针对一些含有相同的微裂缝随机分布概率密度但无序度不同的材料,建立了模拟材料断裂力学行为的二维不连续位移法边界元数值计算模型,实现了材料微裂缝的生长、扩展到最终破坏的全过程数值模拟.从分形几何的新视角深入地揭示了脆性或准脆性无序材料产生尺寸效应的微观机理.材料断裂力学行为的数值模拟结果与Bazant尺寸效应定律相符,不仅与微缺陷的密度有关,更与微缺陷大小随机分布的无序度相关,无序度越大的材料其尺寸效应越明显.得到了用初始分形维数D0表示的关于材料断裂强度的分形维数Dσ经验公式,可以更深入地解释材料的微观尺寸效应机理和断裂过程.
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