James D. Lee
Professor of Engineering and Applied Science 
Office: Academic Center-Room T733
Tel:    (202) 994-5971
Fax:    (202) 994-0238
E-Mail: lee@seas.gwu.edu         jdlee@gwu.edu
Office Hours for Spring 2003: 
M - by appointment                          T - 3:30 to 5:30 pm 
W - by appointment                          R - 3:30 to 5:30 pm 
F - by appointment
Education:

Ph.D. Princeton University, June 1971 
Major - Continuum Mechanics 
Minor - Physics and Applied Mathematics 

M.S. Rice University, June 1967 
Major - Civil Engineering 

B.S. National Taiwan University, June 1964 
Major - Civil Engineering
 

Specialty Areas:
  • Continuum Mechanics 
  • Microcontinuum Physics
  • Finite Element Methods, Meshless Methods 
  • Optimal Control Theory 
  • Solid State Physics
Current Research Interests:
  • Multi-scale theory for multi-physics 
  • Nanotechnology: molecular dynamics and microcontinuum theory
  • Microscopic modeling of coupled thermomechanical and electromagnetic phenomena 
  • Modeling and control of smart materials and structures
  • Meshless analysis of nonlocal field theories
Research assistantship is available for graduate student with background in physics and interest in doing research in the area of molecular dynamics.

Biography:

Since 1990, James D. Lee has taught in two areas of mechanical engineering (solid mechanics, control) at the Department of MAE. He has also been an active researcher in those areas. He is a registered Professional Engineer in Washington, DC and a member of  ASME,  Sigma Xi, American Academy of Mechanics, and New York Academy of Science. 

He has been teaching and/or doing research in universities (Purdue U., West Virginia U., U. of Akron, U. of Minnesota and GWU), industry (The General Tire and Rubber Company), and US government laboratories (NIST and NASA).  His research fields include liquid crystals, fracture mechanics, composite materials, numerical analyses, control, robotics, metal forming process, finite element methods, meshless methods and microcontinuum physics. Most recently, he has been doing research on multi-physics micromorphic theory to bridge the gap between atomistic model and continuum field theory.

He has been a principal investigator of research grants awarded by NASA and NSF. He has directed eight doctoral dissertations and many master theses. He has published more than 100 technical papers including 60 referred journal articles. 
 

Course Director/Instructor:

(1)Electromechanical Control Systems (ME 246)
(2)Advanced Finite Element Methods in Structural Mechanics(EngS 288) 
(3)Finite Element Methods in Engineering Mechanics (EngS 285) 
(4)Engineering Analysis I (ApSc 113) 
(5)Electromechanical Control System Design (ME 182) 
(6)Robotic Systems Design and Applications (ME 197) 
(7)Introduction to Vibration Analysis (ME 134) 
(8)Theory of Elasticity I (EngS 221) 
(9)Composite Materials (EngS 234) 
(10)Analytical Methods in Engineering II (ApSc 212) 
(11)Analytical Methods in Engineering III (ApSc 213) 
(12)Robotic Systems (ME 245) 
(13)Introduction to Continuum Mechanics (EngS 218, MAE 210) 
(14)Fracture Mechanics (EngS 240) 
(15)Applied Finite Element Method (MAE 287)
Publications:
Most Recent Publications Supprted by NSF :

1.  James D Lee and Youping Chen, “A constitutive relations of micromorphic thermoplasticity”, International Journal of Engineering Science, 41, pp387-399, 2003.

2. Youping Chen, James D. Lee and Azim Eskandarian, “Examining physical foundation of continuum theories from viewpoint of phonon dispersion relations”, International Journal of Engineering Science, 41, pp61-83, 2003. 

3.  Youping Chen, James D. Lee and Azim Eskandarian, " Atomistic Counterpart of Micromorphic Theory "  ,  Acta Mechanica, to appear, 2003 

4.  Youping Chen and James D. Lee,    "Determining  Material Constants in Micromorphic Theory through Phonon Dispersion Relations" International Journal of Engineering Science, to appear, 2003.  

5.  Youping Chen and James D. Lee,  "Connecting Molecular Dynamics To Micromorphic Theory Part I: Instantaneous Mechanical Variables ", Physica A: Statistical Mechanics and its Applications, in press.  

