Large displacement models for composites based on Murakami's Zig-Zag Function, Green-Lagrange Strain Tensor, and Generalized Unified Formulation

Abstract

Abstract Murakami's Zig-Zag Function in conjunction of Green-Lagrange Strain- and Second-Piola Kirchhoff Stress-tensors and Generalized Unified Formulation are introduced for the first time to present a class of Zig-Zag theories for composite structures. Transverse strain effects are retained and modeled, making the present approach also suitable for thick structures. Each displacement variable is independently represented with user-selected order of expansion. The stress recovery is achieved with a special procedure in which combination of deformation gradient and Second-Piola Kichhoff transverse stresses are integrated along the thickness of the undeformed geometry. Comparison with available data and commercial codes indicate the effectiveness of the proposed framework for variable kinematics Zig-Zag theories in the presence of large displacements.