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A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness
Journal of Engineering Mathematics ( IF 1.3 ) Pub Date : 2021-05-28 , DOI: 10.1007/s10665-021-10117-3
Carina Witt , Tobias Kaiser , Andreas Menzel

It is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.



中文翻译:

具有纤维抗弯刚度的纤维增强复合材料的有限变形等几何有限元方法

用某些类型的纤维增强材料以增强整体材料的机械性能是许多工程领域的常用技术。特定的模拟方法有助于提前预测这些复合材料的行为。在这方面,一种广泛建立的方法是将纤维方向矢量作为能量函数的附加参数并入,以捕获纤维方向上的特定材料特性。虽然该模型表示材料的横向各向同性,但它无法捕捉由纤维弯曲引起的效应,并且不包括任何可能允许模拟尺寸效应的长度尺度。在这个贡献中,考虑了一种增强方法,该方法依赖于在存储的能量密度函数中引入更高梯度的变形图贡献,并最终允许在模拟中考虑纤维弯曲刚度。各个梯度场通过等几何有限元框架内的 NURBS 基函数利用其特征连续性来近似。在此贡献中针对具有纤维弯曲刚度的纤维增强复合材料提出的等几何有限元方法考虑了有限变形。结果表明,所提出的方法符合代表性边值问题的半解析解。

更新日期:2021-05-28
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