6.  Youping Chen and James D. Lee, "Connecting Molecular Dynamics To Micromorphic Theory  Part II: Balance laws " ,  Physica A: Statistical Mechanics and its Applications, in press.  

7. Youping Chen, James D. Lee and Azim Eskandarian, “ Micropolar Theory and Its Applications to Mesoscopic and Microscopic Problems", Computer Modeling in Engineering & Sciences, accepted for publication.

8. Youping Chen, Azim Eskandarian, Morton S. Oscard and James D. Lee, “Meshless analysis of plasticity with application to crack growth problems”, Theoretical and Applied Fracture Mechanics, to appear.

9. Youping Chen, James D. Lee and Azim Eskandarian, “ Dynamic meshless method applied to nonlocal cracked problems”, Theoretical and Applied Fracture Mechanics, 38, 293-300, 2002

10. James D. Lee, Youping Chen, and Azim Eskandarian,  "A Micromorphic Electromagnetic Theory" Submitted for publication in International Journal of Solid and Structures. 

11. Youping Chen, James D. Lee and Azim Eskandarian, "Atomistic Viewpoint of the Applicability of Micrcontinuum Theories"  Submitted for publication in International Journal of Solid and Structures.  

12.  Youping Chen, James Lee and Azim Eskandarian, “Applicability analysis of continuum theories from viewpoint of phonon dispersion relations”, US 14th Congress of Theoretical and Applied Mechanics, June 22-27, 2002, Blacksburg, Virginia, USA 

13.  Youping Chen, James Lee and Azim Eskandarian, “Connecting Discrete Atomic Model to Microcontinuum Field Theories”, 39th Annual Conference of the Society of Engineering Science, October 13-16, 2002, Pennsylvania.

14.  Youping Chen, James D Lee and Azim Eskandarian, “Finding Material Constants in Micromorphic Theory through Phonon Dispersion Relations”, Proceedings of International Conference of Computational Engineering and Science, July 29 –Aug. 2, 2002, Reno, Nevada.

15. Youping Chen and James D Lee, “Analysis of Phonon Dispersion Relations: From Atomistic Model to Continuum Theory,” Technical Proceedings of the 2002 International conference on Computational Nanoscience”, April 22-25,2002, San Juan, Puerto Rico, U.S.A.

16. Youping Chen, Azim Eskandarian, C-D. Kan and James D Lee, “ Thermo-plastic effects on structural behavior during crush and impact”, Int. J. Vehicle Design, Vol. 30, 22-32, 2002 

17.  Y. Chen, M. Riegelman, J. Li, and M. E. Zaghloul, “Computer Simulations and Design Optimizations of Piezoelectric Resonator”, US 14th Congress of Theoretical and Applied Mechanics, June 22-27, 2002, Blacksburg, Virginia, USA 

18. Youping Chen, James D Lee and Azim Eskandarian, “Local and Nonlocal Meshless Method of Fracture Mechanics”, Proceedings of International Conference of Computational Engineering and Science, July 29 –Aug. 2, 2002, Reno, Nevada.

19.   James D. Lee and Youping Chen  “A Constitutive Theory of Electromagnetic Microcontinuum”, US 14th Congress of Theoretical and Applied Mechanics, June 22-27, 2002, Blacksburg, Virginia, USA.

20.  W. Zeng, M.T. Manzari, J. D. Lee and Y. L. Shen, Fully-coupled Non-linear Analysis of Piezoelectric Solids Involving Domain Switching, International Journal of Numerical Methods in Engineering, Vol. 56, No. 1, 2003, pp. 13-34.

21.  W. Zeng, M.T. Manzari, J. D. Lee and Y. L. Shen, An Analysis of the Effect of Domain Switching on Fracture Behavior of Piezoelectric Solids, Smart Materials and Structures, in press, Vol. 12, 2003.

22.  W. Zeng, M.T. Manzari, J. D. Lee and Y. L. Shen, Domain Switching Effect on Fracture of Piezoelectric Solids, Journal of Mechanics Research Communication, in press, in press, 2003.
 

Other Journal Articles

James D Lee and Youping Chen, “A theory of thermo-visco-elastic-plastic material: thermomechanical coupling in simple shear”, Theoretical and Applied Fracture Mechanics, 35, 187-209, 2001. 
 
