引用本文: 彭培火, 黄朝军. 黏弹性模型微分型本构方程的矩阵形式1)[J]. 力学与实践, 2022, 44(2): 358-367.
PENG Peihuo, HUANG Chaojun. THE MATRIX FORM OF DIFFERENTIAL CONSTITUTIVE EQUATION FOR VISCOELASTIC MODEL1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 358-367.
 Citation: PENG Peihuo, HUANG Chaojun. THE MATRIX FORM OF DIFFERENTIAL CONSTITUTIVE EQUATION FOR VISCOELASTIC MODEL1)[J]. MECHANICS IN ENGINEERING, 2022, 44(2): 358-367.

## THE MATRIX FORM OF DIFFERENTIAL CONSTITUTIVE EQUATION FOR VISCOELASTIC MODEL1)

• 摘要: 针对多个弹性元件和黏性元件以任意连接方式组成的线性黏弹性模型,本文探究了其本构方程的通用矩阵形式表述。首先将研究问题扩展为由Maxwell基本单元构成的标准模型,然后转化为有向图,根据独立路径和闭包围的形式表征出基本应力方程和应变方程,进一步推导得到了任意线性黏弹性模型的微分型本构方程的一般矩阵形式。论文最后总结并建立了一套适合计算机编程的固定范式,利用Python编程实现了该算法、获得了一些数值计算结果。

Abstract: This paper derived the general matrix form for the linear viscoelastic model for arbitrarily linked springs and dampers. Firstly, the underlying linear viscoelastic problem is modeled through the standard model composed of basic Maxwell units. Then the standard model is transformed into a directed graph, and the basic stress equation and strain equation are expressed in the form of independent path and closed enclosure. And then the general matrix form of a differential constitutive equation for an arbitrary viscoelastic model is derived. Finally, a universal paradigm suitable for computer programming is developed, and the relevant algorithm is realized with the Python language along with numerical results.

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