【作者】 张阳；

【导师】 崔俊芝；

【作者基本信息】 西北工业大学 ， 应用数学， 2016， 博士

【摘要】 混凝土材料作为一种典型的多尺度颗粒随机分布复合材料,是在土木、水利、建筑工程等领域应用最广的建筑材料。随着重大土-水-建工程的兴建,土-水-建工程的设计和建造走向精细化,以及计算技术和科学计算的发展,越来越多的学者开始关注混凝土材料及其结构的多尺度建模、材料与结构一体化的多尺度分析,以便更精确地预测和分析混凝土材料及其结构的物理和力学性能,为工程设计和优化提供坚实的理论依据和技术支撑。基于均匀化理论而发展起来的多尺度方法,通过引入材料微-细观随机构造的单胞模型,建立起混凝土微-细观构造与结构件,直到宏观结构性能之间的多尺度关联关系。多尺度方法不仅能有效地预测材料的等效参数,还能够精确地捕捉材料内部的局部构造特征,从而能够更精确地预测材料及其结构在建造期和服役期的力学和热力学性能。本文围绕着混凝土材料及其结构力学性能的预测和分析,开展了相应高阶多尺度模型的理论、算法及其数值模拟技术的研究,主要研究工作及取得的研究成果如下:1.将统计二阶双尺度分析方法应用于混凝土材料力学性能的预测,通过引入统一强度理论计算了相应的抗拉和抗压强度参数。将双尺度计算结果与试验数据作比较,验证了方法的有效性,同时分析了不同骨料类型对等效参数的影响。2.针对随机复合材料粘弹性性能的预测,发展了一种统计二阶双尺度分析方法,给出了相应的算法过程,并将其应用到混凝土材料徐变行为的计算。计算了晚龄期混凝土材料在恒定压力载荷作用下的徐变行为,通过与试验结果的对比验证了该方法的有效性。在此基础上进一步讨论了孔隙率和纤维的空间分布对硬化水泥浆和纤维混凝土材料徐变行为的影响。3.针对周期结构复合材料的老化粘弹性问题,发展了相应的二阶双尺度方法,通过误差分析和数值算例验证了二阶双尺度近似解能够更好地逼近原问题的真实解,说明了二阶校正项的必要性。从计算量的比较来看,采用传统的有限元方法求解这类问题时需要非常精细的网格剖分,使得求解规模非常之大,而二阶双尺度方法将原问题转换成一个宏观均质区域的均匀化问题和几个简单的单胞问题,所需要的计算代价要远小于有限元法。把上述的二阶双尺度公式推广到随机情形,将其用于混凝土材料徐变性能的分析,给出了有效松弛模量及局部单胞上应变和应力场的计算公式。通过数值算例讨论了不同骨料类型和加载龄期对宏观徐变性能的影响,分析了混凝土结构在徐变过程中的应力和应变的重分布情况。4.针对具有细-微观双重小周期构造复合材料的弹性力学问题,发展了一种高阶三尺度分析方法,推导了高阶三尺度近似解表达式,给出了计算位移场的算法流程。高阶三尺度方法的基本思想是通过引入微观尺度单胞,在二阶双尺度解的基础上做进一步的校正,进而更加精确地捕捉材料内部的微观局部振荡行为。通过数值算例说明了引入微观的高阶修正项是完全必要的,所给出的算法是有效的。该三尺度方法可以很容易推广到随机问题,用于混凝土材料及其结构力学性能的预测和分析。更多还原

【Abstract】 Concrete is a kind of typical composite material with the random structure and has been widely used in many fields of civil engineering,such as hydraulic engineering,high speed railway and nuclear power station.As scientific computing has become an important tool of engineering design,many researchers begin to study the multiscale models to predict the physical and mechanical properties of concrete precisely.Further,the multiscale models can provide a better theoretical guidance to the structural design and optimization in engineering.The high order multiscale analysis method based on the homogenization theory can build the bridge between macroscopic and mesoscopic scales.This method can predict the effective material parameters,more than that it also can capture the local characteristics in the structure precisely.Due to this advantage,a better analysis of the mechanical properties for the material and structure can be carried out.In this thesis,we study the high order multiscale method to predict the mechanical properties of concrete.In the first part,a statistical second-order two-scale(SSOTS)method is presented to predict the effective Young’s modulus and the strength parameters.The geometric model of the material cell is generated by the computer simulation method.In the calculation of strength parameters,the unified strength theory is introduced.The SSOTS method is proved to be valid and effective by the comparisons between the numerical results and experiment data.The influence of different aggregate types on the effective properties is also discussed.In the second part,a two-scale method for predicting viscoelastic properties of composite materials with random distribution of particles is developed.Then this method is applied to predict the creep properties of concrete structure with permanent load.Numerical results demonstrate that the two-scale method is valid.Finally,the influences of porosity for cement and the distribution of steel fibers on the creep properties for the material are also discussed.In the third part,a second-order two-scale(SOTS)computational method for ageing linear viscoelastic problem in composite materials with periodic structure is developed.In the time domain,the SOTS formulation for calculating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived.Error estimates of the displacement approximate solutions for SOTS method are also given.By expanding the formulation to the random case,this method is applied to analysis the creep properties of concrete.The numerical results show that the SOTS method is feasible and valid for the ageing viscoelastic problem.The influence of different aggregate types and concrete age on the creep properties is analyzed.And the redistributions of stress and strain in the concrete structure are studied.In the fourth part,a high-order three-scales(HOTS)computational method for mechanical performances of composite structures with small periodic configurations of two-levels is presented.Compared with the classic second-order two-scale method,an additional cell with smaller scale is introduced to capture local characteristics inside basic configuration of smaller scale,and then obtain the more precise approximate solution.Numerical examples for the elastic problem for composites with two-layer periodic structures are given.The results show that the HOTS method presented in this paper is valid and effective.In addition,this HOTS method can be easily generalized to the random case to predict and analysis the mechanical properties of concrete.更多还原