理想线弹性体的等温物态方程
The Isothermal Equation of State for Ideal Linear Elastomers
摘要: 固体的物态方程多为经验公式，少量为基于微观力学的扩展，方程复杂且有效性低，建立有效的理论性的物态方程，一直是业内的梦想。本研究从材料力学角度出发，建立了一种理想线弹性体的2参数等温物态方程，该方程具有Bridgman方程的形式，方程参数仅为弹性模量和泊松比；对75中物质的弹性段数据进行了验证，发现新方程的符合性良好，可靠性佳，拟合精度可控制在3.72%以内。同时得出体积模量的一阶导数是泊松比的单一函数，揭示了这两个参数之间的深刻联系。
Abstract: The equations of state for solids are mostly empirical formulas, with a small number being extensions based on micromechanics. The equations are complex and have low effectiveness. Establishing effective theoretical equations of state has always been a dream in the industry. This study establishes a 2-parameter isothermal equation of state for an ideal linear elastic body from the perspective of material mechanics. The equation takes the form of the Bridgman equation, with only elastic modulus and Poisson’s ratio as its parameters; The elastic segment data of 75 substances were validated, and it was found that the new equation has good consistency, reliability, and fitting accuracy can be controlled within 3.72%. At the same time, the first-order derivative of the bulk modulus is a single function of Poisson’s ratio, revealing the profound connection between these two parameters.
文章引用：温原. 理想线弹性体的等温物态方程[J]. 应用物理, 2024, 14(5): 271-278. https://doi.org/10.12677/app.2024.145031

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