This study proposes new models for thermodynamic properties and thermoelastic constitutive relation of materials with cubic crystal structures. The motion equation of atoms in cubic crystal structures is decomposed into structural deformation and thermal vibration at first. Then based on the thermo-mechanical coupling mechanism, both the thermal and mechanical aspects of structural deformation are investigated. And the thermal vibration equation is built at structural deformation positions by considering the non-harmonic approximation of interatomic potentials. Further, the improved formula of free energy is established as a function of the structural deformation and thermal vibration frequencies, which includes the thermo-mechanical coupling and non-harmonic effects. And the thermodynamic properties, including internal energy, entropy, heat capacity and thermal expansion, are derived from the free energy. Besides, based on the multiplicative decomposition of deformation gradient, the thermoelastic constitutive relation is constructed at finite deformation for cubic crystal materials. Finally, numerical results of the thermodynamic properties, thermoelastic stress–strain relations and elastic constants for face-centered cubic metals Cu, Au and Ag from 0 K to the melting points at 0–50 GPa are provided by comparing with the experimental data to demonstrate the usability of the present models.

中文翻译：

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基于改进自由能的立方晶体结构的热力学性质和热弹性本构关系

本研究提出了具有立方晶体结构的材料的热力学性质和热弹性本构关系的新模型。立方晶体结构中原子的运动方程首先分解为结构变形和热振动。然后基于热-机械耦合机制，研究了结构变形的热和机械方面。考虑原子间势的非调和近似，在结构变形位置建立热振动方程。此外，改进的自由能公式被建立为结构变形和热振动频率的函数，其中包括热机械耦合和非谐波效应。以及热力学性质，包括内能、熵、热容量和热膨胀来自自由能。此外，基于变形梯度的乘法分解，构造了立方晶体材料在有限变形下的热弹性本构关系。最后，通过与实验数据的比较，提供了面心立方金属 Cu、Au 和 Ag 从 0 K 到熔点 0-50 GPa 的热力学性质、热弹性应力-应变关系和弹性常数的数值结果，以证明当前模型的可用性。