Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

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• 作者：John H. Cantrell ; ^{john.h.cantrell@nasa.gov" class="auth_mail}
• 关键词：Elastic constants ; Fluids ; Solids ; Nonlinearity parameters ; Initial pressure
• 刊名：Ultrasonics
• 出版年：July, 2014
• 年：2014
• 卷：54
• 期：5
• 页码：1323-1331
• 全文大小：405 K

文摘

The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p₁. For liquids the second-order elastic constants are C₁₁ = A + p₁, C₁₂ = A 鈭?#xA0;p₁, and the third-order constants are C₁₁₁ = 鈭?B + 5A + 3p₁), C₁₁₂ = 鈭?B + A 鈭?#xA0;p₁), and C₁₂₃ = A 鈭?#xA0;B 鈭?#xA0;p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁ = p₁纬 + p₁, C₁₂ = p₁纬 鈭?#xA0;p₁, and the third-order constants are C₁₁₁ = 鈭?em>p₁(纬² + 4纬 + 3), C₁₁₂ = 鈭?em>p₁(纬² 鈭?#xA0;1), and C₁₂₃ = 鈭?em>p₁ (纬² 鈭?#xA0;2纬 + 1), where 纬 is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄ = (1/2)(C₁₁ 鈭?#xA0;C₁₂) = p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3 脳 10^鈭?. For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material 鈥榥onlinearity parameters鈥?associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.