The material length scale parameter used in couple stress theories is not a material constant

Abstract The purpose of this paper is to clarify that a material length scale parameter of the modified couple stress theory is not constant for an especial material and this parameter changes as size of a structure changes. To determine this value, experimental data for all different sizes are required. The experimental results showed that the value of material length scale parameter has been never fixed and is always changing in various dimensions. Therefore, the modified couple stress theory can be applied for micro- and nano-scales, if the material length scale parameter is individually calculated for these scales. Also, hardening and softening effects of the modified couple stress theory are investigated. Material length scale parameters of different structures made of epoxy, copper, titanium and nickel are reported corresponding to their geometries. Results indicate that geometry especially thickness or diameter has significant influence on the material length scale parameter and the softening and hardening behaviors can be satisfied by the modified couple stress theory.

[1]  David J. Dunstan,et al.  Toward a further understanding of size effects in the torsion of thin metal wires: An experimental and theoretical assessment , 2013 .

[2]  M. Shariati,et al.  A multi-spring model for buckling analysis of cracked Timoshenko nanobeams based on modified couple stress theory , 2017 .

[3]  M. Shariati,et al.  Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory , 2016 .

[4]  P. Tong,et al.  Couple stress based strain gradient theory for elasticity , 2002 .

[5]  A. Daneshmehr,et al.  Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions , 2014 .

[6]  B. Song,et al.  An Improved Experimental Technique to Characterize Micro-Diameter Copper Wires in Torsion , 2015 .

[7]  J. Reddy,et al.  Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory , 2013 .

[8]  S. K. Park,et al.  Bernoulli–Euler beam model based on a modified couple stress theory , 2006 .

[9]  R. Toupin.  Elastic materials with couple-stresses , 1962 .

[10]  Wen-Hui Lin,et al.  Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory , 2015 .

[11]  J. N. Reddy,et al.  A nonlinear modified couple stress-based third-order theory of functionally graded plates , 2012 .

[12]  Abdessattar Abdelkefi,et al.  Modeling and Vibration Characteristics of Cracked Nano-Beams Made of Nanocrystalline Materials , 2016 .

[13]  Ying-hui Li,et al.  Size-dependent post-buckling behaviors of geometrically imperfect microbeams , 2018 .

[14]  C. Lim,et al.  Thermal effects on buckling of shear deformable nanocolumns with von Kármán nonlinearity based on nonlocal stress theory , 2012 .

[15]  M. Shariati,et al.  Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory , 2017 .

[16]  J. N. Reddy,et al.  A microstructure-dependent Timoshenko beam model based on a modified couple stress theory , 2008 .

[17]  George C. Tsiatas,et al.  A new Kirchhoff plate model based on a modified couple stress theory , 2009 .

[18]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[19]  W. T. Koiter.  Couple-stresses in the theory of elasticity , 1963 .

[20]  Ernian Pan,et al.  Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory , 2015 .

[21]  B. Song,et al.  Quasi-Static Torsion Characterization of Micro-diameter Copper Wires , 2011 .

[22]  Lin Wang,et al.  Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory , 2016 .

[23]  J. Lei,et al.  A standard experimental method for determining the material length scale based on modified couple stress theory , 2018, International Journal of Mechanical Sciences.

[24]  Fan Yang,et al.  Experiments and theory in strain gradient elasticity , 2003 .

[25]  H. F. Tiersten,et al.  Effects of couple-stresses in linear elasticity , 1962 .

[26]  M. Shaat,et al.  New insights on the applicability of Eringen’s nonlocal theory , 2017 .

[27]  G. Farrahi,et al.  Size-dependent energy release rate formulation of notched beams based on a modified couple stress theory , 2014 .

[28]  Amir Mehdi Dehrouyeh-Semnani,et al.  On size-dependent Timoshenko beam element based on modified couple stress theory , 2016 .

[29]  Mahmoud Shariati,et al.  Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory , 2016 .

[30]  Jian Lei,et al.  Size-dependent vibration of nickel cantilever microbeams: Experiment and gradient elasticity , 2016 .

[31]  Crack mathematical modeling to study the vibration analysis of cracked micro beams based on the MCST , 2018 .

[32]  J. Reddy.  MICROSTRUCTURE-DEPENDENT COUPLE STRESS THEORIES OF FUNCTIONALLY GRADED BEAMS , 2011 .

[33]  Mohammad Taghi Ahmadian,et al.  A nonlinear Timoshenko beam formulation based on the modified couple stress theory , 2010 .

[34]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[35]  Lin Wang,et al.  Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory , 2015 .

[36]  M. Ghayesh,et al.  NONLINEAR DYNAMICS OF A GEOMETRICALLY IMPERFECT MICROBEAM BASED ON THE MODIFIED COUPLE STRESS THEORY , 2013 .