⚡ electrical engineering

Deformation Mechanisms of Three-Dimensional Angle-Interlock Preforms

This paper presents a multi-mode decoupled hyperelastic constitutive model, implemented in ABAQUS via a VUMAT subroutine, to accurately simulate and predict the nonlinear, anisotropic forming behavior and deformation mechanisms of three-dimensional angle-interlock preforms over complex surfaces.

Original authors: Zhenyu Wang, Yifan Zhang, Jiahui Wei, Qiwei Guo, Daijun Zhang, Chao Li, Junjie Hao, Pengfei Jiang, Tianqi Wang, Li Chen

Published 2026-08-19

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CC BY 4.0

Original authors: Zhenyu Wang, Yifan Zhang, Jiahui Wei, Qiwei Guo, Daijun Zhang, Chao Li, Junjie Hao, Pengfei Jiang, Tianqi Wang, Li Chen

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to wrap a flat sheet of paper perfectly around a basketball. The paper resists; it wants to stay flat, and if you force it, it crumples or tears. Now imagine that sheet is not paper, but a thick, heavy fabric made of thousands of interwoven carbon fibers, designed to become the skeleton of a jet engine or a spacecraft. This material is incredibly strong, but making it take on complex, curved shapes without failing is one of the toughest challenges in modern engineering. The fabric is not a single solid piece; it is a grid of threads that can slide, rotate, and bend, but only in specific ways. If the threads get stuck or forced into a shape they cannot handle, the final part will be weak or ruined. Engineers need to know exactly how this fabric will behave before they ever cut the material, but predicting its movement is like trying to forecast the weather for a single grain of sand in a storm.

A team of researchers from TianGong University and several industry partners in China has taken a significant step toward solving this puzzle. They focused on a specific type of fabric called a three-dimensional angle-interlock preform. Unlike ordinary cloth, which is flat, this material is woven so that threads run not just left-to-right and front-to-back, but also up and down through the thickness of the fabric. This creates a solid, interlocked structure that is far more resistant to falling apart than standard layered materials. The researchers wanted to understand exactly how this thick, three-dimensional fabric deforms when it is pressed over a curved surface, a process known as forming. To do this, they did not just guess or rely on simple rules of thumb. Instead, they built a sophisticated digital model that mimics the physics of the fabric, treating it as a single, continuous material that can stretch, squash, and twist in complex ways.

The team began by testing the real fabric in a laboratory to see how it reacted to different forces. They pulled it apart to see how much it stretched, squeezed it from the top to see how much it compressed, and twisted it to see how the threads rotated against each other. They found that the fabric behaves very differently depending on the direction of the force. When pulled, the threads straighten out and become stiff. When squeezed, the tiny gaps between the threads close up, and the material gets harder to compress. When twisted, the threads slide past one another, but only up to a point, after which they lock together and resist further movement. By measuring these reactions carefully, the researchers identified the specific numbers needed to describe the fabric's behavior. They then fed these numbers into a computer program, creating a virtual version of the fabric that could be tested in a simulated environment.

To check if their digital model was accurate, the researchers performed a real-world experiment. They took a square piece of the carbon fiber fabric and pressed it against a hemispherical dome, much like pushing a flat cloth over the top of a bowl. They watched closely to see how the fabric moved, how much force was required to push it down, and how the threads shifted. They compared these real-world observations with the results from their computer simulation. The match was remarkably close. The model correctly predicted the amount of force needed to form the shape, with a small difference of only about 15 percent in the peak force. More importantly, it accurately showed where the fabric would twist and how the threads would rotate. In the real experiment, the fabric twisted the most in the area where the flat edge met the curved dome, reaching a maximum twist angle of about 37 degrees. The computer model predicted a peak of 34 degrees in the same spot, confirming that the digital tool could see what was happening inside the material.

The study revealed that the main way this fabric adapts to a curved shape is by the threads rotating relative to one another within the plane of the fabric. This is called in-plane shear. As the fabric is pushed over the curve, the square grid of threads turns into a diamond shape, allowing the material to cover the surface without stretching the threads themselves. However, the researchers also discovered a secondary, three-dimensional movement. In the transition zone where the curve changes most sharply, the threads also bend slightly up and down through the thickness of the fabric. This out-of-plane movement helps the fabric conform to the tightest parts of the curve, acting like a hinge that allows the material to settle into the shape more smoothly. Without this subtle bending, the fabric would likely wrinkle or fail to reach the tool surface.

The team also tested what would happen if they started with the threads oriented in a different direction. They found that changing the initial angle of the threads did not change how much the fabric could twist overall, but it did change where the twisting happened. If the threads were aligned with the edges of the mold, the twisting concentrated in the corners. If the threads were rotated, the area of maximum twisting shifted to follow the new direction of the threads. This means that engineers can control where the fabric deforms most by simply changing how they lay the material down before pressing it. This insight is crucial for designing parts that need to be strong in specific directions. The researchers concluded that their new model provides a reliable way to simulate these complex forming processes, offering a clear path to optimizing how these advanced materials are shaped for the next generation of high-performance aircraft and vehicles.

