砌体匀质化过程的数值模拟方法与应用研究
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摘要
砌体匀质化理论融合离散模型和整体连续模型的优点，对研究砌体结构力学模型至关重要。本文对砌体RVE匀质化过程的数值模拟方法进行分析与研究，得到RVE等效材料特性并将等效参数应用于分析砌体墙片的受力性能。本文主要研究成果如下：
阐述了匀质化方法的基本假设、适用条件以及在有限元的实现方法。对匀质化方法的主要研究对象等效体积单元的概念进行描述，从而说明分析研究RVE得到的等效参数可以推广表达整体的力学性能，为RVE力学模型的研究提供理论依据。
考虑RVE各边的应变状态，建立了周期性边界条件，用约束方程推导论述了其在有限元分析中的实现过程。利用python脚本语言编制可用于ABAQUS有限元软件的二次开发程序，在有限元建模时，可实现自动添加周期性边界条件，为砌体RVE在有限元建模的前处理提供有价值的参考。
采用ABAQUS软件并运行周期性边界条件python脚本，建立了砌体RVE的三维有限元实体模型，对RVE单轴、双轴、三轴以及剪压等复杂应力条件下的情况进行模拟分析，得到RVE各向受力特性。得到的RVE强度包络图可以说明砌体的破坏可以分为受压破坏、受拉破坏和剪切破坏。根据正交各向异性弹性矩阵计算得到砌体RVE等效弹性模量、剪切模量以及泊松比。对影响RVE弹性力学性质的因素进行分析，结果表明：加载方向、组元选取方式等均对其有一定影响。
引入损伤因子，根据弹性余能等效原理对损伤因子取值进行推算，为建立匀质化的宏观损伤模型提供参数。
基于ABAQUS软件对砌体墙片建立整体连续模型，采用RVE的等效参数，对试验砌体墙片进行拟静力分析，得到滞回曲线，墙体表现出一定的耗能能力。通过模拟分析可以发现，模拟墙体塑性拉伸应变的分布与试验墙体裂缝的位置较吻合，墙片的延性系数较试验结果偏大。对比分析表明：用匀质化方法建立的整体连续模型不但提供了自由划分网格的优点，同时在一定程度上能够模拟分析砌体墙的整体受力性能，可以采用此法取代部分试验。
The homogenization theory has advantage of discreet element andmacro-continuum model, which is important to study on mechanical model. Accordingto homogenization theory, Numerical simulation method of homogenization processof masonry is analysed. Equivalent material properties of RVE is obtained and theresearch of influence factors of which is done. Based on the equivalent parameters ofthe RVE, macro-continuum model of masonry wall is modeled and analysed.
Basic assumptions and applicable conditions of homogenization approach areoverviewed and implementation methods of homogenization technique in Finiteelement are elaborated. With describing the concept of the representative volumeelement which is the object of study on homogenization approach and proving thatRVE can represent the overall mechanical properties of masonry, the contentmentioned above makes the concept of the RVE more clear, at the same tine，providetheoretical basis for this paper.
Considering strain state on each side of the RVE, periodic boundary conditions isestablished, which constraint equation in finite element analysis is discussed and setup. Python subroutine is developed and with which the periodic boundary conditionscan be generated automatically when creating finite element model. The work of thispaper may offer some reference and gist for research on finite element model of RVEin pre-processing.
With ABAQUS Finite element software and the subroutine of periodic boundaryconditions, three-dimensional finite element model is developed, and the numeriallysimulations of RVE is derived in order to analyse RVE’s equivalent stress state ofuniaxial，blaxial，shear-compression. Strength envelope of the RVE obtained in thisprocess can explain the failure of masonry, which can be defined by there differentmodes,namely, compression failure, tensile failure and shear failure. Acording toorthotropic elastic matrix, equivalent elastic modulus, shear modulus, and Poisson'sratio of the RVE is obtained. And different directions of loading, brick species andcomponent selection modes can affect mechanical properties of the RVE.
In order to create the macroscopic damage model of RVE, damage factor whosevalue is calculated with elastic residual energy equivalence principle is introduced.
Based on ABAQUS software, macro-continuum model of masonry is created.acording to equivalent properties of the RVE, quasi static analysis of autoclaved lime_stone sand brick masonry wall is carried out and hysteresis curve is obtained，showing energy dissipation capacity of the masonry wall. And we can see thatdistributions of the plastic tensile strain in the model is roughly identical with theposition of wall cracks in the experiment. Ductility coefficient of the masonry wall inthe model is a little greater than that in the experiment. By comparing the simulationanalysis results and experiment results, it shows that macro-continuum model basedon homogenization approach not only have the advantage of free grid division but alsowell simulate the mechanical property of masonry wall.
