弹塑性损伤本构关系的显式积分算法研究

EXPLICIT TIME INTEGRATION SCHEME FOR PLASTIC DAMAGE MODEL

首先引入弹塑性损伤本构关系,分别从材料软化与残余应变两个方面,描述伪脆性材料的非线性行为.针对结构动力分析中的强非线性问题,给出了弹塑性损伤本构关系的显式积分算法.算法中引入算子分解的思想,将弹塑性本构关系分成塑性与损伤两个模块.首先求解塑性模块,根据有效应空间塑性演化公式,采用前进欧拉算法,直接构造塑性演化的预测值,并且根据屈服函数的漂移构造了误差限公式,作为衡量显式算法精度的指标.将塑性模块求解的结果代入损伤模块,可以方便地求得损伤变量的演化,并最终得到更新后的应力.整个求解过程不需要迭代,可最大程度的算法稳定性.将论文建立的本构关系显式算法与结构分析显式算法结合,构造了结构显式分析方法,并模拟了两个经典算例,算例结果验证了论文方法的有效性.

The plastic damage model is introduced in the present paper to describe the nonlinear behavior of quasi-brittle material like concrete and rocks.And the corresponding explicit integration scheme is developed to simulate the strong nonlinear performance of structure.Based on the operator splitting method,the scheme is decomposed into two parts,e.g.the plastic part and the damage part.The plastic part is firstly approximated by the forward Euler method,and the plastic evolution is then determined.And the drift of yield condition is introduced as the error bond of the proposed scheme.Then by substituting the results of plastic part into the damage part,the damage variables and the stress tensor are finally updated.By implementing the propose scheme into the structural explicit algorithm,two numerical examples are simulated.The agreement between the simulated results and the conventional results validates the proposed scheme.