基于微裂缝扩展与摩擦的混凝土随机损伤探索

At present, the physical mechanisms of plastic free energy of concrete are unclear. Consequently, concrete damage mechanics, which is built upon rigorous thermodynamic foundations, is caught in an awkward predicament. The purpose of this project is to bring the micro-mechanisms of plastic free energy storage and release into the investigation in stochastic damage of concrete. Research on constitutive relations is carried out along 2 paths, abstract micro-mechanism and concrete micro-mechanism, and then they are employed in stochastic analysis of structures. A combination of microscopic elements is created in a spring bundle model to stand for locked plastic free energy, and the course of free energy release and law of stochastic fracture of a spring bundle are obtained by tests; the microscopic additional elastic strain energy resulting from microcrack friction is introduced into a multiscale damage theory, and extended/generalized finite element analysis is performed to track the coupled growth-friction-growth development of groups of microcracks; stochastic nonlinear analysis of structures based on stochastic damage constitutive relations for concrete is carried out to give the probability distribution evolution processes of structural responses. The project achieves a really integrated stochastic elastoplastic damage description of concrete behavior, lays a more reliable physical foundation for nonlinear analysis of concrete structures, and provides powerful tools for reliability-based design of concrete structures.

目前混凝土塑性自由能的物理机制模糊不清，致使建立在严格的热力学基础之上的混凝土损伤力学陷于尴尬困境。本项目旨在通过描述微裂缝的摩擦行为，将塑性自由能贮存和释放的细观机制纳入到混凝土随机损伤研究中。沿着"抽象细观"和"具象细观"2条思路开展本构关系研究，并将其用于随机结构分析。在微弹簧束模型中创造细观元件组合以代表被锁定的塑性自由能，通过试验获得自由能的释放历程和微弹簧束的随机断裂规律；在多尺度损伤理论中引入由微裂缝摩擦导致的细观附加弹性应变能，通过扩展/广义有限元分析跟踪微裂缝群扩展-摩擦-再扩展的耦合发展过程；开展基于混凝土随机损伤本构关系的随机结构非线性分析，给出结构反应量的概率分布演化进程。实现真正融为一体的混凝土随机弹塑性损伤理论描述，使混凝土结构非线性分析具有更加可靠的物理基础，为混凝土结构可靠性设计提供有力工具。

针对混凝土损伤力学由于塑性自由能的物理机制模糊不清而裹足不前的困境，本项目开展了以下几方面的研究：抽象细观方面，寻求弹塑性自由能的简化直观表示，探索细观弹簧的随机断裂规律，得到宏观损伤变量的随机演化函数。具象细观方面，寻求弹塑性自由能的细观直接描写，从细观弹性应变能推导宏观弹塑性自由能，寻找具有细观力学基础的宏观损伤演化规律。将细观模型植入宏观损伤理论框架，构建完整的3维弹塑性随机损伤本构关系，发展隐式、半隐式回映积分算法。为非线性随机结构分析中采用的代表性样本点的选择，构造点群识别算法。尝试将随机本构用于随机结构。开展钢管混凝土构件试验作为对照。.本项目从细观角度揭示了塑性自由能的物理本质，避免了目前尚难以实际开展的非连续介质有限元分析，为弹塑性自由能给出了便于使用的半解析表达式。抽象细观自由能函数具有明确的物理意义而令人信服，为本构关系奠定了更为坚实的科学基础，为发展多尺度随机损伤力学提供了一条新的途径。本项目通过对微裂缝扩展与摩擦的抽象细观描述，合理反映拉、剪、压不同损伤机制，建立起公开发表的文献中首个全面反映混凝土单边效应和约束效应的本构模型，为混凝土结构（随机）非线性分析提供了有力的基础理论和实用工具。本项目的点群识别算法可减少所需代表点的数目，因而有助于控制今后大规模开展随机结构分析的计算量。