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基于有限元的織物仿真及形變約束方法
A Restraining Method for Finite Element Based Fabric Simulation and Deformation

摘要：近十幾年來，柔性織物仿真逐漸成為計(jì)算機(jī)圖形學(xué)領(lǐng)域的研究熱點(diǎn)。本文對(duì)織物形變仿真的力學(xué)模型，尤其對(duì)織物形變產(chǎn)生的彈性力的計(jì)算方法作了深入的研究，并給出了一種適合本文力學(xué)模型特點(diǎn)的顯隱式結(jié)合的混合積分方法。針對(duì)織物仿真的“超彈性”現(xiàn)象，本文給出了一種適用于線性有限元模型的織物形變約束方法，該方法根據(jù)有限單元的應(yīng)變大小，分段地調(diào)整單元彈性模量，模擬織物形變的非線性性質(zhì)。實(shí)驗(yàn)結(jié)果表明，該方法有效地約束了織物的過度形變。
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.

針對(duì)織物模擬仿真問題的研究是從上個(gè)世紀(jì)80年代中期開始的，關(guān)于織物模擬技術(shù)的綜述文章可以參考[1][2]。96年Ng [1]對(duì)織物模擬的技術(shù)方法進(jìn)行了分類，主要有幾何方法、物理方法，以及混合方法等。05年Kwang-Jin Choi[2]，主要從衣物建模、物理仿真、碰撞處理三個(gè)方面整理總結(jié)了現(xiàn)有的織物仿真技術(shù)。
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.

常見的基于物理的織物模型包括質(zhì)子-彈簧模型（Mass-Spring）和有限元模型(Finite Element Method，F(xiàn)EM)。質(zhì)子-彈簧模型由Provot[3]提出。該模型把織物設(shè)想為一個(gè)質(zhì)點(diǎn)集合，質(zhì)點(diǎn)之間的相互關(guān)系歸結(jié)為質(zhì)點(diǎn)間的彈簧作用。有限元模型方法是一種將網(wǎng)格結(jié)構(gòu)體離散化，再針對(duì)離散模型進(jìn)行數(shù)值分析求解的工程方法。
The common physical based fabrics models are Mass-Spring and Finite Element Method，F(xiàn)EM. 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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