Development of the singular stress analyses for three-dimensional interfacial corners

Abstract

We proposed a new technique to analyze the asymptotic solution around a three dimensional interface corners. We analyzed the scalar parameters of the asymptotic solutions using the H-integral, which is a conservative integral, in conjunction with the finite element analysis. Singular orders of these three-dimensional corners were obtained using the finite element method for the eigen analysis. If λ is an eigen value of a three dimensional corner, -λ-1 is also an eigen value. Complementary eigen values and eigen vectors are used for the H-integral analysis to obtain the scalar parameters. If we select the eigenvalue, -λ-1, as the complementary eigenvalue for the H-integral, the H-integral corresponds with a scalar parameter of the asymptotic solution. We proposed the normalization of the eigenvalues for defining the obtained scalar parameters as the unique values. We demonstrate that the obtained asymptotic solutions correspond well with the stress field obtained by the finite element analyses around three-dimensional interface corners.

Keywords

• three-dimensional corners
• asymptotic solution
• scalar parameter
• eigen value
• h-integral
• conservative integral