Analysis of hyperelastic, viscoplastic steady state flow by the rate equilibrium method

The rate equilibrium method is extended to incorporate hyperelastic based materials. A hyperelastic material known as the compressible neo-Hookean is used to simulate the elastic effect. Several viscoplastic constitutive models are used to simulate the plastic process. Multiplicative decomposition is used to define the elastic and plastic components of the material response. Examples of drawing, rolling and quenching are presented.; The rate equilibrium method is shown to be more convenient in constructing the finite element formulation than the equilibrium method when hyperelastic constitutive models are used in the steady-state analyses. The method converges rapidly for pure elastic problems, although the rate of convergence is found to decrease rapidly as the viscoplastic response increases. Eventually the rate becomes unacceptably slow as the non-elastic components approach those found in most metal forming processes.; An equilibrium check is included as part of the algorithm. The method currently used is to check equilibrium at the centroid of each element. The material derivative of the resulting equilibrium residual is then calculated and its negative is used as a correction term in the rate equilibrium equation. The specified traction on the boundary is obtained through an iteration algorithm. it is believed that the general approach developed in this research for obtaining steady-state solutions of elastic, viscoplastic flows using hyperelastic constitutive equations with multiplicative decomposition of the elastic and plastic response is shown to be a new and potentially powerful method for the analyses of such problems.