基于有限狀態機實現Davidenkov本構模型的研究

摘要： 為解決傳統編程方法在實現非線性本構模型時的可維護性差、二次開發困難等問題，基于有限狀態機（FSM）原理，提出狀態模式驅動和數表驅動的兩種編程實現方法；通過對兩種編程方法的對比，認為FSM結合數表驅動的方法更適合編寫非線性本構程序；隨后對Davidenkov本構模型滯回曲線進行修正，提出兩種滯回曲線構造形式：指向失效點型和指向修正點型。改進的Davidenkov本構模型糾正了“n倍法”模型在失效后，剪應變反向達到上限，而剪應變未進入失效狀態的缺點，使得改進的Davidenkov本構模型在模擬土動應力-應變關系時更加合理，尤其是指向失效點模型在多次加卸載作用下，對土體剪切剛度的模擬情況更為精確;為驗證基于FSM編制的本構程序具有可維護性強、二次開發簡單等特點，依據FSM結合數表驅動的方法編制了Davidenkov及其修正的本構模型程序，以驗證該方法的有效性與正確性。

關鍵詞： 巖土動力學; 非線性本構模型; 有限狀態機; Davidenkov本構模型; 二次開發

中圖分類號： TU435""""" 文獻標志碼：A"" 文章編號： 1000-0844（2025）02-0351-10

DOI：10.20000/j.1000-0844.20230802002

Implementation of the Davidenkov constitutive model

based on finite state machine

DONG Zhengfang1， LI Haojie1， WANG Yongfeng1， JIN Deyin2

（1.School of Civil Engineering and Architecture， Henan University， Kaifeng 475004， Henan， China;

2.JAPAN-CHINA CONSALTANT Co.， Ltd.， Tokyo 134-0086， Japan）

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.

Keywords：

geotechnical dynamics; nonlinear constitutive model; finite state machine; Davidenkov constitutive model; secondary development

0 引言

土體的動應力-應變關系具有嚴重的非線性、滯后性和變形累積性等特點，其本構理論大致可分為黏彈性和彈塑性兩種，黏彈性理論因其直觀簡單、參數少且易獲取等優點而成為目前研究和應用的主流理論^［1］。黏彈性模型包含等效線性和曼辛非線性兩種，后者在前者的基礎上由曼辛法則構造出滯回曲線方程，使得這類模型更接近土體動應力-應變曲線^［2-3］。……