基于参变量变分原理的三维Cosserat体模型弹塑性分析与应变局部化模拟

PARAMETRIC VARIATIONAL PRINCIPLE BASED ELASTIC-PLASTIC ANALYSIS AND STRAIN LOCALIZATION SIMULATION OF 3D COSSERAT CONTINUUM MODEL

基于参变量变分原理,该文发展了三维Cosserat连续体模型弹塑性有限元分析的二次规划算法。由于Cosserat连续体模型的本构方程中存在材料内尺度参数,该模型可以解决经典连续介质理论在分析应变软化问题时病态的有限元网格依赖性问题。数值结果表明所发展的三维Cosserat连续介质弹塑性有限元模型可以有效的模拟应变局部化现象并且该算法具有很好的数值稳定性,同时获得的数值结果具有良好的非网格依赖性。

Based on the parametric variational principle, a quadratic programming method is developed for the elastic-plastic finite element analysis of a 3D Cosserat continuum model. Since the classical continuum model which is lack of internal scale parameter suffers from pathological mesh dependence in the strain localization analysis, the governing equations of the Cosserat continuum model are regularized by adding a rotational degrees-of-freedom and internal scale parameters to the conventional continuum model. Numerical examples are calculated to demonstrate the efficiency of the 3D Cosserat finite element model and the stability of the proposed computational algorithm for numerical simulation of strain localization problems. Particularly, the mesh independent results are ensured.