Shutov Alexey, Rodionov Alexander, Ponomarev Dmitri, Nekrasova Yana
Lavrentyev Institute of Hydrodynamics, Pr. Lavrentyeva 15, 630090 Novosibirsk, Russia.
Saint Petersburg State Marine Technical University, Ul. Lotsmanskaya 3, 190121 Saint Petersburg, Russia.
Polymers (Basel). 2022 Aug 15;14(16):3314. doi: 10.3390/polym14163314.
The concept of representative directions allows for automatic generation of multi-axial constitutive equations, starting from simplified uni-axial material models. In this paper, a modification of the concept is considered suitable for the analysis of fibrous polymeric materials, which are anisotropic in the as-received state. The modification of the concept incorporates an orientation probability density function (OPDF), which explicitly accounts for the material anisotropy. Two versions of the concept are available. The first version utilizes the homogeneous distribution of the representative directions, with the entire anisotropy being contained in the weighting factors. The second encapsulates the anisotropy in the distribution of the representative directions. Due to its nature, the second version allows for a more efficient use of computational power. To promote this efficient version of the concept, we present new algorithms generating required sets of representative directions that match a given OPDF. These methods are based (i) on the minimization of a potential energy, (ii) on the equilibration method, and (iii) on the use of Voronoi cells. These three methods are tested and compared in terms of various OPDFs. The applicability of the computationally efficient modeling method to mechanical behavior of an anisotropic polymeric material is demonstrated. In particular, a calibration procedure is suggested for the practically important case when the OPDF is not known a-priori.
代表性方向的概念允许从简化的单轴材料模型出发自动生成多轴本构方程。本文认为该概念的一种修改形式适用于分析在初始状态下具有各向异性的纤维聚合物材料。该概念的修改形式纳入了一个取向概率密度函数（OPDF），它明确考虑了材料的各向异性。该概念有两个版本。第一个版本利用代表性方向的均匀分布，所有各向异性都包含在加权因子中。第二个版本将各向异性封装在代表性方向的分布中。由于其本质特点，第二个版本能更有效地利用计算能力。为推广该概念的这个高效版本，我们提出了新的算法来生成与给定OPDF匹配的所需代表性方向集。这些方法基于：（i）势能最小化，（ii）平衡法，以及（iii）使用Voronoi单元。针对各种OPDF对这三种方法进行了测试和比较。证明了这种计算高效的建模方法对各向异性聚合物材料力学行为的适用性。特别是，针对OPDF事先未知这种实际重要情况，提出了一种校准程序。
