On loading paths followed inside plastic simple waves in two-dimensional elastic-plastic solids

Abstract

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.