一种基于物理机制的粘弹塑性损伤本构理论及其工程应用

The disastrous failure of engineering structures is often caused by a suddenly applied load, such as the collision, earthquake, and blast loading. Whether the numerical results of mechanical responses of engineering structures under dynamic loading are reliable lies on that whether the constitutive relations describe the dynamic responses of materials accurately. In the project, based on the interatomic energy potentials——pair functional potentials, Cauchy-Born rule, and slip mechanism, a mechanism based visco-elasto-plastic damage constitutive theory will be established under finite deformation. The responses of materials at large strains, different strain rates and complex loading conditions will be described in the viscoelastic, viscoplastic, viscodamage deformation and failure stage. Mechanical responses of materials will be described through the anisotropic properties after damage and plastic deformations, the phenomenon that the mechanical response is dependent on the loading path, strain rate effect and the distortion of subsequent yield surfaces. Based on the theoretical research, the uniaxial tension tests, SHPB( the split Hopkinson pressure bar) tests and drop weight tests on reinforced concrete beams will be conducted in different loading rates. Model parameters will be determined by the test results of uniaxial tension and compression. Using the constitutive relations established in the project, numerical simulation will be performed to simulate the responses of reinforced beams in the tests. Comparison between numerical and experimental results will illustrate the validity and accuracy of the present model in the application of calculating dynamical mechanical responses of materials and structures.

工程结构的灾难性破坏通常是由碰撞、地震和爆炸等强动载的突然加载而引起的，采用数值方法计算结构在动态载荷下的响应结果是否可靠的根本在于所用的本构关系是否能准确描述材料的动态力学行为。本项目以物理学中的原子间势函数——对泛函势、Cauchy-Born准则和滑移机制为理论基础，建立一种基于物理机制的粘弹塑性损伤本构模型，描述材料在有限变形、不同应变率、复杂加载等条件下的粘弹性、粘塑性、粘性损伤直到破坏阶段的力学行为，研究材料在损伤和塑性变形后的各向异性特征、力学响应对加载路径的依赖性、应变率效应、屈服面演化特征。在理论研究的基础上，开展混凝土材料不同应变率下的单轴拉伸试验、SHPB（分离式Hopkinson压杆）压缩试验和钢筋混凝土梁模型的落锤冲击动态响应试验，标定本项目建立的本构模型的参数，验证本构模型用于材料和结构动态响应计算的适用性。

本项目以构建材料的粘弹塑性损伤本构理论为基础，描述材料在有限变形、不同应变率、复杂加载等条件下的粘弹性、粘塑性、粘性损伤直到破坏阶段的力学行为，研究材料在损伤和塑性变形后的各向异性特征、力学响应对加载路径的依赖性、应变率效应、屈服面演化特征，预测结构的弹塑性损伤力学响应。本项目完成的工作如下：.(1) 基于对泛函势和Cauchy-Born准则，考虑滑移率与宏观应变率的关系，推导了不同应变率条件下的本构模型，建立了粘弹塑性损伤本构关系；.(2) 研究了粘弹塑性损伤的迭代算法，将本项目建立的粘弹塑性损伤本构关系利用Fortran程序实现，编制调试基本构元响应函数的标定程序，由实验数据初步标定响应函数，嵌入ABAQUS的用户单元子程序，实现结构响应的计算；.(3)根据多晶材料有限变形条件下的弹塑性损伤本构理论，研究了比例加载条件下的屈服面演化之间的等效关系。根据实验中比例加载条件下的屈服面演化结果，初步验证了等效关系的合理性。同时，屈服面之间的等效关系给出了模拟结果和实验结果的比较，理论分析为模拟结果与实验结果的误差来源分析提供了依据。基于滑移构元的硬化规律和包氏效应对后继屈服面的移动、前凸后扁以及畸变演化规律进行了解释。.(4) 开展了预应力混凝土梁的极限承载能力试验和疲劳试验，为本项目弹塑性损伤本构模型的工程应用验证提供了对象和详细的试验数据。预应力混凝土梁在受载破坏的过程中，混凝土和钢筋两种材料的弹性、塑性乃至断裂的整个过程；疲劳加载则包含着材料的损伤累计。本项目开发的本构方程可描述材料的弹塑性损伤响应，将其作为用户材料子程序嵌入到有限元程序中，可实现预应力混凝土梁极限承载能力和累计破坏的计算。

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