基于连续本构模型的泡沫铝弹塑性断裂问题无网格法分析

Element-free method for elasto-plastic fracture analysis of aluminum foam by a continuum constitutive model

应用无网格伽辽金法对单轴远场拉应力加载下泡沫铝弹塑性断裂问题进行了分析.首先,基于连续本构模型,将泡沫铝考虑成塑性可压缩材料,并通过引入Weibull分布,建立了宏观尺度上的泡沫铝本构关系.其次,在无网格伽辽金法的基础上,采用应力应变增量形式表征材料的弹塑性本构关系,用罚函数法施加本质边界条件,并考虑裂纹区的不连续性,用Newton-Raphson增量迭代实现非线性分析.最后通过算例讨论了概率参数对本构关系的影响,及泡沫铝相对密度与J积分值的变化规律.算例分析表明Weibull分布中的尺度参数对泡沫铝的宏观力学性质和断裂参数J积分有较大影响,而形状参数影响较小.

Element-free Galerkin （EFG） method is applied to solve the elasto-plastic fracture problems of aluminum foams under uniaxial tensile load. Firstly, a continuum constitutive model is taken into account for the plastic compressibility of aluminum foams. The Weibull statistical analysis is used to represent microscopic heterogeneity. Then, the increments of stress and strain are used to characterize the elasto-plastic constitutive relationship on the basis of EFG method with penalty function method. Considering the discontinuity of crack, Newton-Raphson iteration method is used in computation. Lastly, several examples are given to show the influence of parameter on curve of stress-strain and the relation of values of J-integral versus relative density. The numerical analysis for aluminum foams shows that the influence of the scale parameter of Weibull distribution upon macroscopic mechanical properties and fracture parameter J-integral is significant, while the shape parameter is not obvious.