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许多工程材料当变形超过某一极限时由于损伤都会出现应变软化行为。首先从非局部理论出发 ,推导了应变梯度损伤本构方程 ;然后利用一阶拟线性偏微分方程组的特征理论 ,在一维弹性损伤情况下分析了两种不同的本构模型 ,即 Kachanov损伤本构方程与应变梯度损伤本构方程 ,对连续介质损伤力学基本方程适定性的影响。结果表明 ,当损伤发展时 ,与 Kachanov损伤本构模型相关的连续介质损伤力学的基本方程是不适定的 ;而与应变梯度损伤本构模型相关的 ,则无论损伤是否发展 ,其基本方程始终是适定的。这说明在连续介质损伤力学的本构方程中必须考虑材料内部微结构的尺度效应
Many engineering materials exhibit strain softening behavior due to damage when the deformation exceeds a certain limit. First of all, based on the non-local theory, the constitutive equation of strain gradient damage is deduced. Then by using the characteristic theory of the first-order quasilinear partial differential equations, two different constitutive models are analyzed under the one-dimensional elastic damage, that is Kachanov’s damage Constitutive Equation and Strain Gradient Damage Constitutive Equation, Influencing on the Fundamental Equability of Continuum Damage Mechanics. The results show that the basic equations of continuum damage mechanics related to the Kachanov damage constitutive model are ill-posed when the damage is developed. However, the basic equations of damage constitutive model are always Appropriate. This shows that in the continuum damage mechanics constitutive equation, the scale effect of the material’s internal microstructure must be considered