Principles for recovering micro-stress in multi-level analysis

Multi-level stress analysis is widely used to recover the micro-stress of the stress concentration area in composite structures. One common approach is firstly to consider the composite material as a homogeneous material. Effective properties are employed to predict the effective stress and effective displacement fields (or called the macroscopic stress and macroscopic displacement fields). Then, a local domain, which includes the area of interest (normally the stress concentration area), is selected for local microscopic stress analysis, in which the effective stress and/or effective displacement along the local domain boundary are used as boundary conditions. Thus a question arises: can the micro-stress field in the area of interest found from multi-level stress analysis match that from full-field micro-stress analysis? In this paper, two principles and a "local domain test", which is based upon the two principles, are established for multi-level stress analysis. It is shown that micro-stress in the area of interest will be recovered accurately with multi-level analysis if the selected local domain passes the "local domain test." These two principles and the "local domain test" elevate multi-level stress analysis into a more powerful tool.