The objective of this paper is to enable Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) to predict the static failure strength and the initial failure envelop of heterogeneous materials obeying various failure criteria. These predictions are performed using several representative examples of heterogeneous materials such as continuous fiber reinforced composite, particle reinforced composite, discontinuous fiber reinforced composite, and woven composite. The static failure predictions of VAMUCH are partially evaluated with various micromecahnics approaches such as Mori-Tanaka (MT), Double Inclusion (DI), Generalized Methods of Cells (GMC), High Fidelity Generalized Methods of Cells (HFGMC) and also Finite Element Analysis (FEA). The evaluation reveals that MT and DI insufficiently approximate the static failure compared with FEA whereas GMC and HFGMC better predict compared with MT and DI. However GMC and HFGMC poorly predict failure particularly for maximum principal stress failure criterion. GMC shows relatively better agreement with FEA for Tsai-Hill failure criterion. On the contrary, VAMUCH shows excellent agreements with FEA for all aforementioned examples of heterogeneous materials. Moreover, VAMUCH also generates the initial failure envelop for combined axial and transverse shear using maximum shear stress and Tsai-Hill failure criteria. The prediction of combined shear usually cannot be rigourously performed using commercial FEA software due to complex boundary conditions. In general, the outputs of the predictions signify that maximum principal stress criteria is more conservative compared with Tsai-Hill and Tsai-Wu failure criteria. It is also noticed that the predictions of Tsai-Hill and maximum shear stress criteria agree well for shear loading conditions except for the woven composite.
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