Invariant and partially invariant solutions of integro-differential equations for linear thermoviscoelastic aging materials with memory

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• 作者：Long-Qiao Zhou ; Sergey V. Meleshko
• 关键词：Linear thermoviscoelasticity ; Aging materials ; Invariant and partially invariant solutions ; Integro ; differential equations
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：29
• 期：1
• 页码：207-224
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Classical and Continuum Physics; Engineering Thermodynamics, Heat and Mass Transfer; Theoretical and Applied Mechanics; Structural Materials;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0959
• 卷排序：29

文摘

A linear thermoviscoelastic model for homogeneous, aging materials with memory is established. A system of integro-differential equations is obtained by using two motions (a one-dimensional motion and a shearing motion) for this model. Applying the group analysis method to the system of integro-differential equations, the admitted Lie group is determined. Using this admitted Lie group, invariant and partially invariant solutions are found. The present paper gives a first example of application of partially invariant solutions to integro-differential equations.