基于虚拟纤维的各向异性超弹性材料本构模型设计  

Virtual Fiber-Based Constitute Model for Anisotropic Material Design

作　　者：卢子璇 何浩 吴笛[4] 刘学慧[1,2] Lu Zixuan;He Hao;Wu Di;Liu Xuehui(State Key Laboratory of Computer Science,Institute of Software,Chinese Academy of Sciences,Beijing 100190;School of Computing Science and Technology,University of Chinese Academy of Sciences,Beijing 100190;Laboratory of Human-Computer Interaction And Intelligent Information Processing,Institute of Software,Chinese Academy of Sciences,Beijing 100190;Key Laboratory of Microgravity,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190)

机构地区：[1]中国科学院软件研究所计算机科学国家重点实验室,北京100190 [2]中国科学院大学计算机科学与技术学院,北京100190 [3]中国科学院软件研究所人机交互技术与智能信息处理实验室,北京100190 [4]中国科学院力学研究所微重力重点实验室,北京100190

出　　处：《计算机辅助设计与图形学学报》2024年第4期533-542,共10页Journal of Computer-Aided Design & Computer Graphics

摘　　要：为了拓展图形学弹性体模拟中的各向异性超弹性虚拟材料种类,建立了基于虚拟纤维的本构模型.首先从能量可加性出发,将超弹性体应变能量密度函数分解为轴向、剪切、体积分量的纤维加和形式,然后建立单根纤维的轴向应变、剪切应变、体积应变的应变度量,最后推导出各分量的应力表示.仿真实验使用基于四面体的非线性有限元法(finite element method,FEM),半隐式时间积分进行解算,并采用CPU串行算法,测试了不同场景下非线性能量函数以及纤维权重组合对虚拟纤维材料刚度、泊松效应、轴向特性的影响.结果表明,虚拟纤维本构模型具有大变形稳定性,材料参数设置可良好地展现上述物理特性,相比现有的横观各向同性模型具有更丰富的可调节能力.In order to expand types of anisotropic hyperelastic virtual materials for elastic bodies simulation in graphics,this paper established a virtual fiber-based constitutive model.Firstly,the strain energy density function of hyperelastic body was decomposed into fiber addition form of axial,shearing and volumetric component based on energy additivity.Secondly,strain measurement of each component for a single fiber was established.Finally,stress expression of each component was deduced.Simulation experiments used tetrahedral nonlinear finite element method(FEM),semi-implicit time integration and CPU-based serial algorithm to test effects of nonlinear energy function and fiber weight combination on the stiffness,Poisson effect and anisotropic axial characteristics in different scenarios.Results show that the virtual fiber-based model displays desirable physical properties with adopted parameter setting,and is suitable for large deformation simulation.Compared with existing transverse isotropic model,this model also possesses more abundant adjustability.

关 键 词：各向异性材料 有限元 物理动画 虚拟纤维 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]