热弹性材料的自由能表达式及其与物性系数的关系*
The Expression of Free Energy for Thermoelastic Material and Its Relation to the Variable Material Coefficients
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摘要: 本文中,自由能的表达式展开成幂级数,其中,温度增量θ*取到三阶,应变张量γij只取到二阶.由这个表达式可以导出物性系数随温度增量的变化规律.这些规律与参考文献中的实验图线是相符的.不过,自由能表达式中的常数须由实验数据确定.文中指出,变化的弹性模量E和剪切弹性模量G是彼此独立的,而其它的物性系数则与它们相关.Abstract: The expression of free energy is expanded in a power series, in which there aren't any terms of order higher than third in the temperature increments θ* and second in the strains γij in this paper. The regular patterns of the material coefficients changing with temperature increments can be derived from this expression. These regulations accord with the experimental graph in references but the constants in the expression of free energy must be determined by experimental data.It is pointed out that the variable modulus of elasticity E and shearing modulus of elasticity G are independent of each other, but the rest of the coefficients are related to them.
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[1] 竹内洋一郎,《热应力》(中译本),郭廷玮等译,科学出版社(1977). [2] 村松篇良,高温状态下的弹性系数(日文),日本机械学会誌,68, 562 (1965), 1623-1628. [3] Goldsmith, A..T.E. Watermanand H.J. Hirschhorn, Handbook of Thermophysical Properties of Solid Materials. 2, Pergamon Press (1962). [4] Dillon, O.W., A nonlinear thermoelasticity theory, J. Mech. Phys. Solids, 10 (1962). [5] Parkus, H., Thermoelasticity. Springer-Verlag (1976). [6] Oden. J.T., Finite Elements of Nonlinear Continua, McGraw-Hill, Inc. (1972). -
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