Document Type


Date of Degree

Fall 2013

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mechanical Engineering

First Advisor

Jia Lu


This thesis aims to develop a design-oriented simulation approach for cloth analysis. Our approach is built on the framework of NURBS-based isogeometric analysis, which utilizes NURBS as the basis functions of analysis. NURBS is a class of parametric geometry to represent curves and surfaces in computer-aided design (CAD) programs. Recently, NURBS geometry has been used directly in analysis. The overall goal of this thesis is to develop a computation infrastructure that enables cloth analysis directly on NURBS geometry.

The advantage of NURBS in the context of cloth modeling lies in the geometric smoothness. Using NURBS, it's easy to construct surfaces with C1 or higher order of continuity. Compared to C0 finite element geometry, the NURBS geometry is more effective in capturing wrinkles and folders of cloth, which are characteristics of cloth motion. The NURBS geometry enables the use of rotation-free Kirchhoff-Love shell. The rotation-free shell model not only saves freedoms, but also makes the contact/impact treatment much easier.

The major contribution of this work is the development of a NURBS cloth modeling approach. The mechanical model of cloth and its implementation with NURBS geometry will be presented in detail. Proper constitutive laws are employed for fabric materials. Since NURBS geometry from CAD typically contains multiple patches and trimmed patches, a certain treatment is proposed so that geometry can be used directly in analysis.

Another contribution of this work relates to a contact/impact algorithm. Contact problems in cloth simulation have been a bottleneck of continuum-based approach. Since the general contact method doesn't work well for cloth simulation, a special contact treatment is developed. The present contact model distinguishes three types of contact interactions. The first is the persistent contact force. This force in essence is the traditional penalty force, but is applied when a contact pair is within a separation tolerance instead of being penetrated. This essentially smears the abrupt contact reaction into a relatively smooth force defined only a small thickness. The second is trajectory impact, which deals with the reaction when impact occurs in a time step. The treatment ensures that a point stays on a same side of the surface it impacts on. The third is self-intersection. Intersection resorting force is introduced when the initial configuration has self-intersections, or when the trajectory impact force fails to eliminate all the collisions. We proposed a new method, the method of area minimization, to handle intersections.

The contact models have been integrated into an operator-split integration algorithm. A notable feature of this integration is that the contact/impact response is singled out from the momentum equation.

This work also proposes a continuum-based strain limiting scheme. Because the in-plane stiffness of cloth is much higher than the bending stiffness, numerical difficulty is encountered in either implicit or explicit time integration. The strain limiting is a numerical technique that formulates the in-plane response as a constraint problem to allow the use of lower in-plane stiffness.

A number of examples are presented to show the performance of the proposed approach. In the wrinkling study, the simulated wrinkle pattern looks similar with the experimental results. In the contact study, it is found that the current method can accurately recover a constant contact pressure field (press patch test), can handle contacts of multi-layer folds and produce realistic draping effect. The intersection resolution method is illustrated to be robust to various kinds of intersections. The fast projection method can enlarge time steps while limiting the in-plane strain.

The current method is also applied to the analysis of a soft armor. Beginning from CAD models the armor was put on the human body by a try-on simulation. In multi-layer models, the intersection resolution method is used to resolve the intersections between layers. Subsequently, cloth dynamics are simulated for different human motions. Mechanical indexes such as the extra torque caused by the armors, pressure force on the body, and stress in the armor are predicted. Parametric studies are performed to investigate the change in mechanical metrics under altered design parameters.


cloth simulation, isogeometric analysis, soft armor


xiii, 142 pages


Includes bibliographical references (pages 134-142).


Copyright 2013 Chao Zheng