An accurate solution of singular thermoplastic problem of pressure: dependent plasticity

The present paper concerns with a theoretical investigation into heat generation in the continued quasi-static plane strain compression of a thin strip between two rigid, parallel perfectly rough platens. The strip material obeys the double shearing model. The length of the platens is supposed to be much greater than the current strip thickness. The plastic work rate approaches infinity in the vicinity of perfectly rough friction surfaces. Since the plastic work rate is involved in the heat conduction equation, this greatly adds to the difficulties of solutions of this equation. In particular, commercial finite element packages are not capable of solving such boundary value problems. The present approximate solution is given in Lagrangian coordinates. In this case, the original initial/boundary value problem reduces to the standard second initial/boundary value problem for the nonhomogeneous heat conduction equation. Therefore, the Green’s function is available in the literature. An example is provided to illustrate the general solution.