J. D. Lee, M. T. Manzari, Y. L. Shen, and W. Zeng, "A Finite Element Approach to Transcient Thermal Analysis of Work Rolls in Rolling Process," ASME Transactions Journal of Manufacturing Science and Engineering, 122, pp.706-716, 2000. 
 
J. D. Lee and Y. Chen, "Non-Steady-State Elastic-Plastic Behavior of Metal Forming (Rolling) with a generalized Friction Law,"Theoretical and Applied Fracture Mechanics, 33, pp.93-99, 2000. 
 
J. D. Lee and S. Shen, "The Contact and Friction Problem in Rolling Process," Proc. Instn. Mech. Engs., Vol 214, Part K, pp.61-69, 2000. 
 
J. D. Lee, S. Shen, M. T. Manzari, and Y. L. Shen, "Structural Control Algorithms in Earthquake Resistant Design," Journal of Earthquake Engineering, 4, pp.67-96, 2000.
 
J. D. Lee, "A Large-Strain Elastic-Plastic Finite Element Analysis of Rolling Process," Computer Methods in Applied Mechanics and Engineering, 161, pp.315-347, 1998.
 
K. Y. Lee, J. D. Lee, and H. Liebowitz, "Finite Element Analysis of the Slow Crack Growth Process in Mixed Mode Fracture," Engineering Fracture Mechanics, 56, pp.551-577, 1997 .
 
J. D. Lee, H. Liebowitz, and K. Y. Lee, "The Quest of a Universal Fracture Law Governing the Process of Slow Crack Growth," Engineering Fracture Mechanics, 55, pp.61-83, 1996 .
 
M. E. Pachajoa, M. K. Frances, and J. D. Lee, "Stress and Failure Analysis of Composite Structures," Engineering Fracture Mechanics, 50, pp.883-902, 1995.
 
P. M. Haefele and J. D. Lee, "The Constant Stress Term," Engineering Fracture Mechanics, 50, pp.869-882, 1995. 
 
P. M. Haefele and J. D. Lee, "Combination of Finite Element Analysis and Analytical Crack Tip Solution for Mixed Mode Fracture," Engineering fracture Mechanics, 50, pp.849-868, 1995. 
 
H. Liebowitz, J. S. Sandhu, J. D. Lee, and F. C. M. Menandro," Computational Fracture Mechanics: Research and Application," Engineering Fractures Mechanics, 50, pp.653-670, 1995. 
 
H. Liebowitz, J. S. Sandhu, F. C. M. Menandro, and J. D. Lee, "Smart  Computational Fracture of Materials and Structures," Engineering Fracture Mechanics, 50, pp.639-651,  1995.
 
M. E. Pachajoa, K. Y. Lee, and J. D. Lee, "Progressive Failure Analysis of Composite Structures Made of Thermo-Elastic Solids," Composites Engineering, 4, pp. 503-523, 1994. 
 
G. L. Domani and J. D. Lee, "An Investigation of a Dynamic Crack Propagation in a Two-Dimensional Viscoelastic Solid," Engineering Fracture Nechanics, 46, pp.807-813, 1993. 
 
J. D. Lee, "Optimal Control of Flexible Parallel Link Robotic Manipulator," Computers and Structures, 48, pp.375-386, 1993. 
 
J. D. Lee and Z. Geng, "Dynamic Model of Flexible Stewart   Platform,"  Computers and Structures, 48, pp.367-374, 1993. 
 
Z. Geng, L. S. Haynes, J. D. Lee, and R. L. Carroll, "On the Dynamic Model and Kinematic Analysis of a Class of Stewart Platforms," Robotics and Autonomous Systems, 9, pp.237-254, 1992. 
 
J. D. Lee, "Application of Optimal Control Theory to Flexible Robotic Manipulators," Robotics and Computer-Integrated Manufacturing, 7,  pp.327-335, 1990. 
 
J. H. Chiou, J. D. Lee, and A. G. Erdman, "Development of A Three Dimensional Finite Element Proqram for Large Strain Elastic-Plastic Solids," Computers & Structures, 36, pp.631-645, 1990. 
 
J. D. Lee, J. S. Albus, N. G. Dagalakis, and T. Tsai, "Computer Simulation of a Parallel Link Manipulator," Robotics and computer-Integrated Manufacturing, 5, pp.333-342, 1989. 
 
