Although the solution of hyperbolic partial differential equations in elastic-plastic media is of major importance in solid mechanics, the mathematical complexity of such problems increases with the space dimensionality. As a result, the development of analytical solutions is in general not possible. Whereas the wave structure resulting from given external loads is known and well understood for one-dimensional problems, several gaps still need to be filled for problems with more space dimensions. Indeed, the literature related to the propagation of simple waves in elastic-plastic solids is rather sparse since only particular two-dimensional and three-dimensional problems have been considered. Following the general three-dimensional framework of Mandel (1962), the object of the paper is to construct the loading paths followed inside the simple waves under plane strain and plane stress conditions. It is believed that the mathematical and numerical studies of the waves presented here could help define the characteristic structure involved in a Riemann problem.

尽管弹塑性介质中双曲型偏微分方程的求解在固体力学中非常重要，但此类问题的数学复杂性随空间维数而增加。结果，通常不可能开发分析解决方案。尽管对于一维问题已知并很好地理解了由给定外部载荷产生的波浪结构，但对于具有更大空间尺寸的问题，仍需要填补几个空白。确实，与简单波在弹塑性固体中的传播有关的文献很少，因为只考虑了特定的二维和三维问题。按照Mandel（1962）的一般三维框架，本文的目的是在平面应变和平面应力条件下构造简单波内部的载荷路径。可以相信，这里提出的波浪的数学和数值研究可以帮助定义涉及黎曼问题的特征结构。