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What is stress? Who has ever seen stress? Is stress a physical quantity?

What is stress? Who has ever seen stress? Is stress a physical quantity?

Professor Yi-Heng Chen, Xi’an Jiaotong University, 710049, P.R.China

e-mail: yhchen2@mail.xjtu.edu.cn

 

In fact, this question has been bothering the present author for more than 15 years.

As well-known, all previous and present researchers who were/are majoring in solid mechanics in mechanical engineering or aerospace engineering always used the classical concept of stress as they used other physical quantities: displacement or strain etc.

However, there is no one in the world, who has ever seen stress by using any tool!

Moreover, no one really understood what the physical meaning of stress is!

Or instead, no one recognized the detailed fact whether stress is a real physical quantity?

 

In is well-known that for a given geometric coordinate system the displacements of a mass point of a solid are actually physical quantities without any doubt! This is because the displacements of a mass point could be directly seen or measured by using eyes, some advanced optic instruments, or even the electron microscope.

Thus their grads are also physical quantity at the same point where (or around a small region) the continuous first order differentials exist.

 

The major difficulty is what the stress is?

Obviously, the concept of stress is quite different from the strain and displacements at least due to the following three viewpoints:

(1) First, the stress is invisible or un-measurable by using any existing instruments including all optic instruments and electrical instruments, whereas the displacements or strains, as well known, are measurable. For example, some new optic instruments could be used to clarify mere 0.01 micro meter of displacements and 1 micro strain as GOM or other corporations reported. Moreover, some advanced electric microscope has 0.18 nano meter resolving power! 

(2) Second, the classical concept of stress is based on the generalized Hook law in elasticity and then it is extended to treat some structural problems in plasticity such as the plastic deformation theory or plastic fluid theory. More recently, this concept is extended to micro mechanics, damage mechanics, even nano mechanics. However, strictly speaking, this concept is not yielded from experimental observations but from the man’s brain! Thus, it is not a real physical quantity or, in other words, it is a pseudo physical quantity, just an imagined physical quantity! This question is easy to be proved because no one in the literature who claimed that he has seen the stress or he has measured the stress!

(3) Third, in non-linear and inhomogeneous materials under some loadings, there are many crystals (metal) or the particles (ceramic) with the size scale of several micros. Generally speaking, the stress field in an inhomogeneous material is not uniform or even not unique although the strain field or displacement field in the same inhomogeneous material is unique (the strain field could uniquely deduced from the measured displacement field). Due to micro defects nucleation, growth, coalescence etc (a nonreversible thermodynamic process), the measured displacement field varies and the deduced strain field varies as well. But each strain/displacement field might lead to several different stress fields, depending on the different constitutive relations established by researchers (or from researches’ brain). In other words, each constitutive relation would only yield a special stress field. Many constitutive relations would yield many different stress fields but researchers actually don’t see or measure their stress fields.

The things become clear!

The stress concept is actually established from the man’s brain rather than established from real observations!

This is a major obstacle at 21 century in advanced solid mechanics for modern materials because the advanced technology promotes the instruments becoming smaller and smaller such as MEMS or NEMS, and then researchers majoring in solid mechanics face on some challenge to study small scale mechanics such as micro mechanics or nano mechanics. However, no one could tell us whether the stress (as a macroscopic and pseudo physical quantity) concept is still valid in micomechanics or nano mechanics with defects?

If so, he should tell us as why?

If not so, he should tell us what is the possible and alternative physical quantity instead of the stress?

 

This question is very clear as shown in the following figures (attached from websites).

Figure 1 shows a microscope photo. There are many solid particulars in the photo in the inhomogeneous material. The question is what is the stress on the surface of each particular? How large the stress is? Is this valuable to find the detailed distribution of the stress field as the displacement field or strain field? More importantly, from the micro scale viewpoint, whether the imagined stress field, if it exists, could be used to introduce some phenomenological parameters to evaluate the material failure?

