⚡ electrical engineering

A discrete‑natured 3D DEM framework for spatial fracture analysis of unidirectional CFRP composites

This study presents a novel 3D discrete element method framework with a cubic packing scheme that treats unit cells as continuous elements to effectively model transverse fracture in unidirectional CFRP composites, revealing that while fiber distribution minimally affects global mechanical response, fiber volume fraction and radius critically govern stiffness, strength, and damage localization.

Original authors: Dechao Sun, Xiaoxuan Ding, Shuqi Zhang, Jianlin Liu, Zewen Gu, Xiaonan Hou

Published 2026-09-11

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CC BY 4.0

Original authors: Dechao Sun, Xiaoxuan Ding, Shuqi Zhang, Jianlin Liu, Zewen Gu, Xiaonan Hou

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

Modern engineering relies heavily on materials that are strong yet light, such as carbon-fiber-reinforced polymers. These composites are made by embedding thin, rigid carbon threads into a softer plastic glue, creating a structure that can bear heavy loads in aerospace and automotive applications. However, like any material, they have a weakness: when pulled from the side, the plastic glue between the fibers can crack. This type of cracking, known as transverse fracture, often starts as tiny, invisible flaws that grow and link together, eventually causing the entire structure to lose its strength. Understanding exactly how these cracks form and move through the complex maze of fibers and glue is difficult because the damage happens on a scale too small to see easily with standard tools, and the cracks do not travel in straight lines. They twist, turn, and interact with the fibers in three-dimensional space, making it hard to predict when a part might fail.

To solve this puzzle, researchers Dechao Sun and his team at the China University of Petroleum, working with Xiaonan Hou from Lancaster University, developed a new way to simulate these materials on a computer. Instead of treating the material as a smooth, solid block, they broke it down into a vast collection of tiny, individual particles that touch and push against one another. This approach, called the discrete element method, allows the computer to watch how the material behaves as if it were made of millions of microscopic building blocks. The team created a specific three-dimensional model of a cube of this composite material, filling it with virtual carbon fibers and epoxy resin. They then devised a new mathematical rule to connect the stiffness of the tiny connections between these particles to the overall strength of the material. A key innovation in their method is that the model automatically generates the material's tendency to bulge out when squeezed—a property known as Poisson's ratio—simply by watching how the particles move, rather than forcing the computer to use a pre-set number.

When the researchers tested this new model, they found it could accurately reproduce the real-world behavior of the material. The simulation predicted that the material would stretch and break in ways that matched existing laboratory experiments and previous two-dimensional computer models. However, the three-dimensional view revealed something the older models missed: the cracks do not slice through the material all at once like a knife through a loaf of bread. Instead, the crack front advances unevenly. In some spots, the crack moves forward quickly, while in others, it lags behind, creating a jagged, twisting path through the thickness of the material. This uneven progression, which the researchers call crack-front tortuosity, is a crucial detail that only a full three-dimensional view can capture.

The team then used this tool to investigate how different arrangements of the fibers affect the material's strength. They tested whether the random placement of fibers inside the plastic glue changed how the material held up. They found that while the exact path a crack took depended heavily on where the fibers happened to be located, the overall strength and stiffness of the material remained nearly the same regardless of the arrangement. This suggests that for predicting the general performance of the composite, the specific random pattern of fibers matters less than previously thought. However, the amount of fiber packed into the material made a significant difference. Increasing the fiber content from 50 percent to 68 percent made the material stiffer and stronger, but it also made it more brittle, causing it to fail at a lower stretch. The researchers observed that when the fibers were packed too tightly, there was not enough glue between them to absorb the stress, leading to rapid cracking.

Finally, the researchers looked at the size of the fibers themselves, keeping the amount of fiber constant. They discovered that the radius of the fibers, or how thick they were, influenced how the material handled stress. A fiber radius of 3.5 micrometers proved to be the most efficient configuration, offering the best balance between transferring load and allowing the glue to stretch. The simulations showed that the size of the fibers dictated the spacing between them, which in turn controlled where the stress concentrated and where the cracks would start. By mapping the forces between the virtual particles, the team could see exactly how the load shifted from the glue to the fibers and where the material finally gave way. This new three-dimensional framework provides a powerful tool for engineers to understand the hidden mechanics of composite materials, offering a clearer picture of how these complex structures fail and how they might be designed to last longer.

