from axis of rotation. When you talk of displacement of a particle attached to the spring, mass of the particle takes care of the inertia of the particle but the same quantity also happens to be the deformation of the spring. Now this is internal to the spring which takes place as a result of deforming forces one applied by the falling mass because it is attracted by earth and another applied by the reaction of the support attached to earth. As a result of this the spring generates a restoring stress which keeps the attached mass in equilibrium.

I am happy that you have dared to ask this question. In fact concept of inertia is not required in the discussion of Newton's laws at all, when mass suffices. The meaning of inertia in everyday language is sluggishness which means we apply some 'force' on ourself for not doing a thing. But the mass does not apply any force on itself; it just scales down the acceleration any external force can produce in a particle of given mass.

Answer 5

stress ability the quantity of deflection for a given load. For a torsion subject, which ability larger 2d of inertia, or greater beneficial areas for greater figidity. larger modulus will artwork additionally. potential is a diverse remember. maximum engineering aspects fall right into some categories, like brittle and ductile aspects. potential is the optimal load you could practice until now you get everlasting deformation. fantastically unusual to realize this in a brittle fabric, as they in many cases in simple terms ruin, yet greater in all possibility with a ductile fabric like a steel. you have seen a fork or a spoon or a sheet of steel completely deformed yet no longer broken. you have surpassed yield yet no longer in basic terms top for that ductile fabric.