 

Figure 1. The first example of microscope photo attached from website.

 

Figure 2. The second example of microscope photo attached from website.

 

Figure 2 also shows a detailed displacement field as well as the strain field but no one could obtain the detailed stress field although the detailed strain-displacement field could be measured.

 

Figure 3. The third example of microscope photo attached from website.

 

Figure 3 show another displacement field with some surface cracks. However, it is still unclear as what is the stress field although the strain-displacement field could be measured.

 

Moreover, some famous experts have claimed that the stress in their analyses at the nano scale is as large as 100GPa! This stress is over the material elastic modulus? This result privates an evidence that the stress concept is not realistic in nano mechanics with defects.

 

Of course, it is not fair to overthrow the previous contributions based on the so-called stress analyses. Indeed, all classical strength theories including the fracture mechanics were established from the stress analyses which yielded a large amount of fortune and received significant attention from researches!

Also, the author does not wish to simply throw over this concept. This might upside down!

The goal of the present paper is to motivate the further discussions with other researchers who are interested in the topic and to introduce an alternative physical quantity to replace the stress concept, especially in inhomogeneous mechanics, micro mechanics and nano mechanics.

From the physical view point, the configurational force and the associated invariant integrals might be a useful choice instead of working in stress analyses. This is because these concepts are induced directly from Eshelby’s force with defects, which is based on energy balance viewpoint. In fact, the author has some initial attempts at this research direction [1-17] including one book [11] summarizing the potentials applications of the projected conservation laws of Jk-vector and the M-integral and the L-integral.

Other advances in this topic such as the Fatigue Damage Driving Force (FDDF) for a cloud of micro-defects will be reported in the author’s subsequent papers.

 

[1] Chen Yi-Heng., On the contribution of discontinuities in a near-tip stress field to the J-integral, International Journal of Engineering Science, Vol. 34, 819-829(1996).

[2] Han J. J, and Chen Yi-Heng., On the contribution of a micro-hole in the near-tip stress field to the J-integral, International Journal of Fracture, Vol. 85, 169-183(1997).

[3] Zhao L. G, and Chen Yi-Heng., On the contribution of subinterface microcracks near the tip of an interface crack to the J-integral in bimaterial solids, International Journal of Engineering Science, Vol. 35, 387-407(1997).

[4] Chen Yi-Heng., and Zuo Hong, Investigation of macrocrack-microcrack interaction problems in anisotropic elastic solids-Part I. General solution to the problem and application of the J-integral, International Journal of Fracture, Vol. 91, 61-82(1998).

[5] Chen Yi-Heng., and Han J. J.  Macrocrack-microcrack interaction in piezoelectric materials, Part I. Basic formulations and J-analysis, ASME Journal of Applied Mechanics, Vol. 66, No. 2, 514-521 (1999).

[6] Chen Yi-Heng., and Han J.J. Macrocrack-microcrack interaction in piezoelectric materials, Part II. Numerical results and Discussions, ASME Journal of Applied Mechanics, Vol. 66, No. 2, 522-527(1999).[7] Tian W.Y. and Chen Yi-Heng., A semi-infinite interface crack interacting with subinterface matrix cracks in dissimilar anisotropic materials, Part I, Fundamental formulations and the J-integral analysis, International Journal of Solids and Structures, Vol. 37, 7717-7730 (2000). [8] Chen Yi-Heng., and Tian W.Y. A semi-infinite interface crack interacting with subinterface matrix cracks in dissimilar anisotropic materials, Part II, Numerical results and discussions, International Journal of Solids and Structures, Vol.37, 7731-7742 (2000). [9] Chen Yi-Heng., M-integral analysis for two-dimensional solids with strongly interacting cracks, Part I. In an infinite brittle sold, International Journal of Solids and Structures., Vol. 38/18, 3193-3212 (2001).

