基于有限状态机实现Davidenkov本构模型的研究

Implementation of the Davidenkov constitutive model based on finite state machine

摘要:

为解决传统编程方法在实现非线性本构模型时的可维护性差、二次开发困难等问题,基于有限状态机(FSM)原理，提出状态模式驱动和数表驱动的两种编程实现方法；通过对两种编程方法的对比,认为FSM结合数表驱动的方法更适合编写非线性本构程序；随后对Davidenkov本构模型滞回曲线进行修正,提出两种滞回曲线构造形式:指向失效点型和指向修正点型。改进的Davidenkov本构模型纠正了“n倍法”模型在失效后，剪应变反向达到上限，而剪应变未进入失效状态的缺点,使得改进的Davidenkov本构模型在模拟土动应力-应变关系时更加合理,尤其是指向失效点模型在多次加卸载作用下,对土体剪切刚度的模拟情况更为精确;为验证基于FSM编制的本构程序具有可维护性强、二次开发简单等特点,依据FSM结合数表驱动的方法编制了Davidenkov及其修正的本构模型程序,以验证该方法的有效性与正确性。

Abstract:

Two methods based on finite state machine (FSM), namely state model-driven and table-driven, were investigated in this study to solve the problems of poor maintainability and difficult secondary development in the implementation of nonlinear constitutive models using traditional programming methods. Through comparison, the results reveal that the table-driven method can efficiently describe nonlinear constitutive models. Then, the stress-strain hysteretic curve of the Davidenkov constitutive model was modified, from which two construction forms of the hysteretic curve were proposed: failure point and correction point type. The results reveal that the modified Davidenkov model can correct the shortcoming of the “n-fold method” model, in which the shear strain reversely reaches the upper limit shear strain and is unable to enter the failure state, so it is more reasonable to be used in simulating the dynamic stress-strain relationship of soil, especially using the failure point model to simulate the shear stiffness of soil under cyclic loading and unloading. Based on the programming method of FSMs and the table-driven method, the constitutive programs of the Davidenkov model and its modified models were compiled, thereby verifying the effectiveness and correctness of the proposed method.