Composite structures may serve in environments with severe conditions of temperature, moisture, mechanical loads (static and dynamic) and various combinations of these.Numerous experiments have demonstrated that the mechanical and physical properties of composites are dependent on temperature and moisture. It is desired to simulate these phenomena to evaluate the structural performance in service. Due to the hierarchical architecture of composites, multi-scale modelling approach is an ideal tool. It is thus needed to use multi-scale and multi-physics model to predict mechanical response of composites subjected to environmental and mechanical actions. In addition, uncertainties exist in all aspects of a composite structure (constituent material properties, fabrication variables, structural geometry, and service environment, etc.), which result in uncertain structural responses.Hence, a probabilistic multi-scale approach is desired to conduct structural design and analysis of composites.

In practice, the assessment of structural performance in service is a durability problem, and the reliability index is usually used to measurethis in the presence of uncertainties. Thus, a time-dependent reliability analysis method that uses multi-scale finite element method is developed in this paper to evaluate the evolution in time of the structural performance.This simulation method combinesa state-of-the-art computational multi-scale homogenization method with composite mechanics,stochastic finite element analysis, structural reliability and material degradation model. Multi-scale thermo-hydro-mechanical model was used as the basis to develop a probabilistic model using the probabilistic homogenization method.The effective mechanical and physical properties are then supplied to a stochastic structural analysis to obtain the corresponding stochastic structural responses. By doing this, the relationship between structural responses and microscopic random variables such as constituent material properties is established and uncertainties are propagated from micro-level to macro- or structural-level. Finally, linking with structural reliability analysis leads to a multi-scale finite element based reliability method. A case study of a laminated composite plate made of glass fibre reinforced epoxy compositewas conducted to illustrate the procedure fordurability analysis of composite structures.