[10] Chen Yi-Heng., M-integral analysis for two-dimensional solids with strongly interacting cracks, Part II. In the brittle phase of an infinite metal/ceramic bimaterial,  International Journal of Solids and Structures., Vol. 38/18, 3213-3232 (2001).

[11] Books: Advances in conservation laws and energy release rates, Kluwer Academic Publishers, The Netherlands (ISBN 1402005008), 2002.[12] Chen, Y.H., and Lu, T.J., (2003) Recent developments and applications in invariant integrals, ASME Applied Mechanics Reviews, Vol. 56, 515-552.

[13] Li Q, Chen YH. (2008) Surface effect and size dependence on the energy release due to a  nanosized hole expansion in plane elastic materials, ASME Journal Applied Mechanics, Vol. 75, Novermber.

[14] Hu Y.F., and Chen Yi-Heng, (2009), M-integral description for a strip with two holes before and after coalescence, Acta Mechanica, Vol. 204(1), 109-.

[15] Hu Y.F., and Chen Yi-Heng, (2009), M-integral description for a strip with two cracks before and after coalescence, ASME Journal Applied Mechaics, Vol.76, November, 061017-1-12.

[16] Hui T., and Chen Yi-Heng, (2010), The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings, ASME Journal of Applied Mechanics, Vol. 77. 021019-1-9.

[17] Hui T., and Chen Yi-Heng, (2010), The two state M-integral for a nano inclusion in plane elastic materials, ASME Journal of Applied Mechanics, Vol. 77. 024505-1-5.

      

 

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Waht_is_stress_figures.pdf96.09 KB
What is stress_second_.pdf395.61 KB

Comments

I think this is a question of metaphysics.

oafak's picture

The author is right that stress is a definition. He is also right that stress fields are not unique simply because what stress you have depends on the definition you are using. I wonder however why the author is so lenient on the issue of strain while exacting on stress. This author has also not seen strain either. That too is a matter of definition. The dispalcement is of course measurable. Then strain is defined in various ways since there are several gradient functions that you can get on any displacement field.

It is true that other measures of force intensities may be called for. That will not erase the need to use the stress concept as these are likely to be more cumbersome even if more useful in somne specific circumstances.

You misunderstand the opinion arising from me.

Obviously, the strain is a physical quantiy because it is induced from mathematical manipulations such as differetials ect., without any use of the materials constants. Even though the strain might be multiple values as one could use small deformation assumption (the first order approximmation), finite deformation (the first and the second orders approximation), and the gradient deformation.

Any way, of the most significance is that a physical quantity should not depend on a man made constitutive relation (this is a definition arising from one’s brain).

You may want to see this: http://imechanica.org/node/1001

Amit 

I have just read your viewpoint submitted to the website in 2007. In fact I have been doubting  the stress concept since 1995 and reported several lectures in the 21th century, e.g., 2004 in Xi'an,2006 in Harbin,  2008 in Beijing, 2010 in Xi'an.

Also, I discussed my viewpoint with Professor Suo Z in 2005 in Xi'an although he seems not agree with me.

Indeed, this is a fundamental and philosophical question that might induce some impetuously argument among the researchers who are majoring in solid mechanics.

Early in 2000, I had found  that the so-called effective elastic moduli theory has some shortcoming in description of damage and damage evolution. I proposed a M-integral description to replace it. Since then, my students and I also find the Fatigue Damage Driving Force for a cloud of micro defects motivated by the well known Crack Driving Force.

We did many exparimental observations and nummerical simulations which do deonstrate our viewpoint based on the configurational force.

Any way, I would like to discuss with you in the hope that we could find a way to re-build the fundamental system beyond the stress concept.

At present, I am working in a big program arising from NSFC concerned to the configurational force in micro mechanics and nano mechanics with defects.

I deeply hope that you and I could establish a new framework instead of working in stress analysis.

