【作者】 于海祥；

【导师】 武建华；

【作者基本信息】 重庆大学 ， 结构工程， 2009， 博士

【摘要】 以内变量理论和不可逆热力学理论为基础的损伤力学在发展混凝土类工程材料的本构模型方面提供了新的理论框架。基于应变等效假设和有效应力概念的损伤理论是将损伤力学推广到工程应用的重要途径,但该理论的核心问题是如何确定不受损伤发育影响的理想参考受力状态。现存的各种损伤模型所依赖的理想应力-应变关系都是主观假定的,因此通过实验方法寻找近似“不受初始裂纹开展影响”条件下的材料应力-应变特性是亟待解决的问题。本文致力于以损伤力学和弹塑性理论相结合的方法研究混凝土的本构模型,在通过实验得到的混凝土“无损伤发育”应力-应变曲线的基础上提出了一种拉、压分段曲线损伤模型,并将此理想曲线与混凝土塑性理论相结合提出了一种新型的混凝土弹塑性损伤本构模型,通过高效、稳定的数值方法实现了该本构模型在混凝土结构非线性分析中的应用。论文的主要工作和结论如下:①通过对大量的混凝土塑性理论和损伤理论方面文献的研究和分析,指出了从应变等效假设的角度建立损伤模型必须首先确定材料的无损伤参考工作状态;论证了材料的无损伤参考工作状态对建立损伤本构关系的重要性。②通过对混凝土施加围压,使单轴受压混凝土的裂缝发展受到限制,从而研究混凝土在接近无裂纹发展状态(无损伤产生的理想状态)下的受压性能。实验着重考察了不同围压比对混凝土受压应力-应变关系的影响规律,以及围压对混凝土裂缝发展的限制作用,得出了一些与同类实验不同的结果,系统地分析了围压对混凝土受压性能的影响规律。③根据不同围压比下的三轴实验数据,提出了混凝土无损伤发展状态的受压应力-应变关系曲线,并通过实验首次研究了无损伤发展发展状态下的混凝土循环加卸载的应力-应变关系,通过多种途径证实了本文得到的理想应力-应变曲线可以作为一维无损伤受压状态的参考曲线,并为三维弹塑性损伤模型的建立提供了理论基础。④在对比理想曲线与实际实验曲线的基础上建立了符合热力学框架的一维拉、压损伤模型,并根据应力连续性条件确定了其中的控制参数。对混凝土单轴拉、压实验的数值模拟证明了本文所建立的一维分段曲线损伤模型的合理性和准确性。⑤建立了一种损伤和塑性相解耦的并满足热力学基本方程的弹塑性-损伤本构模型。模型的弹塑性部分建立在有效应力空间,并采用拉、压双重强化屈服函数,其单调强化关系采用本文得到的理想状态受压应力-应变曲线;损伤部分采用一维状态下的损伤演化方程,将有效应力张量及强化参数进行正负分解并引入拉、压两个损伤参数以充分体现两种受力机制的组合影响。⑥推导了基于弹性试算-塑性修正-损伤修正过程的应力更新本构积分算法。证明了对于本文所采用的塑性模型,弹性试算步不仅能判断弹塑性状态而且能给出更新后有效应力张量的主方向及主应力的方位角,因此应力更新过程只需计算两个应力不变量,大大减少了计算工作量,提高了算法效率。根据本文模型理论得到了算法一致性切线刚度矩阵并编制了高效计算机程序,对各种荷载工况下的混凝土材料和构件进行了数值模拟,结果表明,本文本构模型能够较好地进行混凝土结构非线性分析。更多还原

【Abstract】 Damage Mechanics based on internal variable theory and irreversible thermodynamic theory provides a novel theoretic framework in developing the constitutive model of engineering materials such as concrete et al. The damage theory by means of hypothesis of strain equivalence and the concept of effective stress can be conveniently used to extend the damage mechanics to engineering application, during which it is the essential problem to determine the reference undamaged state. The existing concrete damage models are almost established on the subjectively presumed undamaged stress-strain relationship and so it is urgent to find the ideal stress-strain curve through experiments. In this paper the author tries to present a new type of concrete constitutive model combining damage theory and plastic theory, and as the result, a subsection curved damage model that can account for both compressive damage and tensile damage is proposed on the basis of the ideal stress-strain curve obtained in this paper, and an elastoplastic damage constitutive model is finally proposed based on the reference ideal stress-strain curve. The model is implemented by efficient and stable numerical method to simulate the nonlinear behaviors of concrete structures. The main tasks and conclusions of this paper are shown below.On the basis of a broad review of the existing references about plastic theory and damage theory, the author points out that it is the key point to determine the ideal state with no damage influence in order to set up the damage model on the basis of the hypothesis of strain equivalence, and proves the importance of the reference undamaged state for establishing the damage constitutive model.The paper carried out compression experiments of concrete specimen with surrounding pressure of different pressure ratio which can effectively prevent the onset and expansion of cracks. In this way the process of ideal state with no damage growth is simulated and some distinct conclusions have been drawn which is different with the similar experiments by others. And also the confining effect of surrounding pressure on uniaxially compressed concrete is systematically studied.The ideally undamaged tress-strain curve of compressed concrete is proposed based on the compression experiments with surrounding pressure, and the behavior of cyclically loaded concrete with proper confining pressure is studied. It is proved in different ways that the ideal stress- strain curve can be taken as the reference curve subjected to no damage. Theoretical and experimental basis has been provided to establish 3dimensional elastoplastic damage constitutive model.On the basis of comparing the ideal curves and the experimental points, the thermodynamically consistent damage growth equations for tension and compression in form of subsection curves are established , the parameters of which are determined by the condition of stress continuity. Simulations to the uniaxially compressed and tensioned concrete prove the validity and the accuracy of the damage model .A triaxial elastoplastic damage model for the failure of concrete is presented, which is thermodynamically consistent and requires only few conventional material properties. The plasticity part is based on the effective stress using a yield function with two hardening variables, one for tensile loading history and the other for compressive loading history. The hardening rule is gained from the ideal stress-strain curve in compression. The damage part is based on the damage growth equation of one dimensional tension and compression. In order to reflect the two distinctly different damage mechanisms in tension and compression, the stress tensor and damage variable are decomposed into positive part and negative part respectively.Constitutive integration of stress evaluation algorithm based on the standard split into an elastic predictor, a plastic correction and also a damage correction using backward Euler scheme is deduced. It is proved for the model proposed that the process of elastic prediction gives the information of the principal directions and the lode angle of the final stress for which it is evaluated. So the number of the unknowns can be further reduced and only the stress invariants need to be solved, and the algorithm efficiency can be largely improved.High efficiency computer program is compiled according to the algorithm consistent stiffness of the model, and simulations in a wide range of loading cases prove the validity of the model in nonlinear structural analysis更多还原