Development and implementation of new triangular finite element based on MGE theory for bi-material analysis

Compared with the classical continuum theory, the modified gradient elastic theory (MGE theory) better explains the size effect, strain and damage localization of materials. In this paper, we constructed a C-1 planar triangular finite element based on the MGE theory. We also derived its finite element format and compiled the corresponding finite element calculation program by the MATLAB software. The program was used to analyze the bi-material shear boundary layer problem with unidirectional infinite length. The results show that the change of the internal characteristic length of the material in the infinite direction (the same direction as the shear stress) has little effect on calculation results of the shear strain, while the change of the internal characteristic length in the finite direction has a certain impact on calculation results of the shear strain, and its impact is even greater on the material with small elastic modulus in the bi-material; when the size of the finite element mesh does not exceed the internal characteristic length of the material, the mesh dependence of calculation results can be eliminated. Compared with the MGE rectangular element, the triangular element constructed in this paper has higher calculation accuracy and better adaptability.