Large rotation isogeometric shell model for alternating stiff/soft curved laminates including warping and interlayer thickness change

Abstract

The mechanics of laminates made up of elastic alternating stiff/soft layers is dominated by bending and membrane actions in the stiff layers, while transverse shear deformations concentrate in the soft interlayers producing significant zigzag warping effects. Additionally, curved geometry and large deformations can induce an interlayer thickness strain affecting the overall response of the laminate. This work presents a rotation-free Total Lagrangian large deformation curved shell model to accurately capture such a structural response. Each stiff layer is modeled as a Kirchhoff–Love shell. Without additional DOFs, each soft interlayer is modeled as a solid-shell by expressing, in finite kinematics, the displacement of top and bottom interfaces as a function of the mid-surface displacement of the upper and lower stiff layers it couples. The model is characterized by a sparse stiffness matrix compared to high-order theories and requires a small number of DOFs (3 per stiff layer) to reproduce the 3D solution. A NURBS discretization meets the high continuity of the weak form with a patch-wise reduced quadrature to avoid locking and enhance efficiency. All thickness integrals are pre-computed just once.