Ph.D. Dissertation of David E. Breen:
A Particle-Based Model for Simulating the Draping Behavior of Woven Cloth

Woven cloth is increasingly being used as an industrial material. With its growing use, for example within composite materials for aircraft and automobiles, comes an increased need for computer-aided design systems that can accurately model and simulate non-rigid woven structures. This thesis presents a model of woven cloth that begins to address this need by providing the ability to reproduce the draping behavior of a variety of fabrics. Here, draping behavior means the final draped configuration of a cloth, which consists of characteristic folds and buckles, over a solid object. To date, most of the efforts to create a model of cloth have focused on conventional techniques based on continuum mechanics and the finite element method, and have not been completely successful.

The model of woven cloth presented in this thesis utilizes a new approach, called particle-based modeling, to simulate the mechanical properties of complex materials. In contrast to continuum techniques, particle modeling is founded on the premise that by directly modeling the microstructures of a material and computationally aggregating their interactions correct macroscopic behavior will emerge. Cloth is not a continuous material, but rather a complex mechanism. Cloth's microstructure consists of threads interlaced in a particular weave pattern. Much of its unique character comes from this underlying structure, with its various highly nonlinear geometric constraints, frictional interactions, and anisotropy.

Thread crossings play an important role in influencing the local behavior of cloth. Therefore, my model treats the thread crossing as the fundamental modeling unit, which is called a ``particle''. It is at the level of these particles that constraints are maintained, in the form of potential energy functions, on the relationships between the threads. Each particle does not necessarily represent a single thread crossing in a fabric. Instead the behavior of the particle is based on the structure and behavior of a thread crossing. The thread-relationship constraints maintained in the particle grid embody four basic mechanical interactions occurring in cloth at the thread level. They are thread collision, thread stretching, thread bending, and trellising.

An important feature of the model is that its thread-relationship constraints can be defined to simulate specific types of woven materials. This is accomplished by deriving the model's energy functions from empirical mechanical data produced from a standard set of fabric measurement equipment, the Kawabata Evaluation System. Given this capability, a woven material may be measured on the Kawabata System, and a model with the material's mechanical properties may then be defined to confidently simulate its draping behavior on a computer.

The validity of my particle-based model of cloth draping behavior has been verified by performing two experiments with three different kinds of woven cloth. A 100\% cotton, a 100\% wool, and a polyester/cotton blend were chosen for these experiments, because these fabrics exhibit different mechanical and draping behaviors. The first experiment recreates in simulation the standard measurement procedures that are applied to cloth and produces simulated mechanical data that favorably compare with the original empirical data. The second experiment performs controlled draping experiments with real cloth, then recreates those experiments with draping simulations utilizing the model. This experiment demonstrates that my model is capable of reproducing the unique large-scale draping structures that are produced by each of the experimental samples.

Last modified on Monday, March 20, 1995.