Formulations of the problems of the theory of an ideally elastic-plastic body
The mathematical correctness of the problem of ideally plastic materials has been studied previously by many authors. In the present paper, various functional formulations are given for the problems of the theory of quasi-static equilibrium of ideally elastic-plastic media. Three problems are considered. The problem A follows from the classical formulations. It is shown that the problem A is equivalent to two partial problems (problems B and C). Problem B represents an evolutionary variational inequality for the stress tensor, which has a unique solution. In problem C, the known stress field is used to determine the velocity field. It is shown that problems A and C have no solution. However, a modified form of each of the problems has a unique solution. An example is given in which problem A has no solution, but its modified form has a unique solution. The paper is much mathematical. Practical engineers may not find interest in it.
scientific article; zbMATH DE number 4020574
scientific article