基于有限元的织物仿真及形变约束方法
A Restraining Method for Finite Element Based Fabric Simulation and Deformation

摘要：近十几年来，柔性织物仿真逐渐成为计算机图形学领域的研究热点。本文对织物形变仿真的力学模型，尤其对织物形变产生的弹性力的计算方法作了深入的研究，并给出了一种适合本文力学模型特点的显隐式结合的混合积分方法。针对织物仿真的“超弹性”现象，本文给出了一种适用于线性有限元模型的织物形变约束方法，该方法根据有限单元的应变大小，分段地调整单元弹性模量，模拟织物形变的非线性性质。实验结果表明，该方法有效地约束了织物的过度形变。
Abstract: For the last more than ten years, flexible fabric simulation has gradually become a research focus in the computer graphics field. This paper makes further research on the mechanical model of fabric deformation simulation, especially on the calculation method of elastic force generated by fabric deformation, and gives an explicit and implicit mixed integration method which is applicable to the characteristics of mechanical model in this paper. With regard to the super-elasticity phenomena of fabric simulation, this paper gives a restraining method for fabric deformation which is applicable to linear finite element model. This method adjusts the element elastic modulus sectionally according to the strain of finite element and simulates the nonlinear property of fabric deformation. The experimental result shows that the method restrains the excessive deformation of fabrics effectively.

针对织物模拟仿真问题的研究是从上个世纪80年代中期开始的，关于织物模拟技术的综述文章可以参考[1][2]。96年Ng [1]对织物模拟的技术方法进行了分类，主要有几何方法、物理方法，以及混合方法等。05年Kwang-Jin Choi[2]，主要从衣物建模、物理仿真、碰撞处理三个方面整理总结了现有的织物仿真技术。
The research on fabric simulation began in the mid 1980s, and the review articles of simulation techniques in fabrics can refer to [1][2]. Ng [1] classifies the techniques of fabric simulation in 1996, which mainly includes geometric method, physical method and mixed method, etc. Kwang-Jin Choi[2] systemized and summarized existing fabric simulation techniques in three aspects of clothing modeling, physical simulation and collision processing in 2005.

常见的基于物理的织物模型包括质子-弹簧模型（Mass-Spring）和有限元模型(Finite Element Method，FEM)。质子-弹簧模型由Provot[3]提出。该模型把织物设想为一个质点集合，质点之间的相互关系归结为质点间的弹簧作用。有限元模型方法是一种将网格结构体离散化，再针对离散模型进行数值分析求解的工程方法。
The common physical based fabrics models are Mass-Spring and Finite Element Method，FEM. Mass-Spring model is put forward by Provot[3] . This model assumes fabrics as gathering of mass points, and the relations among mass points result from spring force among mass points. Method for Finite Element model is a numerical analysis engineering method to discrete model after the discretization of grid structure.

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