Morro Angelo
DIBRIS, Università di Genova, 16145 Genova, Italy.
Materials (Basel). 2022 Apr 7;15(8):2706. doi: 10.3390/ma15082706.
The thermodynamic consistency of linear viscoelastic models is investigated. First, the classical Boltzmann law of stress-strain is considered. The kernel (Boltzmann function) is shown to be consistent only if the half-range sine transform is negative definite. The existence of free-energy functionals is shown to place further restrictions. Next, the Boltzmann function is examined in the unbounded power law form. The consistency is found to hold if the stress functional involves the strain history, not the strain-rate history. The stress is next taken to be given by a fractional order derivative of the strain. In addition to the constitutive equations involving strain-rate histories, finding a free-energy functional, consistent with the second law, seems to be an open problem.
研究了线性粘弹性模型的热力学一致性。首先，考虑经典的应力-应变玻尔兹曼定律。结果表明，只有当半范围正弦变换为负定时，核函数（玻尔兹曼函数）才是一致的。自由能泛函的存在显示出进一步的限制。接下来，研究无界幂律形式的玻尔兹曼函数。结果发现，如果应力泛函涉及应变历史而非应变率历史，则一致性成立。接着将应力视为应变的分数阶导数给出。除了涉及应变率历史的本构方程外，找到一个与第二定律一致的自由能泛函似乎是一个未解决的问题。
