【摘要】 经典连续损伤理论中，通常是由有效应力概念和应变等效假设来建立损伤材料的本构方程。已经发现有效应力概念与应变等效假设存在较大缺陷，基于应变等效假设的损伤本构方程不能正确反映实际材料的损伤行为。为克服经典连续损伤理论存在的缺陷，在严格的不可逆热力学理论基础上，提出了建立损伤本构方程的本构泛函展开法，推导出弹性各向同性损伤材料本构方程的一般形式。研究表明，弹性各向同性损伤可由定义在细观尺度下的一个标量损伤变量来描述，在小应变情况下材料的本构方程中有两个独立的“损伤效应函数”，来表征损伤对材料宏观力学性能的影响。损伤效应函数的具体形式可由细观力学解答确定，从而使连续损伤力学与细观损伤力学有机结合在一起。在广义标准材料理论框架下，利用本构泛函展开法，推导出弹性各向同性损伤演化方程的一般形式。更多还原

【Abstract】 In classical continuum damage theories, the constitutive equations for damaged materials are usually set up by using the concept of effective stress and the strain equivalence principle (or hypothesis), and some limitations of this principle have been found. Because the constitutive equations based on the strain equivalence principle for damaged materials do not reflect the damage behaviour of real materials, the constitutive functional expansion method(CFEM) is developed on the strict theoretical basis of irreversible thermodynamics, and by using the CFEM the constitutive equations for isotropic elastic damaged materials are derived. It is found that two independent “damage effect functions” are related to a single scalar damage variable in the constitutive equations under infinitesimal strain conditions. The detailed expressions of the damage effect functions are investigated by micromechanics, which enables us to relate the continuum damage mechanics with the microscopic damage mechanics. Thus,in the framework of generalized standard materials, the damage evolution equation for isotropic elastic damaged materials has been derived.更多还原