Technical Summary: A Discrete-Natured 3D DEM Framework for Spatial Fracture Analysis of Unidirectional CFRP Composites

Problem Statement
Carbon-fiber-reinforced polymers (CFRPs) are critical in aerospace and automotive applications but suffer from limited damage tolerance, particularly regarding transverse cracking. This failure mode initiates microcracks that propagate through the ply thickness, leading to stiffness degradation and structural compromise. While existing numerical approaches like Continuum Damage Mechanics (CDM), Cohesive Zone Models (CZM), and Extended Finite Element Methods (XFEM) have advanced the field, they often rely on predefined crack paths or struggle with the convergence and complexity of multiple intersecting 3D cracks. Furthermore, existing Discrete Element Method (DEM) studies are predominantly limited to 2D cross-sectional analyses, failing to capture through-thickness crack continuity, 3D damage connectivity, and the spatial stress redistribution inherent in heterogeneous microstructures. There remains a gap in explicit 3D DEM models capable of simulating transverse cracking in unidirectional CFRPs without relying on equivalent anisotropic properties or homogenized structures.

Methodology
The authors propose a novel three-dimensional discrete element method (3D DEM) framework to investigate transverse fracture in carbon-fiber-reinforced epoxy composites. The methodology is built upon the following pillars:

Discrete Modeling: A 49 µm cubic Representative Volume Element (RVE) is constructed using a 3D cubic packing scheme. The microstructure consists of 38 circular fibers (radius 3.5 µm) embedded in an epoxy matrix, with interactions modeled via central-force springs along six orthogonal directions.
Discrete-Natured Calibration: Unlike traditional bonded-particle models that treat bonds as continuum elements requiring simultaneous calibration of normal ( $k_n$ $k_{n}$ ) and tangential ( $k_s$ $k_{s}$ ) stiffnesses, this study introduces an innovative energy equivalence relationship. The model treats each unit cell as a continuous element where macroscopic Poisson's ratio is automatically generated by cell deformation rather than prescribed.
- The framework derives explicit analytical relations (Eqs. 41 and 42) linking microscopic normal stiffness ( $k_n$ ) to macroscopic Young's modulus ( $E$ ) and Poisson's ratio ( $\nu$ ).
- This approach eliminates the need for tangential stiffness ( $k_s$ ) in the calibration process, relying solely on normal stiffness to satisfy the energy equivalence between microscopic contact forces and macroscopic continuum strain.
Validation: The calibrated model is validated against experimental data and 2D DEM results. Simulations are conducted under quasi-static displacement-controlled tensile loading to observe damage evolution, crack propagation, and macroscopic stress-strain responses.

Key Results
The study conducts parametric investigations into the effects of random fiber distribution, fiber volume fraction ( $V_f$ ), and fiber radius ( $r$ ):

Model Validation: The 3D DEM successfully reproduces the macroscopic mechanical behavior of neat epoxy and CFRP RVEs, with simulated Young's modulus and Poisson's ratio deviating by less than 2% from target values. The model captures through-thickness crack continuity and crack-front tortuosity, showing that crack propagation is non-simultaneous along the fiber length, unlike the planar trajectories in 2D models.
Fiber Distribution: While random fiber distributions significantly alter local crack initiation sites and final crack paths (e.g., fluctuating between closely packed fibers), they have a negligible influence on global mechanical responses. Statistically equivalent RVEs exhibit nearly identical stress-strain behavior and Young's modulus evolution.
Fiber Volume Fraction ( $V_f$ ): Increasing $V_f$ (from 50% to 68%) enhances transverse stiffness and peak strength but reduces failure strain, leading to a more brittle post-peak response. Higher $V_f$ induces resin deficiency, promoting localized stress concentration and earlier matrix-dominated damage.
Fiber Radius: At a fixed volume fraction ( $V_f = 60\%$ ), fiber radius governs the balance between interfacial stress transfer and matrix strain accommodation. The configuration with a fiber radius of $r = 3.5$ µm demonstrated the most efficient load-bearing capacity and highest stiffness compared to $r = 3.2$ µm and $r = 3.8$ µm.

Significance and Claims
The paper claims that the proposed 3D DEM framework offers an effective tool for multiscale progressive damage analysis in unidirectional CFRP composites. Its primary significance lies in:

Discrete-Natured Calibration: Providing a rigorous, energy-based mapping from micro-parameters to macro-properties that respects the discontinuous nature of DEM while generating Poisson's ratio naturally.
Spatial Fracture Analysis: Successfully capturing complex 3D failure mechanisms, including through-thickness crack penetration, crack-front tortuosity, and damage coalescence, which are unattainable with 2D simplifications.
Mechanistic Insight: Elucidating that while fiber distribution dictates local fracture patterns, fiber volume fraction is the dominant factor controlling global mechanical performance.

The authors conclude that while the current model effectively addresses transverse fracture in unidirectional laminates, future work is required to incorporate multidirectional fiber layups, refined fiber-matrix interface constitutive relations, and multiscale damage coupling strategies.

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