Intensity of singularity in three-material joints under shear loading: Two-real singularities and power-logarithmic singularities

In the present study, the enriched finite element method is applied to analyze the intensity of singularity in 2D-dissimilar material joints described by 2-real singularities and power-logarithmic singularities. By using this method, the intensity of singularities can be directly evaluated and very refined meshes around the singular point are unnecessary. Eigenvalue and eigenvector analyses are applied to calculate the order of singularity and the asymptotic displacement fields on the enriched elements. Different mesh types (4-node and 8-node element) and different sizes of the enriched region are applied to improve the accuracy of the results. Furthermore, the models with various lengths and thicknesses are used to study an influence of geometry on the intensity of singularity. In conclusion, it is shown that the enriched finite element method can be used to determine the singular stress fields for both 2-real singularities and power-logarithmic singularities. An accuracy of the results can be improved by using higher order polynomial function for element shape function. Finally, a relationship between the intensity of singularity and geometry for three-material model with 2-real singularity is discussed.

► The enriched FEM is extended to solve power-logarithmic singularities.
► An accuracy of the results is improved by using higher order polynomial function.
► An influence of mesh size and enriched region on the intensity of singularity is considered.
► A relationship between the intensity of singularity and geometry is studied.