Monotonicity of input–output mapping related to inverse elastoplastic torsional problem

In this paper, monotonicity of input–output mapping related to inverse elastoplastic torsional problem is studied. In this context, torsional behavior of power-hardening engineering materials is investigated. The equation of the elastoplastic torsion of a strain hardening bar is given by Au≔-∇·(g(∣∇u∣2)∇u)Au≔-∇·g(∣∇u∣2)∇u. Although this equation is nonlinear in pure plastic case, it is reduced into a linear equation in pure elastic case. The reduced equation is solved to find an analytical formula for the torque in pure elastic case. Using a specific plasticity function g=g(ξ2),ξ2=|∇u|2 that corresponds to wide class of materials, namely power-hardening engineering materials as input data, the problem is solved numerically. Moreover a novel comparison principle is proved in elastoplastic case. We obtain some usefull results using this comparison principle. Finally these obtained results are supported by the numerical solution of the nonlinear problem.