基于D-P准则的理想弹塑性本构关系积分研究

研究基于D-P准则的理想弹塑性本构关系积分的特点及相应的子增量法。研究说明,作者提出的基于D-P准则的转移应力解析解,从应力调整过程来说相当于线性预测-径向校正方法;从本构关系积分策略来说相当于最近点投射法。最近点投射法具有一阶精度而且是无条件稳定的,而数值稳定性和一致性条件是弹塑性计算收敛的充要条件;作为广义中点法的一个特例,最近点投射法最能适应大的应变增量。理论分析和计算实例都表明,该方法适合于极限分析,在采用较大的荷载增量步时仍能保持较高的数值稳定性和精度。提出了基于D-P准则的子增量法,其中确定子增量步数的公式兼容了Schreyer等人的子增量数表达式。计算实例说明计算精度的提高与子增量的步数大体成正比,在显著偏离比例加载的情况下,单步法仍能取得较高的精度。对一般极限分析课题采用单步法即可。

ON INTEGRATION ALGORITHMS FOR PERFECT PLASTICITY BASED ON DRUCKER-PRAGER CRITERION

This paper focuses on the integration algorithms for perfect plasticity based on Drucker-Prager criterion. It is shown that the analytic solution of transferred stress, which was proposed by the authors in a previous paper, is equivalent to the so-called closest point projection algorithm. Thus, the analytic solution is of first-order accuracy and unconditional stable. A subincrementing scheme is proposed to combine with the analytic solution. Both theoretical analysis and numerical examples show that the analytic solutions of transferred stress is suitable for limit analyses and can achieve high accuracy to large strain increment even without subincrementing scheme.