阐述了匀质化方法的基本假设、适用条件以及在有限元的实现方法。对匀质化方法的主要研究对象等效体积单元的概念进行描述，从而说明分析研究RVE得到的等效参数可以推广表达整体的力学性能，为RVE力学模型的研究提供理论依据。
考虑RVE各边的应变状态，建立了周期性边界条件，用约束方程推导论述了其在有限元分析中的实现过程。利用python脚本语言编制可用于ABAQUS有限元软件的二次开发程序，在有限元建模时，可实现自动添加周期性边界条件，为砌体RVE在有限元建模的前处理提供有价值的参考。
采用ABAQUS软件并运行周期性边界条件python脚本，建立了砌体RVE的三维有限元实体模型，对RVE单轴、双轴、三轴以及剪压等复杂应力条件下的情况进行模拟分析，得到RVE各向受力特性。得到的RVE强度包络图可以说明砌体的破坏可以分为受压破坏、受拉破坏和剪切破坏。根据正交各向异性弹性矩阵计算得到砌体RVE等效弹性模量、剪切模量以及泊松比。对影响RVE弹性力学性质的因素进行分析，结果表明：加载方向、组元选取方式等均对其有一定影响。
引入损伤因子，根据弹性余能等效原理对损伤因子取值进行推算，为建立匀质化的宏观损伤模型提供参数。
基于ABAQUS软件对砌体墙片建立整体连续模型，采用RVE的等效参数，对试验砌体墙片进行拟静力分析，得到滞回曲线，墙体表现出一定的耗能能力。通过模拟分析可以发现，模拟墙体塑性拉伸应变的分布与试验墙体裂缝的位置较吻合，墙片的延性系数较试验结果偏大。对比分析表明：用匀质化方法建立的整体连续模型不但提供了自由划分网格的优点，同时在一定程度上能够模拟分析砌体墙的整体受力性能，可以采用此法取代部分试验。
The homogenization theory has advantage of discreet element andmacro-continuum model, which is important to study on mechanical model. Accordingto homogenization theory, Numerical simulation method of homogenization processof masonry is analysed. Equivalent material properties of RVE is obtained and theresearch of influence factors of which is done. Based on the equivalent parameters ofthe RVE, macro-continuum model of masonry wall is modeled and analysed.
Basic assumptions and applicable conditions of homogenization approach areoverviewed and implementation methods of homogenization technique in Finiteelement are elaborated. With describing the concept of the representative volumeelement which is the object of study on homogenization approach and proving thatRVE can represent the overall mechanical properties of masonry, the contentmentioned above makes the concept of the RVE more clear, at the same tine，providetheoretical basis for this paper.
Considering strain state on each side of the RVE, periodic boundary conditions isestablished, which constraint equation in finite element analysis is discussed and setup. Python subroutine is developed and with which the periodic boundary conditionscan be generated automatically when creating finite element model. The work of thispaper may offer some reference and gist for research on finite element model of RVEin pre-processing.
With ABAQUS Finite element software and the subroutine of periodic boundaryconditions, three-dimensional finite element model is developed, and the numeriallysimulations of RVE is derived in order to analyse RVE’s equivalent stress state ofuniaxial，blaxial，shear-compression. Strength envelope of the RVE obtained in thisprocess can explain the failure of masonry, which can be defined by there differentmodes,namely, compression failure, tensile failure and shear failure. Acording toorthotropic elastic matrix, equivalent elastic modulus, shear modulus, and Poisson'sratio of the RVE is obtained. And different directions of loading, brick species andcomponent selection modes can affect mechanical properties of the RVE.
In order to create the macroscopic damage model of RVE, damage factor whosevalue is calculated with elastic residual energy equivalence principle is introduced.
Based on ABAQUS software, macro-continuum model of masonry is created.acording to equivalent properties of the RVE, quasi static analysis of autoclaved lime_stone sand brick masonry wall is carried out and hysteresis curve is obtained，showing energy dissipation capacity of the masonry wall. And we can see thatdistributions of the plastic tensile strain in the model is roughly identical with theposition of wall cracks in the experiment. Ductility coefficient of the masonry wall inthe model is a little greater than that in the experiment. By comparing the simulationanalysis results and experiment results, it shows that macro-continuum model basedon homogenization approach not only have the advantage of free grid division but alsowell simulate the mechanical property of masonry wall.
引文
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