A general isogeometric finite element formulation for rotation-free shells with in-plane bending of embedded fibers

Abstract

This paper 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 [1] 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 $C^1$-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.

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References in corpus (4)

• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
• A stabilized finite element formulation for liquid shells and its application to lipid bilayers
• An isogeometric finite element formulation for phase transitions on deforming surfaces
• Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

Cited by in corpus (5)

• A simple and efficient hybrid discretization approach to alleviate membrane locking in isogeometric thin shells
• An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
• A general theory for anisotropic Kirchhoff-Love shells with in-plane bending of embedded fibers
• Response to David Steigmann's discussion of our paper
• A finite strain model for fiber angle plasticity of textile fabrics based on isogeometric shell finite elements