Dear Piska,

This is crucial to define the scale. You may see here for some advices:

http://www.sciencedirect.com/science/article/pii/S095006181630397X

http://www.mdpi.com/2076-3417/7/9/893/htm

Best regards

Łukasz Sadowski

I agee with herbert

Herbert Martins Gomes

Dear Piska,

the definition of a length scale depends on the particular physical process or mechanism to be investigated.

So, let's stick to your example of a steel rod with length equal to 1 m and of diameter 10mm (I see that you work in the field of computationa mechanics and structural mechanics):

(i) if the analysis addresses the mechanical stability of such a rod subject to compression (Euler buckling), the characteristic length scale is in fact directly related to the total dimensions of the structure, it is (the ratio of) length/diameter, more precisely the slenderness, i.e. the ratio of length/r, with r=sqrt(I/A) the radius of gyration, I: moment of inertia, A: cross section. (Notice that buckling as a bifurcation problem implicitly assumes that initial (geometrical) imperfections are not large enough to avoid bifurcation simply by a direct transition of the rod into a bending deformation mode.)

(ii) Imagine the same rod -assumed to have a strongly heterogeneous microstructure (big differences in Young's modulus)- undergoing tensile loading, and deformations in the elastic regime shall be analyzed e.g. by finite element simulations. Then the characteristic length scale refers to the dimensions of a representative volume element RVE that is large enough to capture the statistical relevant information for the computation of an effective elastic stiffness obtained by homogenization.

(iii) If it comes to the failure of a compact, stocky steel rod, where geometrical instabilities like buckling are not likely to occcur but a localized failure in terms of a shear band is observed, then the length scale of material microstructure will come into play like defects that trigger by stress concentrations the nucleation of a shear band. (even in this case a material type of instability can occur, where the acoustic tensor comes into play.)

If the analysis refers to activities more "at the bottom" like strain-hardening in dislocation mediated plasticity, the explanations of Prof. Raabe apply.

So I wanted to illustrate for the example you have given, that one single structure can have several length scales which each depend on the type of (here: mechanical) analysis.

Hope, something in it is helpful, best

Bernhard

Thank you for your answer

Hi Piska,

I'm a current student doing reverent researches about sample size effect. This effect is widely studied with sample sizes at micron and sub-micron scales. I hope these two papers are helpful. In my opinion, this effect is not significant at the scale you intereseted, i.e. 1mm to 1m.

Regards,

Ranming

Greer, J. R., & De Hosson, J. T. M. (2011). Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Progress in Materials Science, 56(6), 654–724. http://doi.org/10.1016/j.pmatsci.2011.01.005

Article Plasticity in Small-Sized Metallic Systems: Intrinsic Versus...

Uchic, M. D. (2004). Sample Dimensions Influence Strength and Crystal Plasticity. Science, 305(5686), 986–989. http://doi.org/10.1126/science.1098993

Article Sample Dimensions Influence Strength and Crystal Plasticity