Analytic matrix technique for boundary value problems in applied plasticity

Abstract

An efficient matrix formalism for finding power series solutions to boundary value problems typical for technological plasticity is developed. Hyperbolic system of two first order quasilinear PDEs that models two-dimensional plastic flow of von Mises material is converted to the telegraph equation by the hodograph transformation. Solutions to the boundary value problems are found in terms of hypergeometric functions. Convergence issue is also addressed. The method is illustrated by two test problems of metal forming.