N. G. Dagalakis, J. S. Albus, B. L. Wang, J. Unger, and J. D.Lee, "Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications," ASME Journal of Offshore Mechanics and Arctic Engineering, 111, pp.183-193, 1989. 
 
J. D. Lee and B. L. Wang, "Dynamic Equations for Two-Link Flexible Robot Arm," Computers & Structures, 29, pp.469-477, 1988. 
 
J. D. Lee and B. L. Wang, "Optimal Control of Flexible robot Arm," Computers & Structures, 29, pp.459-467, 1988. 

J. D. Lee, "Finite Element Procedures for Larqe Strain Elastic-Plastic Theories," Computers & Structures, 28, pp.395-406, 1988. 

J. D. Lee and L. S. Haynes, "Finite Element Analysis of Flexible Fixturing System," J. Engineering For Industry, 109, pp.134-139,1987. 

J. H. Chiou, J. D. Lee, and A. G. Erdman, "Comparison Between Two Theories of Plasticity," Computers & Structures, 24, pp.23-37, 1986. 

J. D. Lee, "Finite Element Formulation of Large Strain Incompressible Elasti-Plastic Solid, Computers & Structures, 22, pp.773-783, 1986. 

J. D. Lee and H. Liebowitz, "Dynamic Crack Propagation in Elastic Solid," Journal de Phyqique, Colloque C5, supplement au no. 8, Tome 46, pp. 257-269, 1985. 

J. D. Lee, S. Du, and H. Liebowitz, "Three-Dimensional Finite Element and Dynamic Analysis of Composite Laminate Subjected to Impact," Computers & Structures, 19, pp.807-813, 1984. 

S. Du and J. D. Lee, "Variations of Various Fracture Parameters during the Process of Subcritical Crack Growth," Engineering Fracture Mechanics, 17, pp.173-183, 1983. 

W. Shen and J. D. Lee, "The Nonlinear Energy Method for Mixed Mode Fracture, " Engineering Fracture Mechanics, 16, pp.783-798, 1982. 

S. Du and J. D. Lee, "Finite Element Analysis of Slow Crack Growth," Engineering Fracture Mechanics, 16, pp.229-245, 1982. 

J. D. Lee, "Three-Dimensional Finite Element Analysis of Damage Accumulation in Composite laminate," Computers & Structures, 15, pp.335-350, 1982. 

J. D. Lee, "Three-Dimensional finite Element Analysis of Layered Fiber-Reinforced Composite Materials," Computers & Structures, 12, pp.319-339, 1980. 

J. D. Lee, H. Liebowitz, and N. Subramonian, "Mechanics of Fracture- Fundamentals and Some Recent Developments," Israel Journal of Technology, 17, pp.273-294, 1979. 

J. D. Lee and H. Liebowitz, "Consideration of Crack Growth and Plasticity in Finite Element Analysis," Computers & Structures, 8, pp.403-410, 1978. 

H. Liebowitz, J. D. Lee, and J. Eftis, "Biaxial Load Effects in Fracture Mechanics," Engineering Fracture Mechanics, 10, pp.315-335, 1978. 

J. D. Lee and H. Liebowitz, "The Nonlinear and Biaxial Effects on Enerqy Release Rate. J-Integral. and Stress Intensity Factor," Engineering Fracture Mechanics, 9, pp.765-779, 1977. 

J. D. Lee and A. C. Eringen, "A Reply to Shahinpoor's Comments on Alignment of Nematic Liquid Crystals," J. Chem. Phys., 63, pp.1321-1322, 1975. 

J. D. Lee and S. L. Koh, "Transverse Plane Motion of an Unidirectional Composite," Letters in Appl. & Engrg. Sci., 1, p. 407, 1973. 

B. M. Chiu and J. D. Lee, "On the Plane Problem in Micropolar Elasticity," Int. J. Engrg. Sci., 11, pp. 997-1012, 1973. 

J. D. Lee and A. C. Eringen, "Continuum Theory of Smectic Liquid Crystals," J. Chem. Phys., 58, pp. 4203-4211, 1973. 

J. D. Lee and A. C. Eringen, "Boundary Effects on Orientation of Nematic Liquid Crystals," J. Chem. Phys., 55, pp. 4509-4512, 1971. 

