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A new laminate theory: simplified, invariant and universal - an update

A new laminate theory: simplified, invariant and universal - an update

This is an updated presentation of the original version delivered at the webinar on the 11th of December 2023.

Double-Double Laminates - A Summary

Traditional laminates in Quad have four fixed ply angles in 0, ±45, 90 with variable ply numbers. Double-double (DD) laminates have four variable angles in [±A/±B] with four fixed single plies as the building block, bounded between [0] and [90]. Quad is discrete and unbounded, cannot interpolate and be homogenized; DD is field-based, continuous, can zoom, and easily homogenized for having repeated building blocks 3 or more. Thus DD is simple and easy to use, and naturally symmetric and can taper to save weight and cost that can be 50 percent or more.

Layup can be continuous (no stop at mid-plane), with no cross-plying, and the resulting laminate will not warp, esay to inspect, repair and provide hard points. Ply drops can be in singles and placed on the exterior surfaces keeping defects, voids, wrinkles and discontinuities away from the laminate interior.

A much higher quality laminate

Many self-inflicted complexities of Quad like the stacking sequence, blending, 4-ply limit on nesting, mid-plane symmetry, 10 percent rule, interlaminar ply angles to be no higher than 45 degree, and load-carrying plies to be placed near the center of laminate can be things of the past. Quad laminates can have dozens of stacking sequences; DD has at most 2. For Quad its subjective selection prevents scaling of one design to another. A wing skin can have hundreds of Quad laminates. It can be replaced by one DD. Laminate stiffness can be defined by trace, and its strength by the area of failure envelope. With two single parameters, materials and laminates can be rated. They are equivalent and equal in stature. They are not random as they have been treated. Scaling is now possible. One panel for calibration will be sufficient to predict the stiffness and strength of all carbon materials and all laminates.

It can be shown that the compressive and shear strengths are not sensitive to materials. Like metals only tensile tests will suffice in many cases. Design allowable will no longer be the barrier for innovation and progress in materials and processes.

History showed conflicts and resolutions between particle versus wave, AC versus DC, digital versus analog, and others. In a more modest scale, DD versus Quad is an ongoing conflict. We wish to show why DD will survive because it is simple, rational, and sensical.


S.W. Tsai, Double-Double: new family of composite laminates, AIAA Journal, November 2021

S.W. Tsai, et al., Double-Double, Stanford Composites Design Group, 2023; free download:

A​bout the presenter

Professor Stephen Tsai, is a Professor Emeritus (Research) of Aeronautics and Astronautics at Stanford University. Professor Tsai's research interest is in the development of design methodology of composite materials and structures. As an emerging technology, composite materials offer unique performances for structures that combine light weight with durability. Keys to the successful utilization of composite materials are predictability in performance and cost effective design of anisotropic, laminated structures. Current emphasis is placed on the understanding of failure modes, and computer simulation for design and cost estimation.

M​ajor Accomplishments

Research by Stephen W. Tsai led to several formulas and failure criteria in composite materials bearing his name, such as Tsai-Wu, which have been implemented almost every commercial software. These criteria have also become standard textbook material and been referred in most of the research articles in design and analysis of composite structures.More recently, his discovery of trace and master ply for carbon composites led to the naming of Tsai’s modulus, and double-double laminates.

There are several awards at international conferences on composite materials to honor his contributions in the field.

  • 1967 Founding Editor of Journal of Composite Materials
  • 1995 Life Member National Academy of Engineering
  • 1998 Life Fellow of American Society of Mechanical Engineers
  • 2010 Fellow of the Society for the Advancement of Material and Process Engineering

Academic Appointments

Boards, Advisory Committees, Professional Organizations

  • Member, National Academy of Engineering (1995 - Present)

Document Details

AuthorsTsai. W S
AudiencesAnalyst Educator Developer
Date 6th February 2024
OrganisationStanford University


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