複合材料具有高比剛度與高比強度等優點，因此在航空與高性能結構領域中扮演重要角色。然而，複合材料在承受低速衝擊後，常產生不易由外觀辨識之內部損傷，例如層間脫層與基材裂縫，進而對結構完整性與後續承載能力造成潛在影響。因此，建立能準確預測低速衝擊損傷行為之數值模型，對複合材料結構設計與損傷評估具有重要意義。
本研究建立一套漸進式損傷分析模型，結合連續損傷力學與三維 LaRC05 破壞準則，用以描述複合材料層內破壞行為；同時透過內聚區模型（Cohesive Zone Model, CZM）模擬層間界面之損傷起始與脫層擴展。為驗證模型之正確性，本文依序進行單元素測試、球形衝擊頭作用於複合材料平板之低速衝擊分析，以及半圓柱衝擊頭作用於 CFRP 梁之線衝擊分析。
分析結果顯示，單元素測試能正確捕捉不同破壞模式下之損傷起始、剛度退化與完全失效行為；低速衝擊模型所得之衝擊力、位移及反應時間曲線亦呈現合理趨勢。進一步觀察損傷分布可發現，模型能有效描述層內基材裂縫與層間脫層之發展情形，其破壞位置與損傷型態皆符合低速衝擊下複合材料之預期損傷機制。
整體而言，本文所建立之數值模型能合理模擬複合材料層合結構於低速衝擊下之漸進式損傷行為，並可作為後續複合材料結構衝擊損傷預測與設計評估之參考依據。

Composite laminates are widely used in aerospace and high-performance structures because of their high specific stiffness and high specific strength. However, under low-velocity impact, composite structures may develop internal damage such as matrix cracking, fiber failure, and interlaminar delamination. These damage modes are often difficult to detect from the surface but may significantly reduce the residual strength and structural integrity of the component. Therefore, an effective numerical method capable of predicting progressive damage under impact loading is important for structural design and damage assessment.
In this study, a progressive damage analysis framework is developed for composite laminates subjected to low-velocity impact. The intralaminar damage behavior is described using a three-dimensional LaRC05 failure criterion combined with a continuum damage mechanics model, while interlaminar delamination is modeled using cohesive zone elements. The proposed model is implemented in ABAQUS/Explicit through a VUMAT user-defined material subroutine.
The model is first verified through single-element tests under fiber tension, fiber compression, matrix tension, and matrix compression. The results confirm that the implemented subroutine can properly predict damage initiation, stiffness degradation, and complete failure for different failure modes. The model is then applied to a flat composite laminate impacted by a spherical impactor. The predicted impact force, displacement response, matrix cracking, and delamination patterns show good agreement with experimental data from the literature. Finally, a CFRP beam subjected to line impact by a semi-cylindrical impactor is simulated to further examine the interaction between matrix cracking and delamination. The numerical results capture the main trend of the force–displacement response, the sequence of crack development, and the delamination growth from the free edges toward the central region.
The results indicate that the proposed modeling approach can reasonably predict both the global impact response and the local damage evolution of composite laminated structures. In addition, the parametric study on the relative strength between intralaminar matrix failure and interlaminar interface failure shows that the model can reflect the competition between matrix cracking and delamination. This framework provides a useful reference for low-velocity impact damage prediction and future composite structure design.

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