Professor Yi-Heng Chen

   I think the argument of the author is true... But a  little more fundamental question, Can we measure a force? We can measure force, using a load cell, but still we are measuring displacement and, from the same stress- strain equation we are  determining the force . (Of course we can measure it using a F= m*a relation, and lets don't consider it right now)

   I feel that  stress is imaginary concept , or just a defenition which we made as a normalised force . Failure and other  theories,  formed in terms of stress, and not in terms of displacement/ strain might be just because of the historical reasons.

   To add a bit more, the fundamental / measurable quantity may not be the quantity which is easily understandable.  Any human being can sense acceleration and it is hard to sense velocity. but people can understand the concept of velocity in a much easier way than that of acceleration. it is the same case with mass and weight also. 

Sreenath.A.M
Asst. Professor
Mechanical Engineering Department
National Institute of Technology
Calicut,India

I believe that you misunderstand my opinion.

According to your argument the temperature is also un-measurable because any instrument you used to measure the temperature in a bottle would change the situation in the bottle and in turn change the original value of the temperature in the bottle without use of the instrument (say, the temperature probe or temperature gage). This is the well known un-measurebale principle in physics far apart from the present discussion. It is obvious that one did measure the temperature approximately within a very small relative error, say, 1% (e.g., your room temperature could be controlled around 22C, which did have a small error, say, 21.8C-22.2C). No one, including you and me, cares the accuracy of this.

However, as regards the stress, no one could measure it approximately in micro scale, say, around a particle or along the boundary between two particles in a matrix material, even though one could use any tool, say, the photoelastic instruments or electric microscope, to measure displacement

Moreover, unlike the stress, the force of course is a physical quantity since it could be approximately measured by using many tools. Different tools might only induce some errors but not induce quite different values of the force. Whereas the stress is a pseudo physical quanty since it could only be evaluated by using a constitutive relation (a definition done by a man’s brain). Different constitutive relations would yield quite different values of the stress and the relative errors might be over 100%!

I should say sorry because we are discussing quite different problems.

Your discussion put me in very unpleasure situation.

Arash_Yavari's picture

Dear Yi-Heng:

In your Word file I see some strange sentences that don't make much sense, e.g.

"(2) Second, the classical concept of stress is based on the generalized Hook law in elasticity and then it is extended to treat some structural problems in plasticity such as the plastic deformation theory or plastic fluid theory. " -----> What is the relation between "Hook's law" and definition of stress?

"Generally speaking, the stress field in an inhomogeneous material is not uniform or even not unique...". -----> What do you mean by "not unique"?

"But each strain/displacement field might lead to several different stress fields, depending on the different constitutive relations established by researchers (or from researches’ brain)." -----> If you pick a strain measure and a constitutive equation, how can you get more than one stress measure? Again, I don't see how this can be relevant to definition of stress.

Instead of citing seventeen papers/books (mostly related to fracture mechanics), could you mention just one paper in which you have addressed this "issue" you see with stress?

Regards,
Arash

Dear Dr.Arash

I only wish to answer one of your question.

 What is the relation between "Hook's law" and definition of stress?

My opinion is that using the measured strain and the Hook's law you could obtain one kind of stress with some material constants. However, using the same strain and another constitutive relation, say, plastic deformation theory, you could obtain another kind of stress. So, the stress is not unique although the strain is unique.

Of the most significance is that each constitutive relation, whatever it is simple or complicated, always includes some material constants arising from definition (man's brain), whereas the strain measurement could be done by some modern optic instriment without any treatment of material constants as the GOM corporation claimed.

Regards

Yi-Heng Chen

Therefore, the stress is a pseudo physical quantity

Arash_Yavari's picture

If you take the same strain (you're thinking about linearized strain) and use another constitutive equation you're looking at another body so stress would be different, in general. You pick a strain measure and then your (free) energy density would be a function of strain. This then gives the corresponding stress measure. I don't really see what the big deal is here.

Regards

Arash

Does the same body under a load has two deformation states?

Or instead, Does the same bady under a load has two stress distribution state?

Please see the figures in pdf I have just attached on.

