Technical Brief

Configurational Forces on Elastic Line Singularities

[+] Author and Article Information
Youjung Seo

Program in Nano Science and Technology,
Graduate School of Convergence Science and Technology,
Seoul National University,
Seoul 08826, Republic of Korea

Gyu-Jin Jung

Department of Mechanical Engineering,
Hanyang University,
Ansan-si 15588, Gyeonggi-do, Republic of Korea

In-Ho Kim

Graduate School of Education,
Ajou University,
Suwon-si 16499, Gyeonggi-do, Republic of Korea

Y. Eugene Pak

Institute of Nano Convergence,
Advanced Institutes of Convergence Technology,
Suwon-si 16229, Gyeonggi-do, Republic of Korea

1Corresponding Author

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 26, 2017; final manuscript received December 14, 2017; published online January 16, 2018. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 85(3), 034501 (Jan 16, 2018) (4 pages) Paper No: JAM-17-1534; doi: 10.1115/1.4038808 History: Received September 26, 2017; Revised December 14, 2017

Configurational forces acting on two-dimensional (2D) elastic line singularities are evaluated by path-independent J-, M-, and L-integrals in the framework of plane strain linear elasticity. The elastic line singularities considered in this study are the edge dislocation, the line force, the nuclei of strain, and the concentrated couple moment that are subjected to far-field loads. The interaction forces between two similar parallel elastic singularities are also calculated. Self-similar expansion force, M, evaluated for the line force shows that it is exactly the negative of the strain energy prelogarithmic factor as in the case for the well-known edge dislocation result. It is also shown that the M-integral result for the nuclei of strain and the L-integral result for the line force yield interesting nonzero expressions under certain circumstances.

Copyright © 2018 by ASME
Topics: Stress , Dislocations
Your Session has timed out. Please sign back in to continue.


Rice, J. , 1968, “ A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35(2), pp. 379–386. [CrossRef]
Cherepanov, G. , 1981, “ Invariant Integrals,” Eng. Fract. Mech., 14(1), pp. 39–58. [CrossRef]
Günther, W. , 1962, “ Über einige randintegrale der elastomechanik,” Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft Band, 14, pp. 53–72.
Knowles, J. , and Sternberg, E. , 1972, “ On a Class of Conservation Laws in Linearized and Finite Elastostatics,” Arch. Ration. Mech. Anal., 44(3), pp. 187–211. [CrossRef]
Budiansky, B. , and Rice, J. R. , 1973, “ Conservation Laws and Energy-Release Rates,” ASME J. Appl. Mech., 40(1), pp. 201–203. [CrossRef]
Pak, Y. E. , Golebiewska-Herrmann, A. , and Herrmann, G. , 1983, Energy Release Rates for Various Defects, Springer, Boston, MA, pp. 1389–1397.
Kienzler, R. , and Herrmann, J. , 2000, Mechanics in Material Space With Applications to Defect and Fracture Mechanics, Springer-Verlag, Berlin.
Eshelby, J. , 1951, “ The Force on an Elastic Singularity,” Philos. Trans. R. Soc. London, Ser. A, 244(877), pp. 87–112. [CrossRef]
Golebiewska-Herrmann, A. , and Herrmann, G. , 1981, “ On Energy-Release Rates for a Plane Crack,” ASME J. Appl. Mech., 48(3), pp. 525–528. [CrossRef]
Pak, Y. E. , and Kim, S. , 2010, “ On the Use of Path-Independent Integrals in Calculating Mixed-Mode Stress Intensity Factors for Elastic and Thermoelastic Cases,” J. Therm. Stresses, 33(7), pp. 661–673. [CrossRef]
Pak, Y. E. , 1990, “ Force on a Piezoelectric Screw Dislocation,” ASME J. Appl. Mech., 57(4), pp. 863–869. [CrossRef]
Lubarda, V. A. , 2016, “ Determination of Interaction Forces Between Parallel Dislocations by the Evaluation of J Integrals of Plane Elasticity,” Continuum Mech. Thermodyn., 28(1), pp. 391–405. [CrossRef]
Nabarro, F. R. N. , 1985, “ Material Forces and Configurational Forces in the Interaction of Elastic Singularities,” Proc. R. Soc. A, 398(1815), pp. 209–222. [CrossRef]
Kachanov, M. , Shafiro, B. , and Tsukrov, I. , 2003, Handbook of Elasticity Solutions, Kluwer Academic Publishers, Dordrecht, The Netherlands. [CrossRef]
Bower, A. F. , 2009, Applied Mechanics of Solids, CRC Press, Boca Raton, FL.
Love, A. E. , 1906, A Treatise of the Mathematical Theory of Elasticity, Cambridge University Press, New York.
Freund, L. B. , 1978, “ Stress Intensity Factor Calculations Based on a Conservation Integral,” Int. J. Solids Struct., 14(3), pp. 241–250. [CrossRef]
Suo, Z. , 1999, “ Zener's Crack and the M-Integral,” ASME J. Appl. Mech., 67(2), pp. 417–418. [CrossRef]
Rice, J. R. , 1985, “ Conserved and Integrals and Energetic Forces,” Fundamentals of Deformation and Fracture, B. A. Bilby , K. J. Miller , and J. R. Willis, eds., Cambridge University Press, Cambridge, UK, pp. 33–56.
Seo, S. Y. , Mishra, D. , Park, C. Y. , and Pak, Y. E. , 2015, “ Energy Release Rates for a Misfitted Spherical Inclusion Under Far-Field Mechanical and Uniform Thermal Loads,” Eur. J. Mech. A, 49, pp. 169–182. [CrossRef]


Grahic Jump Location
Fig. 1

In-plane elastic singularities: (a) edge dislocation, (b) line force, (c) nuclei of strain, and (d) concentrated couple moment, subjected to the far-field loads, σij∞, in an infinite medium

Grahic Jump Location
Fig. 2

In-plane elastic singularities: (a) edge dislocation, (b) line force, (c) nuclei of strain, and (d) concentrated couple moment, interacting with identical parallel line singularities in an infinite medium



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In