基于椭圆形微裂纹变形及扩展的岩石混凝土三维细观损伤模型
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摘要
基于微缺陷的变形及演化的细观损伤模型能够较真实地描述材料的损伤行为,受到了人们的普遍关注。作为一类重要的工程材料,岩石和混凝土内部弥散有大量的微裂纹,故研究其变形行为时,应充分考虑微裂纹的变形与扩展。微裂纹受拉张开、受压闭合,应通过对两种不同模式下微裂纹的变形和扩展的分析,建立任意载荷下的损伤模型。一般地,材料内部的微裂纹可采用椭圆形微裂纹进行描述以较真实地反映微裂纹系统的细观特性。本文考虑材料内部椭圆形微裂纹的变形、扩展、摩擦滑移及偏折扩展对材料变形的影响,基于Taylor方法建立了岩石混凝土的三维细观损伤模型。
将含椭圆形微裂纹的代表性单元(RVE)视为无限大体深埋椭圆形裂纹。本文首先基于无限大弹性基体深埋椭圆形裂纹的变形场,推导了深埋椭圆形裂纹的能量释放率,采用能量平衡方法建立椭圆形裂纹的复合断裂准则;进而考虑椭圆形裂纹的偏折扩展,提出了椭圆形裂纹的初始偏折位置和偏折方向的确定方法。并将椭圆形裂纹退化到深穿透线裂纹和钱币形裂纹的结果与已有的相关结果进行了比较。
论文考虑三轴拉应力下椭圆形微裂纹的变形、扩展,推导了具有任意空间取向的单个张开椭圆形微裂纹引起的附加柔度张量,采用Taylor方法并引入概率密度函数,建立了三轴拉应力下的细观损伤模型,并采用该模型分析了含随机分布椭圆形微裂纹的弹性基体的有效弹性模量。
论文考虑三轴压应力下椭圆形微裂纹的摩擦滑移和偏折扩展,推导了具有任意空间取向的单个闭合椭圆形微裂纹引起的附加柔度张量,提出了一种计算闭合椭圆形微裂纹的偏折变形的简化方法,采用Taylor方法建立了三轴压应力下的细观损伤模型,并利用该模型分析了含微裂纹材料的各向异性特性。
在前面建立的三轴拉应力与三轴压应力下的细观损伤模型的基础上,建立了任意载荷下的细观损伤模型,并将模型与商用有限元软件ABAQUS相结合,编写了用户自定义材料子程序UMAT,利用ABAQUS与该子程序模拟了砂岩的三轴压缩实验与混凝土的单轴拉伸实验。
考虑椭圆形微裂纹间的弱相互作用,基于所发展细观损伤模型的分析方法,采用自洽理论推导了含随机分布椭圆形微裂纹的弹性基体的有效弹性模量,并与基于能量等效原理的分析方法和自洽理论的结果进行了比较。
The micromechanical damage models based on the deformation and growth of microdefects can realistically describe the development of damage, and received extensive attention in past decades. Rocks and concretes contain numerous microcracks, and the deformation and growth of microcracks play important roles in their constitutive behavior and should be included in the description of the deformation such kinds of materials. Microcracks open under tensile stress, and close under compressive stress, the research of the deformation and growth of microcracks as well as their effect should, therefore, take into account the influence of different states of stress. The microcracks in materials can generally be assumed to be elliptic, which can describe more exactly the properties of a microcracks system. In this dissertation, the influence of the deformation, growth, frictional sliding, and kinked growth of microcracks embedded in an infinite isotropic elastic matrix subjected to different stress states on the compliance on the materials are investigated, and then a unified three dimensional micromechanical damage model for the solids with randomly distributed microcracks is formulated with the Taylor’s scheme.
Based on the analysis of the deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, the energy release rate of the elliptic crack and a mixed fracture criterion are obtained by making use of an energy balance approach. Considering the kinked growth of the crack, an analytical approach for the determination of the initial kink location and kink direction of the elliptic crack are suggested. The results corresponding to penny shaped crack and penetrated line crack can be obtained from the proposed model as the special cases of its two limits. The comparison with the results from finite element analysis also verifies the proposed approach.
The deformation and growth of an elliptic microcrack under far-field tensile-shear stress are considered, and the corresponding additional compliance tensor is derived. The description for the response of the material with randomly oriented elliptic microcracks under triaxial tensile stress is obtained by making use of the Taylor’s scheme and an appropriate probability density function, and the effective moduli are deduced.
The frictional sliding and kinked growth of an elliptic microcrack embedded in a representative volume element under triaxial compressive stress are investigated. The additional compliance tensor induced by a single closed elliptic microcrack is derived. A simplified method to calculate the kinked deformation of the closed elliptic microcrack is suggested. The description for the response of a microcracks solid under triaxial compressive stress is obtained with the Taylor’s scheme, and the anisotropic property of the microcracks material is analyzed.
A unified micromechanical damage model is constructed with the combination of the obtained triaxially tensile stress model and triaxially compressive stress model. Associated with commercially available finite element code ABAQUS, a user subroutine UMAT for the materials with randomly orientedly elliptic microcracks is developed and embedded in ABAQUS. The triaxial compression of sandstone and the uniaxial tension of a concrete is simulated and compared with the experimental results.
