Analytical study of transverse cracking in cross-ply laminates under combined loading based on a new coupled micro-meso approach

•A generalized plane strain model is developed for cross-ply composite laminates, including transverse matrix cracks.•The unit cell model contains equally spaced transverse cracks in any of the 90° plies.•The stress field satisfies the equilibrium and continuity equations along with the BCs at the interfaces between the plies.•The method explicitly provides the stresses and displacements functions for any point considering transverse cracking.•The predicted stresses in the unit-cell are in good agreement with the computational micromechanics method and FEM results. In this study, an analytical solution based on plane strain model in classical linear elasticity theory is presented for damage analyses of general cross-ply laminates under combined thermo mechanical loading. Equally spaced transverse cracks are considered in any of the 90° plies allows to apply a unit cell based coupled micro-meso model. Thereby, a unit cell includes transverse cracking in the composite ply level is considered to predict the stress and displacement fields that satisfy the equilibrium equations and continuity conditions. Then, a set of fourth order ordinary differential equations is derived and solved by an analytical method. The exact solutions of the differential equations are presented to determine the stress distributions at any point in the laminate subjected to the thermo mechanical in-plane and out-of-plane loadings. It is shown that the predicted stress distributions in the unit-cell are in good agreement with the results of finite element method and the available analytical methods. This method explicitly provides the stress and displacement functions for any point considering transverse cracking, which is an important inquiry for the continuum damage analyses of composite laminates.