Professor Yi-Heng Chen

Bin Liu's picture

Dear Prof. Chen,

 You might be interested in the discussion on http://imechanica.org/node/3181

 

Dear Professor Chen, 

I apologize for my ignorance but can you please tell me what instruments or as you call it, tools can you use to measure "Force" ? 

 

Regards 

 

JUAN GOMEZ

PhD Computational Mechanics

Professor

Applied Mechanics Group

EAFIT University

Medellin,Colombia

Dear Professor JUAN GOMEZ

Thank you for your question but please focus our attention on stress.

If not, I would like to ask you what instruments you can use to measure temperature?

In fact this is well-known un-measurable principle in physics which is beyond the goal of our discussion.

Regards

Yi-Heng Chen

JUAN GOMEZ

PhD Computational Mechanics

Professor

Applied Mechanics Group

EAFIT University

Medellin,Colombia

Jayadeep U. B.'s picture

Dear Prof. Chen,

You say that force is a physical quantity, but not stress.  I would like to have few clarifications:

1. Do you consider pressure as a physical quantity?

2. How about suface tractions; are they physical quantities?

In case you accept both pressure and surface traction as physical quantities, I don't see any reason why stress should not be a physical quantity.

As far as I understant, the difficulty you are pointing out is the nono-uniqueness of stress as per various stress measures.  But, in my opinion, assuming the "continuum" hypothesis to be valid, Cauchy stress is the "true" stress.  However, the use of Cauchy stress in an analysis presents various difficulties, the first and foremost being that it is defined with respect to the deformed configuration, which is not known apriori.  Hence, various other stress measures are introduced as approximations to Cauchy stress measure.  Hence, the non-uniqueness of stress has more to do with the practical needs of the analysts, than any fundamental issue with the "concept" of stress.

Anyway, I am just a beginner in these areas and would really appreciate getting corrected, if some of my concepts are wrong...

Regards,

Jayadeep

Pressure and tractions are quite different quantities from stresses in micro scale, say, along the surface a micro defect or along the surface between two particles in ceramics.

Of great significance is that the presure or traction on a solid surface is unique but the stress inside the non-homogeneous materials is not unique, depending on which constitutive relation you selected. 

Your question might be induced from my loss of attached figures which I try to attach on.

Professor Yi-Heng Chen

Jayadeep U. B.'s picture

Thanks for the clarification.  But I have few difficulties with your line of reasoning:

1. The constitutive relations are only empirical models.  They assume the existence of stress for their development, and hence cannot be used in deciding about the "soundness" of the concept of stress.

2. While talking about  micromechanics (or nanomechanics), we are going to a domain where the continuum hypothesis becomes more and more invalid.  In this case, not only stress, but all the field quantities (including pressure and surface tractions) become approximate.  Just to take examples, pressure is nothing but a statistical average of momentum transfer during collisions of atoms/molecules, and surface tractions are meaningless, when we don't even have a precise definition of a surface!  That is why I used the qualifier "assuming the continuum hypothesis to be valid" in my earlier reply. 

3. Since you appear to evade the question measurement of force, I shall be more explicit.  As far as I know, all the force measurement techniques rely on measuring some effect of force like the deformations.  Please let us know, if you know about any way of measuring force directly.  Talking about precision instruments does not help, unless we understand their working principles.

4. Measuring strains also have the same problem.  Either we are measuring deformations, or some secondary effects of deformations like change in electrical resistance.  And, hence strain at a point can not be measured as far as I know, only an average strain over a small length (however small it may be) can be measured.

5. Just out of curiosity, is there any way of measuring a vector directly, other than its scalar components?  Stress being a tensor, is a much more difficult situation, and getting access to the point you want to measure will make the measurements meaningless.  Also, pressure in a fluid is nothing but a hydrostatic state of stress.

Regards,

Jayadeep

JUAN GOMEZ

PhD Computational Mechanics

Professor

Applied Mechanics Group

EAFIT University

Medellin,Colombia

To measure a force is simple

We have an device to apply several miro Newtons on an indentation test. The device was made by a famous corporation and they claimed in their introduction that the force put on could be several micro Newton.

