弹塑性材料全状态函数特征研究

Research on Characteristics of All State Function of Elastic-Plastic Materials

摘要: 弹塑性材料是经典弹塑性理论所研究的一种典型材料，应用材料结构全状态函数理论研究这一对象，对于验证理论方法的正确性和适用性具有重要理论意义。采用材料结构全状态函数的理论方法，获得了理想弹塑性材料全状态函数的控制偏微分方程组、状态路径方程和本构关系，以及三组特定状态下的解析解：平面形式、圆柱和球面形式的解。发现理想弹塑性材料全状态函数在形式上与经典弹塑性理论的强度理论形式完全一致，所得到的路径方程与流动法则相似，本构关系也与经典弹塑性理论形式相同。至此，证明了材料结构全状态函数理论应用于理想弹塑性材料，可得到与经典弹塑性理论完全相同的结论和结果。更重要的是材料结构全状态函数的概念、理论及方法，将经典弹塑性理论中的强度理论、流动法则和本构关系完全统一在一个理论框架之下，使其具有了统一的理论基础。

Abstract: Elastic-plastic materials are a typical material researched in classic elastic-plastic theory, and it’s of great theoretical significance to verify the accuracy and applicability of theoretical method based on the research on elastic-perfectly plastic materials with the theories of structural all state function. With the theoretical method of structural all state function, the paper obtains control partial differential equations, path equation and constitutive relation as well as three analytical solutions under special states, namely plane-form solution, cylindrical-form solution and spherical-form solution, of all state function of elastic-perfectly plastic materials. According to the research, it’s discovered that the all state function of elastic-perfectly plastic materials is consistent with strength theory of classic elastic-plastic theory in form completely, and moreover, the path equation obtained is consistent with the flow rule completely and the constitutive relation conforms to the form in classic elastic-plastic theory completely as well. So far, it’s proved that it’s able to obtain conclusions and results completely same with classic elastic-plastic theory by means of applying the theories of structural all state function to elastic-perfectly plastic materials. More importantly, the concepts, theories and methods of all state function unify the strength theory, flow rule and constitutive relation in classic elastic-plastic theory under a theoretical framework and endow them unified theoretical basis.