As part of an ongoing effort to model uncertainty propagation across multiple scales in fibrous laminates, this paper presents a deterministic transformation field analysis for modeling damage progression under membrane forces and bending moments. In this approach, equivalent eigenstresses are computed in the phases and/or plies such that their respective stress components that satisfy the underlying failure criteria are reduced to zero. Superposition of the solutions found for the undamaged laminate under applied loads and under the eigenstress field provide the entire response. Failure criteria are based on stress averages in the fiber and matrix. Damage mechanisms considered are frictional sliding and splitting on matrix planes that are parallel to the fiber direction, and fiber breakage. Model predictions correlate well with published experimental measurements for the stress-strain response as well as failure envelope.
Bahei-El-Din, Yehia; Khire, Ritesh; and Hajela, Prabhat, "Multiscale transformation field analysis of progressive damage in fibrous laminates" (2010). Centre for Advanced Materials. 12.