Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked so...Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.展开更多
Interactors introduced in another recent paper by the authors are fourth order tensors which describes the interacting effects on the effective elastic properties of damaged solids due to spatial distribution of defe...Interactors introduced in another recent paper by the authors are fourth order tensors which describes the interacting effects on the effective elastic properties of damaged solids due to spatial distribution of defects. Based on the concept of interactors, an interacting model for the effective elastic properties of anisotropically damaged solids is proposed. As an application of the proposed model, the anisotropic effective elastic properties of an isotropic matrix material with circular holes in periodically rectangular distribution are theoretically estimated up to third order terms of the porosity and the estimation is compared with numerical results.展开更多
文摘Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.
文摘Interactors introduced in another recent paper by the authors are fourth order tensors which describes the interacting effects on the effective elastic properties of damaged solids due to spatial distribution of defects. Based on the concept of interactors, an interacting model for the effective elastic properties of anisotropically damaged solids is proposed. As an application of the proposed model, the anisotropic effective elastic properties of an isotropic matrix material with circular holes in periodically rectangular distribution are theoretically estimated up to third order terms of the porosity and the estimation is compared with numerical results.
