含损伤复合材料的湿热弹性响应

Hygrothermal elastic response of composites with damage

依据不可逆热力学理论,未引入任何附加假设,建立了湿热弹性各向异性损伤复合材料的一般理论。应用建立损伤本构方程的本构泛函展开法,推导出湿热弹性损伤材料全部本构方程的一般形式,其中包括比自由能密度表达式、应力-应变关系、熵密度方程、损伤应变能释放率表达式、吸湿对偶力表达式、湿-热-固-损伤耦合的热传导方程和损伤演化方程。研究表明,在本构方程中含有若干损伤效应函数,表征损伤对材料宏观力学性能与湿、热性能的影响,其具体形式可由细观力学解确定,从而使连续损伤力学与细观损伤力学有机结合在一起。最后,从细观力学与实验观测两个角度,举例说明损伤效应函数与系数张量的确定方法,为分析变温变湿环境下复合材料的损伤问题提供重要的理论依据。

A general theory for hygrothermal elastic anisotropic damaged composites was developed on the theoretical basis of irreversible thermodynamics without any hypothesis. The constitutive functional expansion method was used for damage constitutive equation. All of the general representations of constitutive equations for hygrothermal elastic damaged materials were derived. These constitutive equations included specific free energy density expression, stress- strain relation, entropy density equation, damage strain energy release rate expression, hygroscopic dual force expression, hygro- thermo- stress- damage coupled heat conduction equation and damage evolution equations. The results show that there are several damage effect functions in constitutive equations, which indicate the influences of damage on the macroscopic mechanics properties and hygrothermal properties of materials. The detailed expressions of the damage effect functions could be determined by micromechanics, which relate the continuum damage mechanics with the microscopic damage mechanics. Finally, the determination methods of damage effect functions and coefficient tensors were illustrated from two aspects of micromechanics and experimental observations, which provided important theory basis for analyzing damage problems of composites under the variable temperature and humidity circumstances.