含损伤材料的热粘塑性本构关系及其应用

对含损伤材料的热粘塑性本构关系进行了较全面和较系统的研究。首先对半径回归方法的本构公式给出了最一般性的严格证明,并讨论了其适用性和局限性。接着以应力空间中的屈服函数和Drucker公设为基础,以材料本构关系的内变量理论为工具,推导并建立了增量型热粘塑性本构关系的普适形式和计算流程。然后结合实践中最常用的几类本构模型,导出了所建立的增量型动态本构关系的具体形式,并简要总结了其各自的特点和意义。最后通过一些典型的波传播和高速冲击问题的算例,介绍了所建立的本构关系及计算方法的具体应用情况和效果,从而展示了其理论意义和应用前景。

Thermo-viscoplastic constitutive relation of damaged materials with application

This paper presents a general and systematic study on the thermo-viscoplastic constitutive relations of damaged materials. In the first part, the rigorous proof of the "radius-regression method" about constitutive calculation is given, and its suitability and limitation are discussed. In the second part, the universal form and computational routine of the incremental thermo-viscoplastic constitutive relation are established, based on the yield function in stress space and Drucker's postulate and by means of the internal variables theory. In the third part, the concrete formula of some very important and useful constitutive forms are derived, and their characteristics and implications are discussed. In the fourth part, with some typical problems of stress wave propagation and impact dynamics as examples the applications and practical effects of our constitutive relation and computational method are shown, and their theoretic value and practical prospects are demonstrated.