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

TL;DR

This paper introduces a comprehensive isogeometric finite element method for rotation-free shells with embedded fibers, capable of simulating complex anisotropic behaviors in large, heterogeneous fibrous materials with high accuracy.

Contribution

It extends Kirchhoff-Love shell theory to include in-plane fiber bending, using only displacement degrees-of-freedom and isogeometric shape functions for enhanced simulation of fibrous shells.

Findings

Demonstrates robustness through benchmark tests

Accurately captures anisotropic deformation modes

Handles large, heterogeneous fibrous materials effectively

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.