摘要
结合损伤力学和分形几何理论，给出分数维空间中分形损伤变量定义ω（ｄ，ζ）及其解析表达式．指出欧氏空间损伤变量ω０实际是分数维空间分形损伤变量ω（ｄ，ζ）当维数取Ｅｕｃｌｉｄｅａｎ维数时的一种特例，将欧氏空间损伤变量定义推广到分数维空间，建立起一种兼顾反映损伤细观结构效应和宏观损伤力学分析需要的损伤定义与描述方法．在此基础上，推导了材料损伤演化律和损伤本构关系的分形表达形式．作为例证，文中分析了单调压缩载荷下混凝土损伤及演化行为．实验对比分析表明：分形损伤模型较好地反映了混凝土实际损伤力学行为．
Of most importance in continuum damage mechanics is how to properly define a damage variable that is available for describing damage degree and its evolution. It plays a key role in correlating macro mechanical responses to their internal micro/meso damage effects in materials. As one of widely accepted effective approaches to define a damage variable, macro phenomenological definition performs a great advantage of being easily utilized in analyzing macro damage mechanical responses of materials and structures. Nevertheless, the definition cannot reflect intrinsic mechanism of damage properties. The majority of phenomenological definitions are deficient in physical meaning, and most of proposed mechanical models for damage evolution and constitutive equation are empirical ones that have very limited applicability. For applying damage mechanics to accurately explaining and elucidating damage and rupture phenomena in materials and structures, it is essential to determine a damage variable that can not only quantitatively state damage intrinsic mechanism but also be easily adopted in macro damage analyses. In the present paper,a fractal damage variable ω(d,ζ) is proposed, which can not only reflect internal damage mechanism but also be fitted to macro damage mechanics analyses. Furthermore, the fractal expressions of damage evolution laws and damage constitutive equation are deduced in terms of definition of fractal damage variable. As an example, damage mechanical behaviors of concrete under uniaxial compressive stress have been discussed by means of the proposed method. It is shown that fractal damage variable ω(d,ζ) to be defined at fractional dimensional space actually is a generalized case of the apparent damage variable ω 0 which is defined at Euclidean space. The fractal damage variable ω(d,ζ) will be the same as ω 0 when the fractal dimension d is equal to Euclidean integer dimension. The concept of damage variable in continuum damage mechanics has been extended from Euclidean space to fractional dimensional space. The discussion also indicates that fractal damage variable ω(d,ζ) depends on fractal dimension d and measure scale ζ . The dependency on measure scale is a hallmark of fractal damage variable to be differed from the apparent damage variable ω 0 . The analyses of fractal damage of concrete implies that fractal damage is higher than apparent damage if the fractal effects of damage is considered. Fractal damage increases when the measure scale decreases. Additionally, the investigation shows that fractal models of damage evolution law and damage constitutive relationship for concrete are better in agreement with the actual damage evolution and stress strain responses. The models quantitatively manifest the dependence of macro mechanical behaviors on their internal micro/meso damage effects.
出处
《力学学报》
EI
CSCD
北大核心
1999年第3期300-310,共11页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家杰出青年科学基金
国家教委跨世纪优秀人才基金
国家自然科学基金
煤炭科学基金
关键词
损伤
分形
分数维空间
分形损伤变量
演化律
damage, fractal, fractional dimensional space, fractal damage variable, fractal damage evolution law, fractal damage constitutive equation