You are a USA professor so I believe you know this device.

Of great significance is that no corporation claimed that their instruments could be used to measure stress inside a non homogeneous material or the surface of a particle in ceramics.

I will attach my figures from which some arguments among us and the researchers discussed above could be clarified.

Professor Yi-Heng Chen

Professor Chen,

 

I find your answer as arrogant and as weak as your original question. The only reason I am asking you about the instruments that you claim can be used to measure force is because the concept of stress would be as physical as the concept of force itself. If in fact as you have claimed, you can DIRECTLY measure force (not displacements) then you can also measure stress and then you would be able to qualify it as physical quantity.

Finally, when somebody answer me a question with another question the only conclusion that I can obtain is that the he(or she) doesn´t know the answer.

Thanks 

 

 

JUAN GOMEZ

PhD Computational Mechanics

Professor

Applied Mechanics Group

EAFIT University

Medellin,Colombia

Dear Professor JUAN GOMEZ

Your reply gave me a shock as you said the word "arrogant"!

May be my English is not so good which gave you an arrogant impression?

I believe that this is because I have not attached the figures.

I deeply hope that you will understand my original viewpoint after I attach my figures on the website.

I try to do it but not successful!

I should very much appreciate if some body would tell me how to attach the figures.

Regards

Professor Yi-Heng Chen

LG's picture

Dear Prof. Chen,    Thank for this interesting discussion.     If i am right, you think to establish new “symbol” to instead the "stress and strain" which was applied for a long time to express an initial simple relationship between "force" and "displacement" for the isotropic, homogeneous and linear elastic rod?  Rather then focus on whether the concepts of “stress” or “strain” are physical quantities?  From what you said above, I suppose this idea was emerged when you did research about the material seem to be non-homogeneous, un-isotropic as well as plastic, the initial simple relationship seem to be more and more complex and un-controlable? So you think why we need also use the original definition of stress and strain to describe the mechanic property of those materials?Anyway, I would like to reiterate the question, "Why we use stress and strain concepts?"  If i am still right, i believe many research can not fully understand why we need this concepts? From my opinion, I think the man who was the father of “Stress and Strain” just wanted to unify the initial relationship for the displacement and force for the simple elastic rod when the did the experiments 100 even 150 years ago.To my understanding, the force                              F=K*delta(L),  Here, K stands for the stiffness or spring constant,  delta(L) is the elastic rod deflectionSo, when he tested different elastic rods which are with different cross sections and different lengths, he found the K seemed to be with variable linear relationships. So he used                          F/A=(KL/A)*(delta(L)/L) , those symbol inside the first parenthesis of the right hand side seem become only one linear curve!      Then, He defined the F/A to be STRESS, and delta(L)/L to be STRAIN, and the KL/A is Elastic Modulus! So, I fully agree with your proposition to eliminate these two symbols if you BELIEVE you can give more concise expressions and sensible definitions to describe the mechanical properties of the materials at say micro, nano scale etc. Best RegardsLiu Gang

 

Thank you for your comments.

Your opinion and my opinion are closely related each other but I still believe that the strain is measurable as many corporations claimed in their introductions.

My opinion is that the stress concept is a phenomenalogical concept which could not be used to describe some problems of micro mechanics.

Please see the figures 1-3 in pdf I have just attached on. 

I will report further figures  for the invalid evidences of the stress concept.

Moreover, of the most signifcance is how to find a new physical quantity to replace the old concept of stress.

Professor Yi-Heng Chen

sir i am agree with you but can you tell me some devices are available to measure Stress directly? please give me some suggestion about this.

No instruments could be used to measure stress in micro scale, to my knowledge.

No corporations claimed that their instruments could be used to measure stress but many corporations claimed that their instruments could be used to measure strain.

Professor Yi-Heng Chen

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