J. D. Lee and A. C. Eringen, "Alignment of Nematic Liquid Crystals," J. Chem. Phys., 55, pp. 4504-4508, 1971. 

J. D. Lee and A. C. Eringen, "Wave Propagation in Nematic Liquid Crystals," J. Chem. Phys., 54, pp. 5027-5034, 1971. 

E. D. Lieberman, J. D. Lee, and F.C. Moon, "Anisotropic Ultrasonic Wave propaqation in a Nematic Liquid Crystal Placed in a Magnetic Field," Applied Physics Letters, 18, pp. 280-281, 1971. 
 

Selected Conference Papers
Youping Chen, James D Lee and Azim Eskandarian, “Meshless Particle Methods for Nonlocal Continua”, in Advances in Computational Engineering & Sciences (edited by Atluri, Nishioka and Kikuchi), Tech Science Press, 2001.

Youping Chen and James D Lee, “On Micropolar Field Theory and Its Applications”, in Advances in Computational Engineering & Sciences (edited by Atluri, Nishioka and Kikuchi), Tech Science Press, 2001.

Lee J. D. and Chen Y. (2001), “A General Theory of Micropolar Thermoplasticity”, Technical Proceedings of the 2001 International conference on Computational Nanoscience”, March 19-21, 2001, Hilton Head Island, South Carolina, USA. 

Y. Chen, J. D. Lee, A. Eskandarian and N. E. Bedewi, "Adiabatic Shear Localization in Impact Problem," Proceedings of International Crashworthiness Conference, London, UK, September, 2000. 

 
J. D. Lee, W. Zeng, and Y. Chen, "Wave Propagation and Temperature Elevation in Composite Laminate," Proceedings of ICCE/7, Denver, Colorado, July, 2000. 
 
J. D. Lee and Y. Chen, "A generalized Friction Law and its Application in Metal Forming (Rolling) Process," Mesomechanics 2000(edited by G. C. Sih), Proceedings of the International Conference on Role of Mesomechanics for Development of Science and Technology, Xi'an, China, June 13-16, pp.315-324, 2000. 
 
S. Shen and J. D. Lee, "Dynamic Crack Propagation in Thermovisco-elastic Solid," CD-ROM Proceeding of the 14th ASCE Engineering Nechanics Division Conference, Austin, Texas, 2000. 
 
J. D. Lee, M. T. Manzari, Y. L. Shen, and W. Zeng, "Finite Element Analysis of Transcient Thermal Problem of Work Rolls in Rolling Process," Proceedings of 1999 ASME IMECE: Symposium on Continuous Casting and Rolling Technologies, pp.39-47, Nashville, TN.1999. 
 
S. Shen and J. D. Lee, "Dynamic Finite Element Analysis of Thermo-mechanical Process in Composite," CD-ROM Proceeding of the 13th ASCE Engineering Mechanics Division Conference, Baltimore, MD, 1999. 
 
J. D. Lee and S. Shen, "Finite Element Analysis of Metal Forming (Rolling) Process," Proceeding of the Joint Conference of the 5th Int. Conf. on Automation Technology and the 1998 Int. Conf. on Production Research, Taipei, Taiwan, 1998. 
 
J. D. Lee, S. Shen, M. T. Manzari, and Y. L. Shen, "Optimal Stochastic Control of Intelligent Structures," Proceedings of The Second World Conference on Structural Control, Kyoto, Japan, pp.1605-1613, 1998. 
 
K. Y. Lee, J. D. Lee, and H. Liebowitz, "Finite Element Analysis of the Slow Crack Growth Process," Proceedings of the Fourth International Conference - Localised Damage 96, Fukuoka, Japan, 1996.
 
J. P. Chiou and J. D. Lee, "Dynamics and Control of a Flexible Parallel Link Robotic Manipulator," Proceedings of the Third International Conference on Automation Technology, V.5, pp.27-34, Taipei, Taiwan, 1994. 
 
Z. Geng, L. S. Haynes, and J. D. Lee, "Stewart Platform as an Intelligent Structure," Robotics and Manufacturing-Recent trends in research, education, and applications (edited by Jamshidi), vol.4, p.419, ASME Press, 1992. 
 
Z. Geng, J. D. Lee, R. L. Carroll, and L. S. Haynes, "Learning Control System Desiqn Based on 2-D Theory -- An Application to Parallel Link Manipulator," Proceedings IEEE International Conference on Robotics and Automation, pp.1510-1517, 1990. 
 
