I was conducting a FEA analysis of a symmetric isotropic structure under a loading condition. I will not mention the material I was using. Under that loading, one part of the structure was in tension and other in compression. When I reversed the loading condition, the part that was in compression previously was now in tension and vice versa. However, the displacements and the Von-Mises stresses that were seen on the part of the structure that was in tension in the initial loading condition, and again which was in tension in the reversed loading condition, I saw a difference in it and I couldn't understand why it was happening. So I thought maybe it is possible for the material to have different elastic modulus and Poisson's ratio under compression and tension. Is this true? If yes, then in most of the FEA softwares, there is option to add only one elastic modulus. Why is that? Is there any specific class of materials where this happens, or we have to conduct experiments to individually check each and every material if their elastic modulus is the same of different under tension and compression?
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The short answer is that it can, but it rarely occurs (most usually in material systems) or it has a noticeable difference. However, the question is what exactly are you noticing in the simulation because it could have many sources. Could you post more details on your FEA analysis/results? – NMech Jun 15 '21 at 05:54
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@NMech, yeah so it just cleared up that the elastic modulus for general metals should be the same under both, tension and compression. Then it appears as if the geometry is not exactly symmetric, thats why I am seeing a difference in the Von-Mises stresses. – Rameez Ul Haq Jun 15 '21 at 11:55
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Again, it would be difficult to assess without looking at your model. – NMech Jun 15 '21 at 12:29
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1Isotropic material properties, nonlinear material properties, and structural symmetry, are independent of each other. Since you don't tell us the material, and the question implies there was time-dependent loading, we don't have enough information to give an useful answer. – alephzero Jun 15 '21 at 12:37
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For small strains of stable materials, the tensile and compressive elastic moduli are equal. This is equivalent to saying that a smooth energy minimum looks like a (symmetric) parabola up close; an energy well in the shape of a parabola characterizes an ideal spring with equal elongation and contraction spring constants.
This approximation works well for metals, ceramics, and crosslinked polymers, for example, whose elastic strain is small (1%, say). This is why you have the option to enter only one Young's modulus, for example. However, the approximation typically does not work for large elastic strains of hyperelastic materials such as elastomers, which may stretch their own length (100% strain) and much more. As shown below (source), the stress–strain slopes are visually identical for slight positive and negative strains but differ for larger strains.
Since the same argument holds for the bulk and shear modulus, it must hold for Poisson's ratio, which is not independent if Young's modulus and either the bulk or shear modulus are specified.
Chemomechanics
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So why is this the case that for general metals, some of the metals have difference in yield/ultimate strength for tension and compression? Although, as you have said, that the elastic modulus should be the same for small strains? And I just want to confirm this, so you mean to say that if I stretch a metal, like Aluminum, with a 100 N force, and imagine it displaces about, say, 1 mm, then if I would compress it with the same force, the compressive displacement should again be equal to 1 mm, right? – Rameez Ul Haq Jun 15 '21 at 11:51
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@RameezUlHaq yield/ultimate stresses are a lot easier to explain (and there are many mechanisms). For example In tension, when a crack forms, in tension it tends to increase, however, in compression effectively the edges of the crack are brought together. Another effect is due to the fact that although in tesnion you can have theoretically more than 100% strain (at least in some materials), in compression that is not achievable. – NMech Jun 15 '21 at 12:28
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@Rameez See this post for the usual (idealized) Elastic Modulus for steel of different grades. https://engineering.stackexchange.com/questions/44686/youngs-modulus-in-astm-specification-a36 – r13 Jun 15 '21 at 17:03
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@NMech, ofcourse I am aware of the crack formation dependence on the type of loading applied. But I am still unsure why can the compressive yield/ultimate be different than the tensile one, for small strains, when both the same elastic modulus. I want to know the reason behind it. Like what is it dependent upon? – Rameez Ul Haq Jun 16 '21 at 12:51
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@r13, no that post was not at all useful for what I have asked here. – Rameez Ul Haq Jun 16 '21 at 12:53
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Typically, you don't consider yield/ultimate stresses at small strains but close to yield/failure. Its only elastic modulus you consider in small strains. – NMech Jun 16 '21 at 12:53
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So what you are saying is that when we are considering yield/fracture of a material, then this would mean that the strain is not ''small'', then in this case we should take into account what elastic modulus we are inputting? (like depending upon what kind of loading is it, compression or tension). I never heard from anyone who does this though. – Rameez Ul Haq Jun 16 '21 at 12:55
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@NMech, you said that, "you don't consider yield/ultimate stresses at small strains but close to yield/failure." First of all, i don't believe this because it depends on the material we are using. As said by chemomechanics, a typical small strain is said to be 1%. Some materials have strains at yield strength below 1% and some have above 1%. Moreover, if I go with your statement that the small strain phenomenon doesn't happen at the yield/tensile strength, then it means that the Elastic modulus should be inputted for compression and tension separately, if I am checking for yield/fracture. – Rameez Ul Haq Jun 16 '21 at 13:43
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@nmech, plus, i still couldn't grasp why and how can the yield/ultimate strength at compression and tension can be different. Like what phenomenon causes them to be different. Micromechanics, nature, etc, I don't know. – Rameez Ul Haq Jun 16 '21 at 13:47
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@RameezUlHaq probably we are talking about different things - since there is a least from my side a language barrier. I don't even know what that "small strain phenomenon" is, that you refer to. So, because, I think you have something very specific in mind (which I've asked you repeatedly to share in your initial post), I don't see any value in pursuing any further this discussion. – NMech Jun 16 '21 at 13:52
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