Technical Summary: Deformation Mechanisms of Three-Dimensional Angle-Interlock Preforms

Problem Statement
Three-dimensional (3D) angle-interlock preforms are critical reinforcements for aerospace, marine, and defense applications due to their superior through-thickness reinforcement and resistance to delamination compared to 2D laminates. However, forming these preforms over complex, double-curvature surfaces induces significant nonlinear, anisotropic, and coupled deformation behaviors. Existing numerical modeling approaches face a trade-off: kinematic models (e.g., Chebyshev nets) lack intrinsic mechanical response prediction, while discrete mesoscopic models (beam/spring elements) are computationally prohibitive for large-scale components. Macroscopic continuum models, particularly those based on hypoelasticity, often suffer from numerical stability issues or non-physical responses depending on the objective stress rate. There is a need for a thermodynamically consistent, computationally efficient macroscopic constitutive model capable of accurately predicting the large-deformation behavior of 3D woven preforms during complex forming processes.

Methodology
The study establishes a multi-mode decoupled anisotropic hyperelastic constitutive framework to simulate the forming of a 1/3 twill 3D angle-interlock preform.

Theoretical Framework: Based on finite-deformation hyperelasticity, the model utilizes structural tensors and mixed invariants derived from the right Cauchy–Green deformation tensor ( $C$ ) and material direction vectors. The total strain energy density function ( $\psi$ ) is decomposed into four fundamental, decoupled modes: warp/weft tension, through-thickness compression, in-plane shear, and out-of-plane shear.
Material Characterization: Experiments were conducted on TG800HX-12K carbon fiber preforms to characterize mechanical responses under uniaxial tension, transverse compression, bias-extension (in-plane shear), and out-of-plane shear.
Parameter Identification: Experimental load-displacement data were converted into strain energy densities. Polynomial functions were fitted to these energy responses to identify material parameters for the constitutive model.
Implementation: The model was implemented in ABAQUS/Explicit via a VUMAT user material subroutine.
Validation: The model was validated against hemispherical forming experiments using a 300 mm × 300 mm preform. Validation metrics included macroscopic load-displacement responses, in-plane shear angle distributions, boundary draw-in contours, and out-of-plane shear characteristics.

Key Contributions

Constitutive Model Development: The paper proposes a multi-mode decoupled hyperelastic model specifically tailored for 3D angle-interlock architectures. It explicitly formulates strain energy functions for tension, thickness compression, in-plane shear, and out-of-plane shear using physical invariants, ensuring thermodynamic consistency.
Experimental-Computational Integration: The study provides a comprehensive dataset of mechanical characterization for 3D angle-interlock preforms and demonstrates a robust workflow for identifying constitutive parameters from these tests.
Deformation Mechanism Analysis: The research elucidates the specific roles of different deformation modes during complex forming, distinguishing between the dominant in-plane shear mechanisms and the localized out-of-plane shear effects.
Orientation Sensitivity: The study investigates the influence of initial yarn orientation ([0°/90°], [±45°], and asymmetric [30°/−60°]) on the spatial distribution of shear fields and boundary evolution.

Results

Model Accuracy: The constitutive model successfully predicted the forming behavior with a relative error of 15.2% in peak load and 6.3% in peak shear angle along the 45° path on the convex side. It accurately reproduced the nonlinear load-displacement response and the directional dependence of boundary draw-in.
Deformation Modes:
- In-plane Shear: Identified as the dominant deformation mode for accommodating double-curvature surfaces. The maximum in-plane shear angle reached 37.4°, concentrated in the curvature transition region between the punch-contact area and the flange.
- Out-of-plane Shear: While generally lower in magnitude (max ~17.5°), out-of-plane shear was found to be critical in the curvature transition zones, facilitating local surface conformity through through-thickness yarn deflection.
Yarn Orientation Effects: Changing the initial yarn orientation significantly altered the spatial distribution of high-shear regions and the evolution of the boundary contour. However, the magnitude of the maximum shear angle remained relatively unaffected by orientation changes. Asymmetric orientations ([30°/−60°]) induced non-uniform shear distributions and boundary twisting.

Significance
The paper claims that the established multi-mode decoupled hyperelastic model provides a reliable reference for the forming simulation and process optimization of 3D woven preforms over complex surfaces. By accurately capturing the nonlinear mechanical behavior and the interplay of different deformation modes, the model supports the design of yarn orientations to regulate local deformation concentrations. The authors note that while the current decoupled approach is effective, future work will focus on developing a coupled constitutive model to account for interactions between tension, compression, and shear modes for even more accurate characterization.

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