中文摘要：

利用混凝土材料的细观随机损伤物理模型获取混凝土应力—应变关系的概率密度描述.以细观物理模型为基础,利用K-L（Karhunen-Loeve）正交分解和密度演化方法得到了单轴受力状态任意应变处应力的概率密度函数估计.将数值计算结果与试验结果进行概率密度层次的对比.研究证实：可以采用这一方法描述混凝土受力本构关系的概率密度演化过程.

英文摘要：

Efforts are made to grasp the probability information of the stress strain relationship.Firstly,a class of mesoscopic damage mechanics models of concrete is listed to understand the mesoscopic damage evolution characteristics of concrete material.Then the Karhunen-Loeve orthogonal decomposition is adopted to simulate the stochastic field mentioned in the former model.Based on the generalized probability density evolution method（PDEM）,probability density function（PDF） of stress strain relationship in unaxial loading condition and its evolution are provided.In the end,the comparison between the theoretical and experimental results verifies that the probability density evolution process of constitutive relationship for concrete material can be obtained from this method.