Multiscale modeling of laminated thin-shell structures with Direct FE[formula omitted

Abstract

Shell finite element is computationally efficient and thereby favored in large-scale structural analysis. With the application of advanced materials, understanding the relation between micro-heterogeneities and structural behavior is important. To this end, we propose a multiscale method in the current contribution for modeling thin-walled fiber reinforced composite laminates with Mindlin–Reissner shell theory and Direct FE2. By exploiting the length scales in layered structure together with a shell formulation degenerated from continuum solid element, both in-plane and through-thickness periodicity can be assumed. A single-fiber unit cell attached to each Gauss point is employed as a representative volume element (RVE) rather than a through-thickness microstructure. In this way, the scale transitions are naturally dealt with using a first-order homogenization framework, in which the downscaling of transverse shear strain, commonly troublesome for the through-thickness RVE, is straightforward. The other merit inherited from Direct FE2 is that the two-scale problem is formulated in a single finite element analysis wherein the macro and micro DOFs are coupled based on the downscaling kinematics. It avoids the upscaling of the macroscopic stresses and tangents in the conventional nested FE2 scheme, which is challenging in the case of complex microstructural response. The developed method is then verified through several benchmarking examples, including a flat plate and two curve shells. Isotropic materials and composite laminates with homogeneous and heterogeneous RVEs have been examined. Two examples with plasticity and cohesive cracks are further presented to showcase its potential in modeling damage propagation in composite structures.