有限元素模擬結合免映射積分法探討蜂巢狀複合材料之降伏面演化

Abstract

本研究針對蜂巢狀複合材料在多軸載重條件下之降伏面演化行為進行有限元素模擬與量化分析，系統探討不同幾何設計參數對降伏面形貌之影響。模擬架構採用一套具材料異向性、拉壓不對稱及非線性異向性硬化行為之彈塑性組成模型，並搭配前人為處理混合控制問題所建立之免映射數值積分方法，以使用者材料副程式（UMAT）形式實作於商用有限元素分析軟體 ABAQUS 中。為確認該模組之數值正確性與穩定性，本研究設計五種複雜載重歷程進行單元素模擬，並與理論解析解比較，同時進行網格收斂分析與時間增量敏感性測試，並參考前人對邊界效應與尺寸影響之討論，補充本研究模型所需之前處理驗證工作。降伏面分析方面，採用等效塑性應變增量作為降伏點判定準則，結合探測與預加載路徑設計，針對兩類幾何變化條件──剛性基材體積佔比與單元格構型──進行降伏面演化分析，並引入面積比、長寬比與包辛格效應等三項量化指標，對不同條件下之降伏面幾何變化與方向性行為進行比較。模擬結果證實所建構之 UMAT 模組具備高度準確性與穩定性，等效塑性應變增量準則亦能有效捕捉接續降伏點與硬化行為；整體而言，本研究建立一套可應用於蜂巢狀複合材料降伏面分析之模擬流程，對未來仿生結構與功能性複合材料之塑性行為預測具有實用潛力。

This study conducts finite element simulations and quantitative analysis to investigate the yield surface evolution of cellular composites under multiaxial loading, focusing on the influence of geometric design parameters on the shape and behavior of yield surfaces. The simulation framework adopts an elastoplastic constitutive model incorporating material anisotropy, tension–compression asymmetry, and nonlinear anisotropic hardening, combined with a previously developed return-free numerical integration method for mixed control problems. The model is implemented into the commercial finite element software ABAQUS via a user-defined material subroutine (UMAT). To verify the numerical stability and accuracy of the implementation, five representative complex loading paths are simulated using a single-element model and compared against analytical solutions. Mesh convergence analysis, time increment sensitivity tests, and preprocessing validations—such as boundary and size effects—are also conducted to ensure model reliability. Yield surfaces are evaluated using the equivalent plastic strain increment (EPSI) criterion, combined with a series of probing and pre-loading paths. Two geometric design variations—the volume fraction of the stiff matrix and the unit cell configuration (hexagonal vs. auxetic)—are analyzed in relation to the evolution of yield surfaces. Additionally, three quantitative indicators—area ratio, aspect ratio, and the Bauschinger effect—are introduced to compare directional behavior and geometric changes of the yield surfaces under different conditions. Simulation results confirm the high accuracy and stability of the implemented UMAT model and demonstrate the effectiveness of the EPSI criterion in capturing successive yield points and hardening evolution. Overall, this study establishes a simulation framework for yield surface analysis of cellular composites, offering practical potential for future applications in bio-inspired structures and functional composite materials.