In this paper, analysis of the M-integral in plane elasticity is carried out. An infinite plate with any number of inclusions and cracks and with any applied forces and remote tractions is considered. To study the problem, the mutual work difference integral (abbreviated as MWDI) is introduced, which is defined by the difference of works done by each other stress field on a large circle. The concept of the derivative stress field is also introduced, which is a real elasticity solution and is derived from the physical stress field. It is found that the M-integral on a large circle is equal to a MWDI from the physical stress field and a derivative stress field. Finally, the expression for M-integral on a large circle is obtained. The variation for the M-integral with respect to the coordinate transformation is addressed. An illustrative example for the use of M-integral is presented.
Skip Nav Destination
Article navigation
July 2004
Brief Notes
Analysis of the M-Integral in Plane Elasticity
Y. Z. Chen,
Y. Z. Chen
Division of Engineering Mechanics, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China
Search for other works by this author on:
Kang Yong Lee
Kang Yong Lee
Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
Search for other works by this author on:
Y. Z. Chen
Division of Engineering Mechanics, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China
Kang Yong Lee
Department of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 12, 2001; final revision, December 13, 2003. Associate Editor: B. M. Moran.
J. Appl. Mech. Jul 2004, 71(4): 572-574 (3 pages)
Published Online: September 7, 2004
Article history
Received:
July 12, 2001
Revised:
December 13, 2003
Online:
September 7, 2004
Citation
Chen , Y. Z., and Lee , K. Y. (September 7, 2004). "Analysis of the M-Integral in Plane Elasticity ." ASME. J. Appl. Mech. July 2004; 71(4): 572–574. https://doi.org/10.1115/1.1748271
Download citation file:
Get Email Alerts
Enhancement of Synchronization in Nonlinear MEMS Oscillator Based on Electrothermal Adjustment
J. Appl. Mech (April 2025)
Related Articles
Some Properties of J -Integral in Plane Elasticity
J. Appl. Mech (March,2002)
Stress singularities in classical elasticity—II: Asymptotic identification
Appl. Mech. Rev (September,2004)
Trefftz Finite Element Method and Its Applications
Appl. Mech. Rev (September,2005)
Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack
J. Appl. Mech (March,1995)
Related Chapters
Recent Developments in J Ic Testing
Developments in Fracture Mechanics Test Methods Standardization
Processing/Structure/Properties Relationships in Polymer Blends for the Development of Functional Polymer Foams
Advances in Multidisciplinary Engineering
Applications
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow