| 线弹性体本构方程对称性的逆命题研究 |
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| 引用本文： | 王怀磊, 苏振超. 线弹性体本构方程对称性的逆命题研究[J]. 力学与实践, 2014, 36(4): 483-485. doi: 10.6052/1000-0879-13-206 |
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| 作者姓名： | 王怀磊 苏振超 |
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| 作者单位： | 1 南京航空航天大学机械结构力学及控制国家重点实验室, 南京210016; 2 厦门大学嘉庚学院土木工程系, 福建漳州363105 |
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| 基金项目： | 国家自然科学基金（11172126）和江苏高校优势学科建设工程资助项目. |
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| 摘 要： | 基于线弹性体本构方程系数矩阵的对称性，提出了其对应的逆命题问题，即若材料本构方程是线性且对称的，能否由此确定物体是完全弹性的?论文通过构造势函数的方法对该问题给出了肯定的回答，从而论证了对于符合线性本构关系的材料，其本构方程的对称性与物体的完全弹性相互蕴含，因而是相互等价的.
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| 关 键 词： | 完全弹性体 线弹性 本构关系 对称性 逆命题 |
| 收稿时间： | 2013-05-20 |
| 修稿时间： | 2013-09-13 |
THE INVERSE PROPOSITION ABOUT THE SYMMETRY OF LINEAR CONSTITUTIVE LAW |
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| WANG Huailei, SU Zhenchaoy. THE INVERSE PROPOSITION ABOUT THE SYMMETRY OF LINEAR CONSTITUTIVE LAW[J]. Mechanics in Engineering, 2014, 36(4): 483-485. doi: 10.6052/1000-0879-13-206 |
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| Authors: | WANG Huailei SU Zhenchaoy |
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| Affiliation: | 1 State Key Laboratory of Mechanics and Control for Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2 Department of Civil Engineering, Tan Kah Kee College, Xiamen University, Fujian, Zhangzhou 363105, China |
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| Abstract: | From the symmetry of the coefficient matrix of the constitutive law of linear elastic bodies, one may motivated to consider the corresponding inverse proposition, i.e. whether or not the symmetry of the linear constitutive law implies the perfect elasticity of the body. A positive answer of this question may be made via the construction of an elastic potential function for the body,which indicates that the symmetry of the constitutive equation and the perfect elasticity of body are equivalent. |
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| Keywords: | perfectly elastic body|linear elasticity|constitutive law|symmetry|converse proposition |
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