Z. Geng, J. D. Lee, R. L. Carroll, and J. Xie, "Learninq Control System Desiqn for a Parallel Link Robot Manipulator," Proceedings of IEEE International Symposium on Intelligent Control 1990, pp.102-107, 1990. 
 
J. D. Lee, "Finite Element Analysis of Elastic-Plastic Solids at Larqe Strain," Recent Advances in Engineering Sciences (edited by Koh and Speziale), Lecture Notes in Engineering, 39, pp.96-107, Springer-Verlag, Berlin, 1989. 
 
J. D. Lee, J. S. Albus, N. G. Dagalakis, and T. Tsai, "Performance Measures of a Robotic Micropositioner," Robotics and Manufacturing edited by Jamshidi, Luh, Seraji and Starr), pp.1047-1056, ASME Press, 1988. 
 
J. Unger, N. G. Dagalakis, T. Tsai, and J. D. Lee, "Optimum Stiffness Study for a Parallel Link Robot Crane Under Horizontal Force," Robotics and Manufacturing (edited by Jamshidi, Luh, Seraji and Starr),  pp.1037-1046, ASME Press, 1988.
 
J. D. Lee, L. S. Haynes, B. L. Wang, and K. H. Tsai, "Control of Flexible Robot Arm," Modeling and Control of Robotic Manipulators and Manufacturing Processes (edited by Shoureshi, Youcef-Toumi, Kazerooni), ASME Press, 1987. 
 
J. D. Lee and B. L. Wang, "Finite Element Analysis of Curved Composite   Laminate," Proceedings of International Symposium on Composite Materials and Structures, Beijing, China, June 1986. 
 
M. J. Lii and J. D. Lee, "Modal Analysis of Elastic Wave Propagation," proceedings of the 3rd International Modal Analysis Conference, held at Orlando, Florida, January 1985. 
 
J. D. Lee, "Three-Dimensional Finite Element Analysis of Cumulative Damaqe in Layered Composite," (in Russian) Strength and Failure of Composite Materials (Edited by V.P. Tamuj), Riga, Zinatne, 1983. 
 
H. Liebowitz, J. D. Lee, and N. Subramonian, "Concepts of Linear and Nonlinear Fracture Mechanics," Defects and Fracture (edited by Sih and Zorski), Martinus Nijhoff Publishers, Haque, 1982. 
 
D. L. Jones, J. D. Lee, and H. Liebowitz, "Development of the Nonlinear Enerqy Method for Fracture Toughness Determination," Advances in Fracture Research (Fracture 81), (edited by Francois, et al), vol.4, pp.1769-1778, Pergamon Press, 1982. 
 
H. Liebowitz, J. D. Lee, and N. Subramonian, "Some Aspects of the Mechanics of Fracture," Proceedings of the Symposium on Mechanical Behavior of Materials, pp.5-36, 1980, held in Argentina. 
 
H. Liebowitz, J. D. Lee, and N. Subramonian, "Effects of Plasticity and Crack Geometry on Fracture," Transactions of the 5th International Conference on Structural Mechanics in Reactor technology, G6/2, 1979. 
 
H. Liebowitz, J. D. Lee, and N. Subramonian, "The Fracture Criteria for Crack Growth Under Biaxial Loading," Nonlinear and Dynamic Fracture Mechanics (edited by Perrone and Atluri), pp.157-169, ASME Press, 1979. 
 
J. D. Lee, H. Liebowitz, and N. Subramonian, "Theoretical and Experimental Biaxial Studies," Fracture Mechanics (edited by Perrone, Liebowitz, Mulville, and Pilkey), University of Virginia Press, 1978. 
 
J. D. Lee, "Theory of Fracture Mechanics Based Upon Plasticity," Recent Advances in Engineering Science, Volume 7 (edited by T.S.Chang), Scientific Publication, Inc., Boston, pp.133-140, 1976. 

J. D. Lee and A. C. Eringen, "Relations of Two continuum Theories of Liquid Crystals," Ordered Fluids and Liquid Crystals (edited by Porter and Johnson), pp.315-330, American Chemical Society Publications, 1974. 

A. C. Eringen and J. D. Lee, "Continuum Theory of Cholesteric Liquid Crystals," Ordered Fluids and Liquid Crystals (edited by Porter and Johnson), pp.383-402, American Chemical Society Publication, 1974.