MLPG法在塑性大变形和应变局部化问题中的应用

把无网格Petrov-Galerkin(MLPG)法推广应用于弹塑性材料大变形和应变局部化问题。把空间坐标表示的基本变量在材料坐标上进行积分,避免了更新积分子域的形状。形函数及其对材料坐标的导数在迭代开始前计算并存储。形函数对空间坐标的导数及空间坐标下的子域边界外法线方向使用张量变换得到。采用乘法分解超弹塑性本构模型,以便模拟更大的变形。算例表明,所推导的非线性M LPG方法能够精确模拟弹塑性材料的大变形,并能模拟应变弱化材料由于不稳定塑性变形导致的应变局部化现象。

MLPG method for large deformations and strain localization of elasto-plastic materials

The meshless local Petrov-Galerkin(MLPG) method was extended to large deformation and strain localization problems of plastic materials.To avoid frequent shape updates of the local subdomains,the fundamental variables are represented with a spatial configuration,with the numerical quadrature conducted on the material configuration.The shape function and its derivative are computed and stored only at the beginning of the iteration.The derivatives of the shape functions of the spatial coordinate are pushed back to the material coordinate by a tensor transformation.A multiplicative constitutive model of the hyperelasto-plasticity is used to simulate the large deformations.Numerical examples show that the nonlinear MLPG method can accurately simulate large deformations of elastoplastic materials and the strain localization induced by material instabilities of the strain softened materials.