Issue 49

M. Hamdi et alii, Frattura ed Integrità Strutturale, 49 (2019) 321-330; DOI: 10.3221/IGF-ESIS.49.32 323 Table 1 : Different structures and their SGs (subfigures amended from Massart, et al. [19] and Sevostianov, et al. [20]). For example, for 3D structural analysis requiring 3D properties, the RVE must be 3D [16]. Moreover, traction and displacement boundary conditions, which are indispensable in RVE-based models, are not needed in MSG. Interested readers can refer to Yu [15] for more details on MSG. The MSG is developed based on the principle of minimum information loss which states that a homogenized body can be obtained by minimizing the information loss when constructing homogenized body out of original, heterogeneous body. For linearly elastic material, this information can be the strain energy density. Specifically, the displacement of original body can be expressed in terms of corresponding homogenized body as: ( , ) ( , ) i i i u x y u x y    (1) Structure SG 1D 2D 3D