弹性、弹塑性材料显式模拟计算中的准静态加载速度研究

摘 要：动力学显式算法采用时间积分原理，其较静力学隐式算法在强非线性问题中的适用性更广。为将此方法应用到岩土等非线性材料的计算中，考虑到显式算法中动能的影响会导致结果波动，分析动力学显式算法在模拟计算中的准静态加载速度的选取十分必要,如何在缩短模拟消耗时间与结果准确性之间寻求平衡是本文研究重点。研究中提出以加载-位移曲线的波动比来评价准静态计算效果，首先开展弹性材料的平面应变模拟试验以分析弹模、密度、泊松比、围压4个参数对准静态加载速度取值的影响，结果表明：弹模、泊松比、围压的增大会提高准静态加载速度；密度的增大则会减小准静态加载速度。通过对各影响因素与准静态加载速度的相关性分析给出了准静态加载速度取值的经验公式。最后，选取能够反映砂土复杂力学特性的弹塑性本构模型，开展其平面应变模拟试验，对比分析准静态加载速度经验公式在弹性材料与弹塑性材料中的适用性差异，并提出应用建议公式。

Study on quasi-static loading velocity in explicit calculation of elastic and elastic-plastic materials

Abstract: The dynamic explicit algorithm is based on the principle of time integration. It is more applicable to nonlinear problems than the static implicit algorithm. In order to use this method to calculate nonlinear materials including rock and soil, it is extremely necessary to analyze selection of quasi-static loading speed of the dynamic explicit algorithm in simulation calculation, because the kinetic energy influences in the explicit algorithm will result in fluctuation of results. How to look for balance as reducing simulated consumption time and result accuracy is the research emphasis in this thesis. The fluctuation ratio of the load-displacement curve is proposed in this research to evaluate the effect of quasi-static calculation. First of all, the plane strain simulation test of elastic materials is conducted to analyze the effect of the elastic modulus, density, Poisson’s ratio and confining pressure on the value of quasi-static load speed. The findings indicate that the increase of elastic modulus, Poisson’s ratio and confining pressure will increase quasi-static load speed, while the increase of density will reduce the quasi-static load speed. Correlation analysis between each influence factor and quasi-static load speed gives the empirical formula of quasi-static load speed. At last, the elastic-plastic constitutive model that can reveal complicated mechanical property of sandy soil is selected to develop the plane strain simulation test. The applicability difference in the empirical formula of quasi-static load speed between elastic materials and elastic-plastic materials is conducted contrastive analysis, and the application suggestion formula is proposed.