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.

翻译：本文提出了一种适用于嵌入纤维的无旋转壳的一般非线性等几何有限元公式，能够捕捉拉伸、剪切、扭转和弯曲（包括面内和面外）中的各向异性。这些能力允许模拟带有或无基体的大尺寸异质纤维材料片材，例如纺织品、复合材料和多孔结构。该工作是我们早期理论工作[1]的计算扩展，将现有的Kirchhoff-Love壳理论扩展至包含初始直线或弯曲纤维的面内弯曲抗力。该公式仅需位移自由度即可捕捉所有提及的变形模式。为此，采用等几何形函数以满足跨单元边界的弯曲所需的$C^1$连续性。所提出的公式可容纳广泛材料模型，例如无需显式厚度积分的表面超弹性。为应对纤维压缩可能导致的材料不稳定性，添加了稳定化方案。通过多个基准算例验证了所提计算公式的鲁棒性和准确性。