本研究旨在探討物質點法(Material Point Method， MPM)應用於鋼筋混凝土梁裂縫生成模擬之可行性。研究建立三維鋼筋混凝土梁MPM數值模型，以最大拉應力準則判定混凝土裂縫生成；當混凝土物質點之最大主應力達到開裂模數時，將其標記為破壞物質點，保留失效狀態並將後續應力歸零，以其累積分布描述裂縫生成與破壞帶演化。鋼筋則採物質點材料指定方式建立。 本文以一組主要模型設定作為基準，分別比較端部邊界束制條件、端部束制位置與等效支承作用範圍，以及不同鋼筋配置之影響，並透過破壞物質點、最大主拉應力、梁縱向正向應力S_xx及平均S_xx－力作用點位移量關係進行判讀。分析結果顯示，主要跨中裂縫由梁底初始缺陷附近開始生成，其後逐步發展為多處破壞帶；端部束制條件與作用位置主要影響裂縫形成後之破壞空間分布及局部應力重新分布。鋼筋配置則主要影響破壞發展時序、分散程度與局部縱向應力傳遞，其中未配置鋼筋之算例較早形成集中破壞，而全梁配置縱向主筋與剪力筋垂直肢之算例於較長位移範圍內仍維持較明顯之局部平均S_xx反應。 綜合而言，本文所建立之MPM模型與後處理流程可用以辨識鋼筋混凝土梁裂縫生成位置、破壞演化及不同模型條件下之局部受力差異，顯示MPM具有應用於鋼筋混凝土梁裂縫生成分析之可行性。惟本文尚未納入完整張力軟化、斷裂能控制、鋼筋－混凝土界面滑移及實驗定量驗證，因此研究結果主要適用於裂縫生成行為之可行性分析與算例比較。;This study investigates the feasibility of applying the Material Point Method (MPM) to crack initiation and propagation analysis of reinforced concrete beams. A three-dimensional MPM model was established， and the maximum tensile stress criterion was adopted to determine concrete cracking. When the maximum principal stress of a concrete material point reached the modulus of rupture， the point was marked as failed， its failure state was retained， and its subsequent stress contribution was set to zero. The cumulative distribution of failed material points was then used to describe crack initiation and damage-band evolution. Reinforcement was represented by assigning steel material properties to material points within prescribed reinforcement regions. A baseline model was used to compare the effects of end boundary restraint conditions， end-restraint location and equivalent support range， and reinforcement configuration. The results were evaluated using failed material point distributions， maximum principal tensile stress， longitudinal normal stress S_xx， and the mean S_xx-loading-point displacement response. The results show that the primary midspan crack initiated near the prescribed bottom defect and subsequently developed into multiple damage bands. Changes in end restraint mainly affected post-cracking damage distribution and local stress redistribution. Reinforcement configuration mainly influenced the timing and distribution of damage development and local longitudinal stress transfer. The unreinforced case developed concentrated damage at an earlier loading stage， whereas the case with longitudinal reinforcement and vertical stirrup legs distributed throughout the beam maintained a more pronounced positive local mean S_xxresponse over a longer displacement range. Overall， the proposed MPM model and post-processing framework can be used to identify crack initiation locations， damage evolution， and differences in local mechanical response under different model conditions， demonstrating the feasibility of MPM for reinforced concrete beam crack analysis. However， tension softening， fracture-energy control， steel-concrete interface slip， and quantitative experimental validation were not fully incorporated. Therefore， the present results are primarily intended for feasibility assessment and comparative analysis of crack behavior.
