A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.
The non-linear behavior of continuous fiber reinforced C/SiC ceramic matrix composites(CMCs)under tensile loading is modeled by three-dimensional representative volume element(RVE)models of the composite. The theoretical background of the multi-scale approach solved by the finite element method(FEM)is recalled firstly.Then the geometric characters of three kinds of damage mechanisms,i.e.micro matrix cracks,fiber/matrix interface debonding and fiber fracture,are studied.Three kinds of RVE are proposed to model the microstructure of C/SiC with above damage mechanisms respectively.The matrix cracking is modeled by critical matrix strain energy(CMSE)principle while a maximum shear stress criterion is used for modeling fiber/matrix interface debonding. The behavior of fiber fracture is modeled by the famous Weibull statistic theory.A numerical example of continuous fiber reinforced C/SiC composite under tensile loading is performed.The results show that the stress/strain curve predicted by the developed model agrees with experimental data.
