I saw a question on the internet that is exactly the same as yours followed with many responses.   

http://www.eng-tips.com/viewthread.cfm?qid=381089

Let's consider stress-strain behavior.

Inelastic: Stress-strain curve is not linear

Plastic: Residual strain remains after unload.

In many cases, they are used in the same meaning, but definition is different as shown above. Rubber is a good example to distinguish them. Stress-strain curve is not linear (therefore, inelastic), but it comes back to original shape after unload (therefore, non-plastic).

In structural engineering, especially in the most common construction materials such as concrete, steel, and the recently emerged FRP products, the constitutive model is represented either by, straight line, curved line, or a combination of the two. in most cases straight line represents the "linear elastic behavior"; However, a horizontal straight line sometimes drawn to represent the plastic region to indicate the engineering stress-strain curves in some courses of the second year of engineering. In biomechanics, constitutive models tend to be completely different, other types of elasticity are generated by different materials. Rubber and soft tissues for example exhibit J-shaped elastic stress-strain curves. "Inelastic" is somehow a broad term, using precise terms that accurately describe the behavior of the materials is usually more attractive in science communities.

Dear Chalise,

let me say a few words about your question. When a body is loaded in elastic range, doens't mater if it follows Hooke's law (linear stress strain relationship) or not (a curve), the most important fact is that when the load is drop out completely, the body will be back to its original state with no deformation.

When it reaches certain value of stress, mainly the metals (steel, aluminium, copper, titanium, etc.), and the load is retired, some residual strain, called plastic strain, is presented and will not disappear except if the body is reloaded again but in the opposite sense, if it is possible to do so. The stress at which the plastic strains begins to appear is called "yield stress" and for mild steel this path change is very easy to identify trough the tension test diagram. For others materials and metals (aluminium and its alloys) the point where this behavior begin is not so clear and is defined by a stress corresponding to a certain amount of plastic strain (2 mm/m, for example), or best, by the so called residual strain.

These two guidelines (differences) give answer to what is elastic behavior only. I understand that "plastic" behavior comes from the ideal material, that left the linear behavior at the yield stress, and once at this stress, it can reach any value of strain without any increase in stress. When you unload this material, you will only retire the elastic strain. All that material catch in strain will be plastic, or be it, will be residual strain after unloading.

This is the ideal model of the plastic theory, which permitted several works about limit load and the plastic hinge formation that brings the structure to collapse. Up to certain values of loads, stress, materials (steel)  and strains, this theory can be applied and was applied  between years1960-70.

But research moved on, and the stability behavior and the formation of the called plastic-hinge interact and there's not such direct hinge behavior, the yield grows in to the section, so there's part of the section that still work elastically while other parts of the same section are under plastic flow (yielding).

This knowledge is more abroad today, many different models had appeared to simulate the beginning and the expansion of the yielding not only in the called more high stressed section of the body, but also in the nearby ones. Then, recognizing that both behaviors are presented in the model, the usual term to define this behavior is "inelastic".

My work research is on advanced analysis using plastic zone models. This mean to make a direct analysis where the members plasticity (not points, parts of the member, along its length) is present and changes not only the strength but most of all interact with member and structural buckling. Hope you like to go on studying plasticity and you'll see more clearly what I'm telling you now.  For example, look at

Chen,W.F. and Sohal, I. (1995) – “Plastic Design and Second-Order Analysis of Steel Frames" – Spring-Verlag -  New York.

I know this book is 20 years old, but is very good for you to begin and learn.Sure I like this subject so much,  sorry to be longer then I wanted.

Good luck! (I corrected mis typed words only in 24/11/2021, sorry).

Thank you very much to all of you  for your informative answers now I got the difference very well

viscoelastic, anelastic, plastic, viscoplastic, damage, ... can be considered as inelastic behaviors, ie not purely elastic (linear or not)

Dear Bharat Chalise,

Please check the attached figure.

Regards

Waleed

I would like to say something about Dr. Nozomu YOSHIDA's answer, which said "Inelastic: Stress-strain curve is not linear".

This statement leads to incorrect direction because there are materials like mild steel, copper, aluminium and even rubber, which behave elastically but without obbeying Hooke's law in some parts of the stress-strain diagram.

Or best, the elastic modulus is not a constant (like Young modulus), but it changes according to the strain. The material represented by the Ramberg-Osgood model observes this kind of behavior.

So it must be cleared that:

1. For pure elastic material following Hooke's law, stress-strain diagram is a straight line.

2. For some elastic materials that not obbey Hooke's law, the diagram is not a straight line, it is a curve, and sometimes, one part is straight complemented by a curve part.

3. The inelastic behavior has a nonlinear diagram (true!), but not every nonlinear diagram mean that material has inelastic behavior.

That is it.

Let me give you an answer from a great book I have read recently,

Elastic materials are (history and rate) independent with no permanent deformations regardless if the constitutive law is linear or not. In addition, there are not hoop stresses" the loading and unloading curves are identical". this means ones you know the stress you can find the strain easily and vice versa. any property outside this section converts elastic materials to inelastic materials.

Inelastic materials are history dependent (and , or) rate dependent with (permanent deformation or not) and ( with linear or not linear constitutive law). i.e. visco-elastic, visco-plastic, plastic, etc.

Stress alone is not enough to find the strain and vice versa " you need to know the rate of the applied stress (rate dependent), or the time when the stress is firstly applied, or if you are in loading or unloading portion ( history dependent).

At the end, most of materials have inelastic properties.