We have several types and sizes of an object with particular homogeneous material and we want to analyze their stiffness and hardening after applying loads. I suppose we have the same elastic modulus for all of them despite different geometry. Although we'll have different tangent modulus, because tangent modulus is related to elongation at different situations (break and yield strength). Is that right?
Thanks in advance.
Dear Sadegh, I believe you're correct, supposing that the critical stress (st) in an intermediate column exceeds the proportional limit of the material (spl), then the Young's modulus at that particular stress-strain point is no longer E, but it decreases to the local tangent value, Et.
If you consider your material linear elastic (i.e. the elastic modulus does not change within the elastic range) and you use the same material for all your samples, then it is right to assume that the elastic modulus is the same for all your samples despite different geometries. Elastic modulus is a material parameter that does not depend on the geometry. What depends on the geometry is the relationship between external forces and stress.
However if the material is not linear elastic, then the tangent modulus changes with strain. Again, it is a material parameter so it does not change with the geometry. But for a given applied load, two different geometries will lead to two different stress/strain states.
Thanks Gusztav and Aline. I got the point that Elastic moduli does not change with geometry because it is a "linear ratio of stress/strain" and Tangent moduli calculates the slope of stress-strain curve after yield point in the non linear plastic domain and it is also ratio of stress/strain so no dependency on volume change.
The problem is that, we have "same material type" of objects but different Hardness (I assume Hardness is not a material property) and different Volume. I thought different Hardness means different stiffness, so there would be difference in the elasticity of those objects, hence they would have different plasticity as well (considering non linear material). Therefore, do you think that do we have to consider different Elastic modulus, yield point and ultimate strength for those objects? and base on these, different tangent moduli?
Thanks
Dear Sadegh,
Hardness is actually a material property, related to the material stiffness (modulus) but not only (surface treatment, viscoelasticity, etc). Do you only have data about the material hardness ? the relevance of hardness depends on the type of loading you apply : for quasi-static tensile tests, stiffness comes into play while for rebound hardness, hardness comes into play.
I would say that there is no reason for your materials to have the same stiffness with different hardness ; it could be so, but it is definitely no straightforward.
Dear Aline. Thanks for your answer.
I have Hardness and Volume information about my data. Actually, it is Calcium score in the artery for different patients, thus only hardness and volume can be expected. There're several definitions about hardness while I dug the books, I concluded it depends on one is looking for hardness of elasticity or hardness of plasticity. I took the definition which says "resistance to plastic deformation", so deformation after yield point leading to rupture/break. But since I have CT and Haunsfield Unit gives me the stiffness of the tissues in the image, thus I consider for each calcified plaque, stiffness is changing as well. Hence we'll have change before yield point in the elastic region.
Therefore, based on above information, I concluded that I need to consider both elastoplasticity of different calciums.
Btw, I'm trying to assess the rupture and penetration of the calcified plaques imposed by different loads. Therefore I'm focusing on hardness of materials, since I have to distinguish hard and soft plaques using those mechanical parameters. If you have any source or sample article in your mind that'd be great help.
Thanks for your help.
Dear Sadegh
You said it right... with same elastic modulus, slope in non-linear domain for tangent modulus is a varying one... this can be modeled thro piecewise non-linear approach... For example, if we have Yield and Tensile strength at break, it can be modeled thro "BISO" the same scenario can be modeled by "MISO" with multiple points, this refers to ANSYS... As I have worked with ABAQUS, it is also possible in ABAQUS or for that matter in any non-linear commercial codes... One of the papers modeling non-linearity in ANSYS in my list of publication may be useful, pl. feel free to down load .
Cheers
LR
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