Analysis of the invariant integrals in plane elasticity containing a nanosized hole

作者：Li Q^*; Chen H; Hui T

来源：Acta Mechanica, 2008, 199(1-4): 143-150.

DOI：10.1007/s00707-007-0537-6

Invariant integrals widely used in fracture mechanics of macroscopic elasticity are extended to study nanomaterials with defects. As an initial attempt, an elastic plane containing a nanosized elliptical or circular hole is considered in this paper, from which some basic properties of the invariant integrals (e.g., J(k) -integral vector and M-integral) are analyzed. Due to the high surface-to-volume ratio for reinforcing particles at nanometer scales, the surface effect along the nanosized hole is considered in the analysis. It is concluded that both components of the J (k) -integral vector vanish when the contour selected to calculate the integral encloses the whole nanosized hole. This leads to the independence of the M-integral from the global coordinate rotation or shift. Of great interest is that the value of the M-integral is significantly influenced by the size of the nanosized hole and the remote loading, whereas this value is independent of the surface effect when the surface energy density along the surface of the nanosized hole is assumed to be independent of the elastic strain.

• 出版日期2008-8
• 单位西安交通大学