CUDA架構下相場法裂紋模擬：平行化架構參數調整與效能分析

Abstract

大自然在數萬年演化下，許多生物材料已經發展出其特殊優異的抵抗裂紋增生結構，像是骨頭、牙齒、珍珠質、海綿骨針、蟹類外骨骼等，其中某些生物材料像是珍珠質成分有著極高的脆性材料佔比，但卻能表現出超過該脆性材料數十倍的韌性，如此優異的增韌機制是目前人造材料無法達到的，許多學者與工程師希望能了解這些生物材料特殊結構抵抗裂紋的機制；相場法近幾年被大量用於許多裂紋研究中，並被證實在模擬裂紋方面具有相當可靠的準確性，同時相場法因具備獨有不須特別追蹤複雜裂紋邊界的性質，相當適合模擬生物材料中的裂紋生長行為，然而由於相場法在模擬尺度上使用材料破裂過程區作為尺度大小約為µm，而生物材為了描述其特殊結構，所設定的模型尺寸計算所需花費的時間會相當可觀。 近幾年隨著電腦高速運算的崛起，發展出許多有效率的計算架構，而本研究團隊透過Nvidia公司推出的CUDA架構來幫助我們提升計算效率，該方法雖然能有效提升計算效率，但在程式模型架構上須同時遵守硬體與軟體眾多規則才能完全發揮硬體資源效能，為了使相場法裂紋模型，能有效率的幫助我們進行模擬分析，我們透過對於平行計算架構的環境參數調整與測試，藉此來達到提升計算效率的方式，另一部分將模型加入共享記憶體使用，透過該記憶體能在計算時提供更低的資料傳輸延遲縮短模擬時間，達成對於團隊日後裂紋模擬效率上的提升。

Throughout thousands of years of natural evolution, various biological materials such as bones, teeth, nacre, sponge spicule, and crustacean exoskeletons have developed unique crack-resistant structures. Some biological materials, like nacre, possess high proportions of brittle components yet demonstrate toughness several times greater than the brittle material. This outstanding toughening mechanism remains beyond the capabilities of current synthetic materials. Scholars and engineers aspire to understand the specific structural mechanisms in these biological materials that resist crack propagation. In recent years, the phase-field method has been extensively employed in crack studies, proving its considerable accuracy in simulating crack behavior. The phase-field method is particularly suitable for simulating crack growth in biological materials due to its unique ability to avoid tracking complex crack boundaries. However, its use of material fracture processes at a scale of approximately µm poses a substantial computational time challenge when modeling the unique structures of biological materials. With the rise of high-speed computing, our research team utilized Nvidia’s CUDA architecture to enhance computational efficiency. While effective, achieving optimal hardware resource utilization requires adherence to numerous hardware and software rules in the programming model. To efficiently utilize the phase-field method for crack modeling and simulation analysis, we adjusted and tested environmental parameters for parallel computing architecture, aiming to enhance computational efficiency. Additionally, we incorporated shared memory usage into the model to reduce data transfer latency during computation, thereby shortening simulation time and contributing to the team’s future efficiency in crack simulations.