Research Of Cloth Deformation Simulation Based On Mass-Spring Model

In modern society, the technique of cloth simulation is close related to many computer applications such as online shopping, fashion design, animation, movies, PC games and so on. So the research of cloth deformation simulation has become a hot topic in the Computer Graphics in recent years. As a typical flexible film material, the fabric with small bending stiffness wrinkles easily and is sensitive to external forces. Therefore, the analysis involing large deformations, large rotation and institutional movement are inevitable in a flexible fabric simulation. Those problems associated with mechanical properties often lead to bad fidelity and low computational efficiency in fabric deformation simulation. Thus it is important to establish a physical model which can describe the mechanical characteristics of the fabric and to develop the simulation technology of fabric for achieving satisfied calculation accuracy and computational efficiency.Among the regular fabric deformation simulation methods, the classical finite element method has high precision, but exist some difficulties in solving problems about singular stiffnes matrix, prestress and convergence. Compared with finite element method, the Mass Spring Model is a kind of model based on Newton’s second law, and it often used to simulate the nonlinear problem with large rotation since its simplicity, easy programming and high computational efficiency. Nevertheless, it often leads to low computational accuracy in simulating the fabric deformation because MSM cannot describe the mechanical characteristics of fabric accurately, and the corresponding spring coefficient is selected by no laws. In this paper, new MSMs are proposed according to fabric mechanical properties and the deformation algorithm are improved to solve nonlinear problems with large and rotation, in order to attain ideal precision and efficiency at the same time.(1) Based on the condition that the stiffness matrix of triangular element in MSM is precisely equal to the matrix of FEM, new mass-spring model with one additional node(MSMON) is presented and the corresponding spring coefficients of MSMON are deduced, moreover, a deformation algorithm of MSMON is set up. The numerical examples show that MSMON can accurately describe the deformation characteristics of flexible fabric.(2) Due to the spring stiffness coefficient expressions of MSMON may appear numerical computing problems because of the denominator is zero in particular material parameters situations. Similarly, another new mass-spring model with three additional nodes(MSMTN) is presented to achieve the stiffness matrix of triangular element in MSM is precisely equal to the matrix of FEM. The expression derivation of the spring coefficient in MSMTN has been given. And MSMTN can apply for any isotropic material parameters and triangle element shape.(3) The MSMON and MSMTN can describe the mechanical characteristics of isotropic flexible fabric accurately, so the MSMON and MSMTN are generalized for the orthotropic material of fabric. The analytic expressions of spring coefficient in the MSMON and MSMTN is derivation, the deformation algorithm are established based on them for orthotropic material of fabric.(4) In the condition of the fabric is a large stain and perstressed, the low calculation accuracy is still existent when applying MSM for simulating the deformation of the fabric. The increment calculation method of fabric deformation based on proposed MSM is presented, which can simulate the progress of the fabric large deformation accurately.(5) The proposed increment calculation method is applied to analyze the wrinkled membrane structures. A membrane structure under shear loads is studied in the appearance of wrinkle, the formation and the development process. The influence of the wrinkled membrane structures at the condition of different structural parameters and different initial disturbance is to analyze.The theoretical analysis and numerical examples show that the presented two kinds of improved spring-mass model can well characterize the fabric mechanical properties, and the corresponding deformation algorithm can accurately analyzed the influence of the geometric large deformation. Simulation results of some available test data prove that this model and algorithm is more accurate and proficient. At the same time, the models can be widely used for any isotropic and orthogonal anisotropic fabric materials, and division of arbitrary triangular elements. Finally, this paper put forward the lack of research work and future prospects.