Multiscale Modeling of Delamination Damage in Laminated Structures

Modeling the response of laminated composite structures to mechanical and environmental loadings is complicated, even in the elastic phase, by the multilayered material architecture and the presence of unavoidable imperfections and flaws at the layer interfaces; stress and displacement fields exhibit complex zig-zag through-thickness distributions and discontinuities. When damage begins, localized propagation of delamination cracks, which may lead to catastrophic failures, exacerbates the difficulties. The problem cannot be solved using equivalent single-layer theories or continuum damage models, and is typically tackled through discrete-layer cohesive-crack approaches and computationally expensive numerical solutions. A novel multiscale model is presented in this chapter for plates with arbitrary layups and numbers of layers and delaminations subjected to mechanical and environmental loadings. The model derives homogenized dynamic equilibrium equations which depend on a number of variables equal to that of equivalent single-layer theories, allows efficient and accurate closed form solution of problems that would otherwise necessitate a numerical treatment and sets up the bases for a more efficient numerical solution of complex problems. Explicit expressions are presented for stresses and displacements in thick and highly anisotropic wide plates with continuous imperfect interfaces and delaminations subjected to steady-state thermo-mechanical loading. Closed form solutions of the dynamic problem in simply supported wide plates highlight the important effects of the interfacial imperfections on natural frequencies and modes of vibration and frequency gaps.