The effect of the interaction between the elliptic microcracks on the elastic properties of the microcracked materials is considered. The effective elastic moduli of the material with random orientation of elliptic microcracks are obtained, and the comparison with those obtained with energy equivalent principle based on self-consistent scheme shows completely identical.
将含椭圆形微裂纹的代表性单元(RVE)视为无限大体深埋椭圆形裂纹。本文首先基于无限大弹性基体深埋椭圆形裂纹的变形场,推导了深埋椭圆形裂纹的能量释放率,采用能量平衡方法建立椭圆形裂纹的复合断裂准则;进而考虑椭圆形裂纹的偏折扩展,提出了椭圆形裂纹的初始偏折位置和偏折方向的确定方法。并将椭圆形裂纹退化到深穿透线裂纹和钱币形裂纹的结果与已有的相关结果进行了比较。
论文考虑三轴拉应力下椭圆形微裂纹的变形、扩展,推导了具有任意空间取向的单个张开椭圆形微裂纹引起的附加柔度张量,采用Taylor方法并引入概率密度函数,建立了三轴拉应力下的细观损伤模型,并采用该模型分析了含随机分布椭圆形微裂纹的弹性基体的有效弹性模量。
论文考虑三轴压应力下椭圆形微裂纹的摩擦滑移和偏折扩展,推导了具有任意空间取向的单个闭合椭圆形微裂纹引起的附加柔度张量,提出了一种计算闭合椭圆形微裂纹的偏折变形的简化方法,采用Taylor方法建立了三轴压应力下的细观损伤模型,并利用该模型分析了含微裂纹材料的各向异性特性。
在前面建立的三轴拉应力与三轴压应力下的细观损伤模型的基础上,建立了任意载荷下的细观损伤模型,并将模型与商用有限元软件ABAQUS相结合,编写了用户自定义材料子程序UMAT,利用ABAQUS与该子程序模拟了砂岩的三轴压缩实验与混凝土的单轴拉伸实验。
考虑椭圆形微裂纹间的弱相互作用,基于所发展细观损伤模型的分析方法,采用自洽理论推导了含随机分布椭圆形微裂纹的弹性基体的有效弹性模量,并与基于能量等效原理的分析方法和自洽理论的结果进行了比较。
The micromechanical damage models based on the deformation and growth of microdefects can realistically describe the development of damage, and received extensive attention in past decades. Rocks and concretes contain numerous microcracks, and the deformation and growth of microcracks play important roles in their constitutive behavior and should be included in the description of the deformation such kinds of materials. Microcracks open under tensile stress, and close under compressive stress, the research of the deformation and growth of microcracks as well as their effect should, therefore, take into account the influence of different states of stress. The microcracks in materials can generally be assumed to be elliptic, which can describe more exactly the properties of a microcracks system. In this dissertation, the influence of the deformation, growth, frictional sliding, and kinked growth of microcracks embedded in an infinite isotropic elastic matrix subjected to different stress states on the compliance on the materials are investigated, and then a unified three dimensional micromechanical damage model for the solids with randomly distributed microcracks is formulated with the Taylor’s scheme.
Based on the analysis of the deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, the energy release rate of the elliptic crack and a mixed fracture criterion are obtained by making use of an energy balance approach. Considering the kinked growth of the crack, an analytical approach for the determination of the initial kink location and kink direction of the elliptic crack are suggested. The results corresponding to penny shaped crack and penetrated line crack can be obtained from the proposed model as the special cases of its two limits. The comparison with the results from finite element analysis also verifies the proposed approach.
The deformation and growth of an elliptic microcrack under far-field tensile-shear stress are considered, and the corresponding additional compliance tensor is derived. The description for the response of the material with randomly oriented elliptic microcracks under triaxial tensile stress is obtained by making use of the Taylor’s scheme and an appropriate probability density function, and the effective moduli are deduced.
The frictional sliding and kinked growth of an elliptic microcrack embedded in a representative volume element under triaxial compressive stress are investigated. The additional compliance tensor induced by a single closed elliptic microcrack is derived. A simplified method to calculate the kinked deformation of the closed elliptic microcrack is suggested. The description for the response of a microcracks solid under triaxial compressive stress is obtained with the Taylor’s scheme, and the anisotropic property of the microcracks material is analyzed.
A unified micromechanical damage model is constructed with the combination of the obtained triaxially tensile stress model and triaxially compressive stress model. Associated with commercially available finite element code ABAQUS, a user subroutine UMAT for the materials with randomly orientedly elliptic microcracks is developed and embedded in ABAQUS. The triaxial compression of sandstone and the uniaxial tension of a concrete is simulated and compared with the experimental results.
The effect of the interaction between the elliptic microcracks on the elastic properties of the microcracked materials is considered. The effective elastic moduli of the material with random orientation of elliptic microcracks are obtained, and the comparison with those obtained with energy equivalent principle based on self-consistent scheme shows completely identical.
引文
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