A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers. (5th April 2022)

• Record Type: Journal Article
• Authors: Duong, Thang X.; Itskov, Mikhail; Sauer, Roger A.
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 14(2022)
• Page Start: 3115
• Page End: 3147
• Publication Date: 2022-04-05
• Subjects: fibrous composites -- in‐plane bending -- isogeometric analysis -- material instability -- nonlinear Kirchhoff‐Love shells -- strain gradient theory; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6937
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: This article presents a general, nonlinear isogeometric finite element formulation for rotation‐free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting, and bending—both in‐plane and out‐of‐plane. These capabilities allow for the simulation of large sheets of heterogeneous and fibrous materials either with or without matrix, such as textiles, composites, and pantographic structures. The work is a computational extension of our earlier theoretical work that extends existing Kirchhoff‐Love shell theory to incorporate the in‐plane bending resistance of initially straight or curved fibers. The formulation requires only displacement degrees‐of‐freedom to capture all mentioned modes of deformation. To this end, isogeometric shape functions are used in order to satisfy the required C 1 $$ {C}^1 $$ ‐continuity for bending across element boundaries. The proposed formulation can admit a wide range of material models, such as surface hyperelasticity that does not require any explicit thickness integration. To deal with possible material instability due to fiber compression, a stabilization scheme is added. Several benchmark examples are used to demonstrate the robustness and accuracy of the proposed computational formulation.