材料应变局部化分析中不同内尺度律参数间相互作用问题的讨论

梯度塑性和与速率相关的本构模型在动力学应变分析中会起到引入材料内尺度律的作用。利用这两种模型进行动力学软化与应变局部化分析均会使有限元计算的数值结果不再具有网格依赖性。讨论了这两种模型各自所具有的内尺度律效应，研究了两种模型综合使用条件下的内尺度律结果，给出了参数相互作用条件下内尺度律的计算方法。该方法具有一般性。利用该方法，进一步揭示了率相关与梯度塑性模型各自所具有的内尺度律的数学本质，并以数值算例说明了理论预测的正确性。

Discussion on Interaction between Different Intrinsic Length Scale Parameters for Material Strain Localization Analysis

Both gradient-dependent and rate-dependent constitutive models introduce intrinsic length scales in dynamic strain localization analysis of engineering materials. The intrinsic length scales in the two different constitutive models are discussed,respectively. The ways to predict the intrinsic length scales the two constitutive models are different and the expressions of the intrinsic length scale are also different from each other. To give a prediction of the intrinsic length scales for the general case with the two models,both the length curves corresponding to the damping effect and wave length versus wave number are computed. The internal length scales derived respectively from the damping effect,which is typical for the visco-plastic model,and the wave length is obtained from the critical wave number with unimaginary velocity. An intrinsic length scale domain with upper and lower bound values is obtained which includes the actual length scale. The proposed method can explain the results obtained with the two models. The way proposed here for prediction of the intrinsic length scale is more general than those commonly used to explain the phenomena observed in both the viscoplastic and gradient dependent models. Moreover,it has also been found that the sensitivity of the internal length scale for the visco-plastic parameter is higher than that for the gradient dependent parameter. Numerical example is given and the results are confirmed with those of theoretical analysis.