Implicit integration with a substepping scheme of the zero-elastic range SANISAND-Z model for sand
Implicit integration with a substepping scheme of the zero-elastic range SANISAND-Z model for sand
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DOI：
10.1016/j.compgeo.2023.105899
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发表时间：
2024-01
影响因子：
5.3
通讯作者：
Cheng Chen;Zhonghua Sun;Xun Wu;Yong Wang
中科院分区：
文献类型：
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作者：
Cheng Chen;Zhonghua Sun;Xun Wu;Yong Wang
SANISAND-Z模型是一个零弹性范围边界曲面模型。零弹性范围使模型逐渐非线性，因而模型公式的常微分方程组具有内在的隐式。考虑到用后向欧拉法对模型进行积分时计算结果严重依赖积分步长的问题，本文提出了一种带子步进方案的两阶段对角隐式龙格-库塔算法。采用嵌入的局部积分误差估计实现了降噪方案。基于ABAQUS软件的自定义材料子程序接口UMAT，采用提出的数值积分算法对SANISAND-Z模型进行了数值实现。通过单调和循环单元试验以及条形基础荷载的实例，对所提出的数值积分算法的性能进行了深入的研究。结果表明，该算法比后向欧拉法更准确、更高效。
The SANISAND-Z model is a zero-elastic range boundary surface model. The zero-elastic range makes the model incrementally nonlinear, and consequently, the system of ordinary differential equations of the model formulation is intrinsically implicit. Considering that the calculation results are heavily dependent on the integration step size when the backward Euler method is used to integrate the model, a two-stage diagonally implicit Runge-Kutta algorithm with a substepping scheme is proposed in this study. The substepping scheme is achieved by an embedded local integration error estimate. Based on the user-defined material subroutine interface UMAT of ABAQUS software, the SANISAND-Z model is numerically implemented with the proposed numerical integration algorithm. By monotonic and cyclic element tests and the case of strip footing loading, the performance of the proposed numerical integration algorithm is thoroughly investigated. The results show that the proposed algorithm is more accurate and efficient than the backward Euler method.